Support vector machines (8.6.2011)

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Support vector machines (8.6.2011)
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10.5446/357 (DOI)
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Technische Universität Braunschweig
Institut für Informationssysteme
Balke, Wolf-Tilo
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This lecture provides an introduction to the fields of information retrieval and web search. We will discuss how relevant information can be found in very large and mostly unstructured data collections; this is particularly interesting in cases where users cannot provide a clear formulation of their current information need. Web search engines like Google are a typical application of the techniques covered by this course.
Discrete group Group action Curve Solid geometry Shape (magazine) Special unitary group Computer programming Neuroinformatik Measurement Sign (mathematics) Web service Different (Kate Ryan album) Social class Physical system Theory of relativity Structural load Electronic mailing list Staff (military) Bit Bulletin board system Demoscene Category of being Arithmetic mean Process (computing) Ring (mathematics) Order (biology) Heuristic Figurate number Quicksort Escape character Spacetime Geometry Point (geometry) Slide rule Control flow Similarity (geometry) Event horizon Machine vision Element (mathematics) Number Frequency Goodness of fit Term (mathematics) Energy level Representation (politics) Data structure Address space World Wide Web Consortium Pairwise comparison Focus (optics) Information State of matter Independence (probability theory) Line (geometry) Cartesian coordinate system System call Shape (magazine) Word Personal digital assistant Query language Information retrieval Network topology Statement (computer science) Video game Iteration Musical ensemble Game theory Hyperplane Library (computing) State observer Transportation theory (mathematics) State of matter Code Length Decision theory Multiplication sign 1 (number) Sheaf (mathematics) Mereology Information retrieval Mathematics Bit rate Diagram Endliche Modelltheorie Series (mathematics) Stability theory Vulnerability (computing) Area World Wide Web Consortium Algorithm Closed set Feedback Measurement Hypothesis Degree (graph theory) Type theory Vector space Linearization Whiteboard Task (computing) Resultant Ocean current Divisor Support vector machine Gene cluster Virtual machine Electronic mailing list Menu (computing) Trigonometric functions Wave packet Revision control Causality Root Natural number String (computer science) Touch typing Software testing Condition number Task (computing) Polygon mesh Performance appraisal Film editing Computer animation Search engine (computing)
Thomas Bayes Computer animation Algorithm Adaptive behavior Dew point Special unitary group Relevance feedback World Wide Web Consortium
Thomas Bayes Nonlinear system Computer animation Algorithm Support vector machine Function (mathematics) Object (grammar) Maxima and minima output Summierbarkeit Special unitary group World Wide Web Consortium
Building Support vector machine Line (geometry) Bit Mereology Line (geometry) Binary file Special unitary group Flow separation Computer animation Set (mathematics) Social class Spacetime Representation (politics) Task (computing) Hyperplane Linear map World Wide Web Consortium
Presentation of a group Code View (database) Sheaf (mathematics) Special unitary group Perspective (visual) Measurement Mathematics Uniformer Raum Hypermedia Different (Kate Ryan album) Set (mathematics) Error message Hyperplane Social class God Area Clique-width Concentric Closed set Point (geometry) Moment (mathematics) Maxima and minima Mereology Flow separation Measurement Linearization Whiteboard Representation (politics) Task (computing) Spacetime Point (geometry) Support vector machine Line (geometry) Connectivity (graph theory) Virtual machine Wave packet 2 (number) Flow separation Term (mathematics) Linear map World Wide Web Consortium Noise (electronics) Information management Standard deviation Support vector machine Distribution (mathematics) Line (geometry) Binary file System call Symbol table Computer animation Social class Boundary value problem Library (computing)
Computer animation Support vector machine Point (geometry) Maxima and minima Special unitary group Linear map
Fraction (mathematics) Error message Computer animation Support vector machine Point (geometry) Division (mathematics) Maxima and minima Social class World Wide Web Consortium
Point (geometry) Momentum Support vector machine Direction (geometry) Multiplication sign Division (mathematics) Maxima and minima Special unitary group Scalability Dimensional analysis Number Population density Term (mathematics) Bridging (networking) Maize Nichtlineares Gleichungssystem Summierbarkeit World Wide Web Consortium Shift operator Point (geometry) Planning Line (geometry) Type theory Fraction (mathematics) Error message Computer animation Linearization System identification Social class Hyperplane Spacetime
Length Direction (geometry) View (database) Multiplication sign Mereology Special unitary group Set (mathematics) Negative number Row (database) Position operator Hyperplane Physical system Social class Constraint (mathematics) Real number Point (geometry) Sampling (statistics) Type theory Order (biology) Right angle Whiteboard Physical system Spacetime Point (geometry) Support vector machine Constraint (mathematics) Real number Connectivity (graph theory) Distance Shift operator Scalability Product (business) Wave packet Prime ideal Nichtlineares Gleichungssystem Linear map World Wide Web Consortium Shift operator Scaling (geometry) Planning Line (geometry) Subject indexing Uniform resource locator Computer animation Scalar field Social class Game theory Boundary value problem Hyperplane
Point (geometry) Length Equals sign Maxima and minima Limit (category theory) Protein Distance Shift operator Special unitary group Event horizon Number Prime ideal Sign (mathematics) Mathematics Bit rate Strategy game Touch typing Negative number Nichtlineares Gleichungssystem Absolute value Hyperplane Linear map Physical system World Wide Web Consortium Data type Default (computer science) Shift operator Logical constant Constraint (mathematics) Optimization problem Moment (mathematics) Planning Maxima and minima Line (geometry) RAID Flow separation Type theory Computer animation Scalar field Personal digital assistant Order (biology) Right angle Hyperplane Resultant Spacetime
Point (geometry) Length Constraint (mathematics) Multiplication sign Maxima and minima Parameter (computer programming) Shape (magazine) Distance Special unitary group Number Negative number Spacetime Endliche Modelltheorie Hyperplane World Wide Web Consortium Shift operator Constraint (mathematics) Slide rule Clique-width Optimization problem Prisoner's dilemma Maxima and minima System call Distance Algebra Computer animation Website Convex hull Hyperplane Spacetime
Presentation of a group Length State of matter Multiplication sign Execution unit First-order logic Special unitary group Computer programming Mathematics Sign (mathematics) Bit rate Negative number Area Algorithm Constraint (mathematics) Optimization problem Moment (mathematics) Maxima and minima Root Telecommunication Reading (process) Resultant Spacetime Point (geometry) Slide rule Functional (mathematics) Divisor Constraint (mathematics) Maxima and minima Distance Number Wave packet Quadratic equation Causality Average Operator (mathematics) Selectivity (electronic) Divisor Mathematical optimization World Wide Web Consortium Standard deviation Support vector machine Physical law Planning Line (geometry) System call Computer animation Personal digital assistant Calculation Hyperplane Mathematical optimization Square number Form (programming)
Support vector machine Constraint (mathematics) Multiplication sign Virtual machine Maxima and minima Control flow Maxima and minima Transformation (genetics) Mereology Special unitary group Computer programming Lagrange-Methode Population density Computer animation Quadratic equation Linearization Binary multiplier Representation (politics) Right angle Whiteboard Relevance feedback Mathematical optimization Data structure World Wide Web Consortium
Computer file Support vector machine Transformation (genetics) Constraint (mathematics) Maxima and minima 3 (number) Special unitary group Lagrange-Methode Number Duality (mathematics) Uniformer Raum Representation (politics) Relevance feedback Mathematical optimization World Wide Web Consortium Support vector machine Shift operator Theory of relativity Optimization problem Feedback Planning Transformation (genetics) Computer programming Process (computing) Computer animation Quadratic equation Duality (mathematics) Order (biology) Binary multiplier Mathematical optimization Data structure
Logical constant Presentation of a group Multiplication sign Correspondence (mathematics) Direction (geometry) Parameter (computer programming) Special unitary group Neuroinformatik Fraction (mathematics) Derivation (linguistics) Duality (mathematics) Mechanism design Sign (mathematics) Coefficient of determination Bit rate Labour Party (Malta) Different (Kate Ryan album) Negative number Series (mathematics) Extension (kinesiology) Category of being Position operator Physical system Exception handling Social class Area Metropolitan area network Constraint (mathematics) Optimization problem Point (geometry) Bit Term (mathematics) Product (business) Duality (mathematics) Chain Order (biology) Right angle Spacetime Point (geometry) Laptop Functional (mathematics) Beat (acoustics) Computer file Divisor Support vector machine Maxima and minima Online help Distance Event horizon Number Wave packet Operator (mathematics) Representation (politics) Software testing Nichtlineares Gleichungssystem World Wide Web Consortium Support vector machine Shift operator Scaling (geometry) Planning Human migration Sign (mathematics) Computer animation Scalar field Personal digital assistant Function (mathematics) Game theory Hyperplane Mathematical optimization Freezing
Information management Support vector machine Point (geometry) Term (mathematics) Special unitary group Product (business) Sign (mathematics) Duality (mathematics) Computer animation Scalar field Function (mathematics) Set (mathematics) Category of being World Wide Web Consortium
Error message Computer animation Constraint (mathematics) Personal digital assistant Point (geometry) Maxima and minima Total S.A. Mathematical optimization World Wide Web Consortium
Point (geometry) Divisor Constraint (mathematics) Parameter (computer programming) Distance Total S.A. Food energy Wave packet Mathematics Personal digital assistant Set (mathematics) Addressing mode World Wide Web Consortium Noise (electronics) Addition Information management Software bug Shift operator Logical constant Constraint (mathematics) Theory of relativity Matching (graph theory) Interior (topology) Planning Line (geometry) Flow separation Stochastic differential equation Error message Computer animation Personal digital assistant Chain 5 (number) Hyperplane
Information management Duality (mathematics) Execution unit Error message Computer animation Constraint (mathematics) Maxima and minima Computer music Correlation and dependence World Wide Web Consortium
Rifling Presentation of a group Multiplication sign Execution unit Range (statistics) Set (mathematics) Bound state Icosahedron Mereology Special unitary group Medical imaging Web service Sign (mathematics) Machine learning Labour Party (Malta) Spherical cap Different (Kate Ryan album) Set (mathematics) Negative number Videoconferencing Circle Endliche Modelltheorie Multiplication Position operator Social class Physical system Fitness function Thermal expansion Bit Category of being Type theory Process (computing) Order (biology) Linearization Website Right angle Heuristic Quicksort Whiteboard Spacetime Point (geometry) Support vector machine Transformation (genetics) Real number Virtual machine Maxima and minima Field (computer science) Product (business) Power (physics) Number Wave packet Goodness of fit Nonlinear system Causality Term (mathematics) String (computer science) Software testing Data structure Summierbarkeit Metropolitan area network World Wide Web Consortium Information Cellular automaton Weight Expression Content (media) Planning Coma Berenices Basis <Mathematik> Line (geometry) Film editing Computer animation Visualization (computer graphics) Personal digital assistant Video game Social class Hyperplane Freezing
Nonlinear system Computer animation Set (mathematics) Spacetime Noise Maize Exception handling Special unitary group Summierbarkeit Linear map World Wide Web Consortium
Axiom of choice Presentation of a group Pixel Group action Randomization Logistic distribution Chaos (cosmogony) Special unitary group Dimensional analysis Neuroinformatik Medical imaging Labour Party (Malta) Different (Kate Ryan album) Hypermedia Kernel (computing) Negative number Social class Physical system Metropolitan area network Theory of relativity Constraint (mathematics) Texture mapping Interior (topology) Electronic mailing list Sound effect Maxima and minima Product (business) Category of being Message passing Process (computing) Telecommunication Order (biology) Summierbarkeit Ranking Reading (process) Spacetime Point (geometry) Web page Slide rule Computer file Transformation (genetics) Digital library Scalability Number Product (business) Frequency Latent heat Term (mathematics) Boundary value problem Metropolitan area network Prolog World Wide Web Consortium Information management Distribution (mathematics) Support vector machine Scaling (geometry) Information Basis <Mathematik> Line (geometry) Cartesian coordinate system System call Sign (mathematics) Uniform boundedness principle Personal digital assistant Network topology Information retrieval Video game Iteration Game theory Musical ensemble Table (information) Hyperplane Mathematical optimization Family Library (computing) Code Length Multiplication sign Direction (geometry) Decision theory 1 (number) Honeywell-Holding Parameter (computer programming) Function (mathematics) Mereology Derivation (linguistics) Mathematics Visualization (computer graphics) Moving average Electronic visual display Algebra Perimeter Position operator Rhombus Area Covering space Source code Pattern recognition Polynomial Closed set Feedback Measurement Flow separation Degree (graph theory) Type theory Vector space Linearization Website Right angle Whiteboard Resultant Laptop Trail Functional (mathematics) Link (knot theory) Support vector machine Data recovery Virtual machine Electronic program guide Heat transfer Login Graph coloring Wave packet Prime ideal Nonlinear system Causality Average Green's function Spacetime OSI model Software testing Task (computing) Boolean algebra Addition Raw image format Dependent and independent variables Cellular automaton Division (mathematics) Transformation (genetics) Computational complexity theory Subject indexing Computer animation Search engine (computing) Speech synthesis Abstraction
Regulärer Ausdruck <Textverarbeitung> Polynomial Texture mapping Range (statistics) Transformation (genetics) Special unitary group Product (business) Sign (mathematics) Nonlinear system Degree (graph theory) Computer animation Scalar field Kernel (computing) Function (mathematics) Spacetime Mathematical optimization World Wide Web Consortium Data type
Pattern recognition Metropolitan area network Execution unit Support vector machine Demo (music) Web page Euler angles Statistics Chain Nonlinear system Sic Computer animation Dedekind cut Software Moving average Physical law Row (database) Summierbarkeit World Wide Web Consortium Wide area network
Sic Computer animation Support vector machine Web page World Wide Web Consortium Wide area network
Pattern recognition Information management Support vector machine Demo (music) Web page Length Ext functor Statistics Special unitary group Vector space model Information retrieval Nonlinear system Computer animation Software World Wide Web Consortium
Support vector machine Web page Special unitary group Information retrieval Thomas Bayes Radial basis function Computer animation Set (mathematics) Query language Ranking Category of being World Wide Web Consortium Data type
Standard deviation Nonlinear system Computer animation Support vector machine Function (mathematics) Constraint (mathematics) Row (database) Ranking Special unitary group Equivalence relation Task (computing) World Wide Web Consortium
Algorithm Feedback 3 (number) Electronic mailing list Special unitary group Arm Variance Value-added network Information retrieval Query language Ranking Information Process (computing) World Wide Web Consortium Metropolitan area network Execution unit Information management Magneto-optical drive Interior (topology) Web crawler Similarity (geometry) Computer animation Uniform resource name Function (mathematics) Different (Kate Ryan album) Computer music
Pattern recognition Stochastic differential equation Computer animation Structural load Numerical digit First-order logic Hill differential equation Discrete element method World Wide Web Consortium
Table (information) Support vector machine Numerical digit Sine Bit rate Special unitary group Invariant (mathematics) Nonlinear system Error message Computer animation Social class Software testing Summierbarkeit World Wide Web Consortium
Random number Flow separation Computer animation Support vector machine Texture mapping Set (mathematics) Spacetime Mereology Testmenge Special unitary group Data type World Wide Web Consortium
Point (geometry) Group action Characteristic polynomial Set (mathematics) Regular graph Mereology Special unitary group Variance Wave packet Latent heat Degree (graph theory) Set (mathematics) Negative number Software testing Maize Kolmogorov complexity Error message Data type World Wide Web Consortium Area Information Characteristic polynomial Fitness function Cartesian coordinate system Error message Computer animation Personal digital assistant Website Quicksort Mathematical optimization
Information retrieval Computer animation IRIS-T World Wide Web Consortium
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about the step and goal point the diagram for example of the 1st step that say this documentaries of and the 1st 1 than the decision would be 100 per cent and the recall would be some time well you below 1 usually because many relevant documents and then it might happen that this document isn't the 2nd 1 so we called it stays the same but the decision is lower because this 1 if the document is relevant than the recaulk increase of Disney freezes this case some nice sought to use shape and is all about usually used use a kind of smoothing technique to get a better diagram unjust takes ritual many many queries and that's how things about a legal diagrams overlooking the debate strange but this is really from these discrete evaluation of steps in the right place on the list are at next 1 0 went the cost of the state and how it can be exploited for a major Huatai because the of was basic said that if to documents are event or to documents both not run of and then they tend to be no other way so if if to documents are rather than to some query then they tend to be close together in the space or the other around if to documents act those in the in the documents based on the size based on what kind of space to the right of similar their use of those redolent of those of service based Medea that we are able to model all documents based in a way that they are groups of revenue and unknown rather and documents and rather than the number is not makes it clusters of during the document space so again this prop achieve exploited far cost with scenes are examples for some 3 could use this to Costa all results said into different groups use this brief if we get return to 1 rather than document from some Costa Rica could use this to extend the result all documents lying this cost to get to get a batterie called on Baguet used his full escape again under mediation all kinds of browsing so that a lot of things 1 can do with Cassarino are and is usually relies on the cost of this to 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good doesn't require an extra reference string so it would simply tried to measure for similar documents are that are in the same clusters of this intracluster celebrity this should be high and on the other hand we can compel how different how documents are similar documents from different classes are so we would expect them to be very disallowed otherwise they should have gone to the same class of this code intracluster celebrity and it should be as low as possible so this some ideas and measurement you could all the used to cheque whether the classroom got away some are is you designed to give a reasonable results because usually you don't have the time or don't want to take the at fault for creating a menu reference Clustering so that tried and into the custody comparison could be could be a hint of how good adjusting of calls this allways depends on this American measures to use of the child and some way we ate to human human standing of documents in the celebrity to usually a some kind of time cosines emerging 2 space more work squad with the but it's not no guarantee just just against to get an idea where the fastest put or or or or other bad became next Monday at The Caymmi's grid with an for Class during on well idea simply is to identify a fixed number of Clusters found in some kind of documents based and that of other juristic approach is to start with a new shows seats some from documents and space to assuming that this document at the centre of a new Clusters than this to be a sign 1 of the documents to the Costa which is closed to to the document and that we recompute about this and that point of each Cluster and reiterate that idea and we have some kind of stable solution all we have done enough iterations all of the changes between iterations possible enough of them any possible around stopping conditions the Soham and and the deal you to minimize found minimize intact Clusters celebrity and maximise in rock last minute Italy of some kind of mathematical idea presented in the nature of this case to the House of implemented in the Restricted kameez and under some conditions 1 can prove that the are is actually gives them the best solution in terms of immigration program before last in the lecture all right next 1 with the dendrogram and how it can be used on Dendrograms basic early as some kind of a three year found which depicts different class to sponsor you start at the board level the latest you that every documented in the in the collection folds Clusters and then you have some measure of justice celebrity and then you're looking for the most simmer payoff Clusters so here say bought liver and he of all the initiative Clusters 1 document each and then talks on please see that these 2 clusters of the area very similar according to some measures of classes military at different kinds of the those with advantages and the and and assuming that is that most of the payout and we can join them here and his you the similarity off 0 point 9 1 of something like this and then the can continue now comparing discussed or the other and again or Costas to to each other 1 and then to find the next most simmer off Clusters this could be for example that these 2 would be a celebrity of says point 8 5 like this and then the game gone on to of all collection of cousin some way interesting because the American decide where want to break down but the into into a reasonable compromise went 1 the line for example that no 1 2 3 4 5 just 1 of the most Clusters made life on the line so it simply a visit is a king of the high rocket because to structure in some kind of document collection depending on the celebrity measure and depending on a celebrity measure between last so of all work for this week long sought sunlight idea of raw kills Algorithm for you relevant feedback on so they can write the areas that the user get returns list of results from some kind of are the either which is usually the vector space with between 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point of of discussing with the could be number and solid works are usually at the 11th Street that has worked and time spent baby close document collections libraries today on with them problem it's quite easy to get results at the the top of the results as the of them and that 1 of the Observer but that is a bit is behind in the series and that it was in my early in the area of 1 of my bandages and disadvantages so disadvantages told this and other disadvantage might be of public drift away at the at the legs uncle so if the hole in the talks about that the Camden and nobody talks about the tree than the ideal most likely to shift during adults into the company direct into with all information about the the because it sold predominant so many advantages advantage is of calls that you are able to focus to exults into into some kind of making direct and and Hybrid to fit out results that are quite strange on the not the most popular way of seeing things so if it if you looking for for mainstream topics in search than usual you get good results to the given that you have some way to to tax band and and is David some way so that it is still unity of the of the bag so next 1 now we talked last week by of transportation method integrated fuel and no 1 or 2 but the applications to its seen some example to see some more today so too but might be spending sections of simply assuming the document collection is a can be split into band not spam and we just lay some some new book commands when it sounded and use the money was to be to detect for someone unknown documents that they are more likely to spend to be spam are more likely to be be really documents is also is usually done by comparing celebrities so that the new document is verisimilitude known spam documents and and times with his new document document also spent so long another Applications is for example testifying documents appointed topics to supply on more focused kind of cut of search of subliterature search 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around if I know the cost membership and we have to have to make some time ability statements about the correct eristics of documents belong to the last day that we can estimated the probability from training collection because training collection we know what documents belonged to the Klaus and what document doesn't belong to the class and the and the seat 1 of the properties of the documents in the class and not in the class and them a based the only we can use this information to the direct way to estimate is Paul ability when you documents is pleased idea to what is called not used it busy coordinate use of because it is used to that of the appearance of different terms but different document properties is independent so if discussed this before the break as more the publicity retriever it all the same problem that it makes you computations Angelo really really easy but of cause synonyms definitely not independent Antonin's of dozens of men to Kelly related words for some Kent and talk of everywhere likely to occur get up and not really independent all of them from the area of any of just any terms that related in some because sense of hype ability of together than they would by just randomness or and and a chance if I assuming the and so it is a problem ever based applications and for it to be treated for were quite well on so either of these independence assumption is not a big problem cold or it just where some kind of Heuristic and the fury behind it doesn't really matter what or so nobody knows that doesn't Médecins current today some nice idea underlying these approaches and they were so that through usually most of what the disease or interesting for information to be sold last month was adaptive boosting the when it was useful and how does it work so that boosting some kind of Meetup techniques for whom making it desiccation methods that it could be done by 5 classifying some kind of iterative across as so if I have some training said he had training said David found then began trading a classified using the trading said for example to take a night based classified have learnt some published it model and then we take a look at what oxaliplatin training set off or what examples in some CODE out tests said a classic as if I'd wrong but this model and then began we wait of the trainee examples to give wrongly testified excelled at a Higher Paulton's and correctly testified excelled at lower bulletins and then we can reclassified all again using a nice pays for example and now we we have a strong Bolton on the of the mistakes of the 1st model and so again we get a whole series of more that all of that all used to to testify are down and by a re rating of the correct as occasions and misclassified items win able by combining all of these different loads to get a better application at all of the weaknesses of this classified can be can be can be can be fixed by this 1 but this 1 altogether that make about testified that idea saw it if you have a problem with some has occasionally within the doesn't seem to think of 50 dead and tried at the boosting usually Buchanan Gatineau Falmouth increase of 5 to 10 per cent at with of cost depends on your under the command collection but usually adept at boosting give some advantage alright now to the topic of today's lectures on its again about civilised occasion today will see some of these the most successful for the most advance best desiccation on was No to mankind so called the board victim machines and the Assembly and now the approach for supervised desiccation so stupid victim machines Rialto pick today and to give a brief brief summary of of last last week to realise desiccation simply means of giving some examples of the way out some human has larity that sounded political into which classes of public they belong and they use this information to train some kind of a model of which can be used to to classifying you documents according to according to the Human manual occasions but some but if some of said this damages not spend your nose to reach the Web program than we learnt some kind of testify from this information and and now able using it testified to find out whether a new spent 1 or and with continuous feedback from from the user we are able to make up that and that I'm over time and it seemed the 3 order rhythms and now to talk about what victimage seemed so that different kinds of the public to machines with start with most of the 1 Salenius public to machines and that will go 1 step further and and show more what once techniques and held works of highlights under the brief under conditions Ali who make some assumptions of which were made life much easier than the next lights we do a little bit miles off and then the next 10 or 15 slides but it's all not not too difficult and this all to be called me some assumptions that make them out but it easier to understand the with you may be by Richard occasion ask so documents either belonged to of the class hand on don't belong to a class had attacked and as early 1 single are time engine focus occasions and 1 of them or of and event of belongs to a that this topic of Dundee below to and the public would whatever so and the 2nd assumption is results quite common full types of the occasion reasons that based human that an item in the document to be testified can be represented as some kind of dementia no real so if space consisting of the demand and so many many more and fraud and each documented just point and space and each coordinate this some real number so that the usual approach to the occasion and the task now is to find Linear classified so called hyperplanes Racine examples of the divide the hold the whole items space into 2 part so on the left side of documents likened belonging to the class and on the other side of this divider or document and not so simply try to cut the space into 2 off the pace like some both to them and training said so he could be out to excess and each document point in this space so that could be the biggest case were found that whenever you like to have some of the tough bestselling it has advised by separated the space by a straight line for example is 1 of this 1 all this 1 so that many of the ways to do this and all the other Linear not classified so simply point aligned all if it is freedom and based using a play in order to have a high Adam and space and the code hyperplane basically some kind of needy on geometric figure that divides the space into too hot so it again the some ways to move my painting to see the 50 that 1 different ways to do this next 1 next 1 next and are the best arises so that there are so many ways to do it to do it which 1 would be best to with you into Asian about this which signed would be would be the best 1 to use
So go back a bit soporifically in clean picture so which which line would be best if you want a build Alenia classified UK air and what about what about this 1 good idea
To close to the point and the autumn of this 1 the great care what want what about this month that as the we have to say tuition are basically the idea is to find the line dividing the space at least room on both both sides to be due to make a gap says classification of sound it could easily be that they are very amid points in this in this class which we have not training said and if we would use it very very very testified the closed off training sounded works some of this 1 year that could be easily happened that there is some kind of de point this very very committed very close to the the to the 1 class which gets misclassified if we of the use of used aligned with too close to the club so that the idea is to find it as a which is somewhere in the middle the some space just to be on the safe side given or training at Sellafield on the next side is to offer derives from some mathematical approach how to find the good a good line and what propagated should have come to usually when you when you were with the victim machines and you read something about it you get a lot for the lowest was some kind of very able to enable you would be able to understand and the goal of this letter is to give him a standing call this fall the love discovered useful for that 2 machines where this really comes from was this idea its distilled alleviate that nobody tells about it because the usually renewed DuSable victim machines user user beautiful but it is not the problem that easy to sold in terms of mathematical imitation but which is not easy to understand why to go the other way around start of understanding that arrived at the complex presentation again found so as it seemed that some all the idea of of mounting seems to be applauded for the findings defying a good idea of where to find the quality of the air classified so much in simply means the space between between the points where the where the media Classifier is close to a close to the view that they are Classifier imagined on this side would be this with the air of this 1 because there is point and on the other side it might be this and or take together is the so-called much of the with the bomb recoating creased without hinting at the point of the Mall much in the bed of the the of given excelled at different mountains different ways to do it so that we arrive at the notion of a look maximum mountain testified and the maximum on testified that is the Linear Classifier that gives the maximum in so that it seemed maximum on Jan seems to to be a good year and so is to find a maximum much intensified given some tennis became selected maximising classified is the symbols kind of supply that to machines that 1 can use and also called Linnaeus for victims she of the victim ashamed may sound complicated when you read about them a use libraries to them that essentially they are just about the idea of maximum much interest occasion but lettuce you find out that the allways this such maximise intensified and and that all that based allways can be divided by 9 not play in either playing into 2 area of what sounded could be that there is another that point of it could be that this deployment is located here because we have made some Austin measurement all or just of some of the wind misclassified this point and we won't be able to to find the mountain testify because it is no way to go and I'm between the blue and the green points so it's a simple the moment that there is a way to do this and Leila explain how we can cope with a situation where we we have some some noise of some of the data became mathematical I went speaks of Linear separability is just a century going to make for the moment so another Poland concept other sole called support vector also and that's where I put that to machines get the name from the point that does not exactly of those de points that are pushing against the on not touching the mountain here and maybe this 1 and this 1 and this 1 end this 1 these are supply points or if you want to want to see points as because of possible that these are the so called deployed victims and board victim Machine simply tries to find the maximum not classified which is directly related to their supposed that of a day to be a boy seemed that Maximov intensification is some kind of their intuitive idea so much much into classes sounds good at found that some some all reasons why this should be a good year some sort with followed seeing that largest Mongeon is acutely the calls it seems to God contest against smaller error so sold as they before if have to build a symbol deviations anointed should and if you have signed the close to the rich and that it and might at the back of every step of the points but misclassified by the line of living space on both sides allways gives if some some of them my gin against against house which would go so another 1 which is really important is this year so this approach is quite robust growth was again changes in the depth of its go 1 side technicon see high adding new training de points which don't really seem to change much than the maximise and has a violinist would victim Machine doesn't change but because it simply depends on just depends only depends on the supply dictates that this would make the machines only defined by those points the most critical in terms of classification so it doesn't look at points lying very close outside so that it doesn't matter what points at all Hollyhock points look that could be could be really could be classified in a very Safeway so that has no doubt about that as occasion but maximum much intensified concentrate only on those points that seem to be hottest classify so that is also a good way to do this found so that although some theoretical ideal won't go into now that 1 of the modification is a good idea slightly now people at a wide to write a very very thick books about the re offers occasion and then assuming that the dinner and some minor line distribution and 1 can prove that as much interest as vacation as the IRA made under some assumptions so you from the perspective of the machines are a good idea and probably what's most called for a API below the it just works well the but the machines usually are among the classified as that work best for any given kind of get out of Calstock's sections but usually for real but the to machines for my full their close to the city of estimated has filed want us on the best available five alright so now we have to do some of the mouth and we want to fully lines of code and how to find the best of what a jazz a five because we because good approach to see the ball picture and goal line somewhere because we need an idea was doing that cost and not within the ski instructors account of all the nice approach though that sets defined trading that 1st so that we see with them and training example and the point of space that have been able to find some new Moon into and only to the US or not belonging to the club's so and the cheques on could be represented as a payout consisting of a component why and that I'd be in the eyes training example and why I'm is the real lecture of representing the item to be testified of the document to be classified and that I'd it's just that they would of the class minus 1 means this items that belonged to the class and plus 1 means designed to belong to the club to the FA in the presentation of first class and second class doesn't so it to buy an return of has occasion
Here is an example of what some of this point as scoring its minus 1 1 and doesn't belong to the club and for the miners and the picture and this 1 has called in 5 minus 1 and belonged to the club and the White the last so when doing maximum identification we would expect the the line to the of the dividing dividing lines to be located somewhere near Ameriya no idea where I went to calculated and bridges but we are doing next became the 1st of all what of violent Linear separated so high Ohio can we find out about which which lines in space actually seperate on debt said into 2 pieces and for that we need to we called from the not denied brought some of you may have learnt school some of you may Remember this from some momenta lecture at the University of general any hyperplanes so 9 playing all that and more time in the space is quite hyperplane can be defined committee fine by some kind of role backed off the dimension the role that the W and some Scalability some number as idea simply is that the road that determined in which which direction the hyperplane dense particular to of this this would be the select W showing the erection in which is perpendicular with the through the height and the number of scalability his related to the shift of the hype obtained from the origin of the open spaces of and all the terms we could be presented hyperplane like this type of plane consists of all those points in the given full which is equation here on X might apply to with are role that talk
The scale scalability and plus the is exactly the rope and those are exactly those points lying on the high plains of some of you might remember this so and if read my about the scale had simply the product of 1 of components of W and Vectibix might applied and some of plus the and they should give 0 so that the definition of IBM playing It is a sad W usually used in all the talk of this in decked of the high complained that means it pinguicula to it all too would not enjoyment of the estate is a shift from the Order of the Golden systems and all excitable line joined index sample by plane or just index on this just lined follows this equations so WellPoint's ex wife satisfying this equation light on the on the line here and all points giving it a value lodger than the role of located on this side of the high planes and all points giving a value smaller than 0 on located on this side of the high point of dividing space into 2 and 1 equation to determine which side the point is located quite easy to a talk about this only into limited space in the following because for like of planes and high is exactly the same but I get a lot of scaleable alright became so you can start by findings to constraints that every of separating heidiklein maximising Classifier must satisfied so for any type of any training example we have is the trainee example of does not belonged to the cost so it's Layla's minus 1 than the definition of the plane so W B this equation must be smaller than 0 must be negative sold simply a negative they will be negative for the view of the locations equations if you say so on the other hand all positive exiled that have a positive value so negative examples idea positive examples he of cost so that many many ways to do this but no matter out which which claimed we want to use the want to satisfy these 2 constraints so next real on duty find some more constraints so that find highly end up with only 1 hyperplane namely the next mountains of playing a game of sold with within if some hyperplane or some some kind is that separating line of all said then that must be some way to escape of all classes and I'm minus which of those not in the euro such that found if 3 at are minus and are last by at the time minus us at us up tracked the OMX OMX across from what equations than we would exactly touch also pointing well-supplied victims of No and no matter how what we put us all separating high complained that some room to the left and some room to the right and if we extend or a plate of those directions at some point we will touch one off the 1 1 day appointed beachside and are minus system respecify specifies how much we need to extend on a plane to the 1 side to meet the 1st negative example this of the minus some way and is part of its kind of distance to with the to the next posted example went and and the mountains would be just are minus last Applus and some of Boston some way so and so as note that up last and all miners are not just be the Amajan with him so a 3 if I would take this point and this point many different this point and this point and simply would Calculate the European distance between these points the distance would be different from are minus because I'm minus is simply as a kind of shift and the X and why also depending on the length contribute to differently so we might remember this from from order Brock so this basic and and shift constrained using using the equations but does not have to do something with the actual lengths in the space of later why is to a order go on really it know assuming that we have some Cebrat thing hyperplane followed said and we know scales of plus and minus that give us the space to the left and right and now we just want to come and get some mobilised type of playing that deadlines simply in the middle between the or less board back and are right to point because because as 15 it doesn't make any sense to draw 9 closer to the ball the way some of them to the negative 1 of the other way around but simply want to have all of separating line in the middle of both the House of right between both classes so we can do this by just taking are minus and that this should constraint to both direct and divided by troops and then use use just this Everett shift as there is a shift from the direct and so also use eco should constraints CEO of last and it can simply be fined a and see after 3 of defined the Prime to be the last of these Everett shift that this 1 is also separating height have plane because it diets last just in the Middle between the 2 hyperplanes touching the positive and negative
So this was a wise initial hyperplanes which has been too close to the negative Exxon blows and then we look he and he alone and move this month right to the middle of by re defining constrained and now we have a way to to get in on the NYSE moment eyes had a plane that last directly in the middle given any said submitted separating became so now we have 1 can safely assuming that we already have given the complained that last directly in the milk and now we want to calculate some how large the mountain really is into both because in the end we want to find the hyperplane having the maximum amount so we to believe that is to try all possible separating hyperplanes cake late the mountain for each of them and then simply take the type of plane having the maximum much and for this we we need a new default leader to to peculate not and and to do this Ezio weekend we can again Allardyce equations world so within in the device W in order to constrained the Prime and all mountain with are prime buyout prime so we get some kind of you mountains and the justifying so by by dividing the Holy equations by by a given positive number 2 dozen change either in adult because on the on the right side Dessau's 0 and after dividing 0 by some number 2 0 0 and after dividing the left side of the creation by some of the number of the creation it is designed so that you so kind of misation we find W prime crime this W divided by upright and the Prime prime is this is justified by the Prime divided upright and and this type of plane still is that it separating hyperplanes and eschews shift constant this 1 because he will have a one year high complained and the hyperplanes touching also point that just this type of plane with a one handed and origin hyperplane with a one stop strategy was again some kind of no motivation and all given some plane we are able to find an all night 1 which having you to shift constraints to the left and to the right to carry on the good together to sell its stake is that separating hyperplane than the allways is is the hype on such as is still that such that the mountains to both sides to the positive and negative excelled at the same with and the bounding high complaints to the left and the right eye shifted the raid by 1 so of what the benefit of doing this so that it now seems that for any that separate hyperplane days since the special that type of thing we are now able to leave it all a search for the best hyperplanes only to those planes having Wallace satisfying these constraint which make Optimization problems and it easier so the renowned for get about the cost of all possible hyperplanes and now concentrate also which on the high plains heaven you would not into both direct and because the always use such high protein so and again been doing this is that it's a good idea to use Leiocassis find that uses equispaced to both sides of the some of and full moon step for this for doing this and not for such space because we want to search for the type of plane having the maximum much and we want to go through all possible the planes and find the 1 I had in the UK not in all such cases is the set of for up the role that those at the top of that and because it has a lot of plain old shifts so far possible hyperplanes this which are separating hyperplanes of the space was a negative and the constraints is that exactly because the if you've done this is known as a gin we not concede that at some point a White playing touches 1 negative exiled that is exactly at the point where this equations minus 1 because we had introduces minds one-shift and and we have a constraint that the height of the looking for half the probity that that is a positive example just 1 shift away from it so now has a specified these constraints the question is what really is the mounting ways of such a high rate is up do next so we can use some results we not under about are so that this assuming we've given such a high the plane's satisfying this equation here and there a hyperplanes touching the negative and the was events on the shifted by 1 minus 1 into each direction so that and we know from many underground around that the distance from the height the distance of the hyperplanes that systems are quoted space this goes right there somewhere that we know that the distance of a high complained to the origin of the corridor and days which would be you is exactly distance in the European sand is exciting the length of the back to to beat the violated by the length of the victims W don't approve it paid and it is and because of this we know that the distance from this line to the or it to to the origin of the coronets based because he is the plus 1 is just length of the absolute you it is the plus 1 divided by the length of W and the distance of this type of plane through the Order of the Golden space is the miners 1 absolute value divided by the length of W
And then they concede that the model which is exactly troop divided by the length of W because the is the same in both distances and the dissidents only differ by a number of to that of the mountain with a through divided by the length of the role that the defining the height of playing so and if we want to maximise of mountain with subject with a constraint 15 on site before then or last the to made the length of the respect of the dilemma of how large the mountain is the Supreme mini-mill among all by the playing of a early we get following Optimization problem and the solution offers Optimization problem is the 1 that hyperplane paving the the maximum much not so we want to find her parameters W and these so wanted definition of high complaint dividing or space that satisfies satisfies the following swathes of so we want the high complained that Mike and then the next this this number maximises Temudgin with and that same time satisfies with a constraint strange but that's positive Exxon of the next Kazakhstan but is exactly 1 shift away and the negative sites like 1 shift in the negative sideways end of calls that is 1 point touching the touching the shifted large the at the shape of 1 of the as once about sector and that the other is the point of so as or gold is maximise the magic of the mountain will ways be taken as big as possible and this means that the don't need these 2 constraints because if you want to maximise the mountain
Then we will allways makes not large enough that is so large that we have the quality but this place so it doesn't make any sense to to use a solution I due to look at some hyperplane that has this as long distance to the next supplied vector than average as a has not has allowed the distance to the next appalled that than 1 of these can can become quantities a we don't need these to any more than the current state of its dividend up who want to maximise the mountain full of these by of does not such space and the constraints simply are these 2 him of each any although to wonder that the train it sounded the negative line on the left side of are playing and distance should be at least 1 hand on the right side of all points of the law was founded sublime the right side and the distance should be Italy's 1 so there is enough space between Australia sounded and or dividing hyperplane so long Nextstep would be to make this time but simpler so if you want to maximise to would you guided by the length of W we could also medium eyes just this number because century the same either to solutions and the 1 in the 1st Solution has not value here and then it will all ways have smaller value and we just take it because at the moment only function so we could also called instead of minimising just the length of W collective W we could be my last 0 point point 5 times the length of W squid so does seem to make any and sense but idea that is because this length but down found that W S P W is a vector are remember is all allways something like this W where last W to where so all the cold coronets Quay and then where would take out of it so everyone to what you make calculations in algorithms but I via the result was a good idea to squalor this 1 to get rid of to get rid of this Webroot because it Greywood's all was quite expensive operation and of this column stews stasis same Bacall's squaring positive number again is among the tone operation and this won't change of communication from the so followed that we could also add some factors 0 point 5 which doesn't change anything Optimization problems and actually there is no good reason why we should do with a spot in the medical Monday's the read this some kind of standard full halted find these kind of problems and I usually put your point 5 in front of the house to be minimised maximise and that the only reason why this year
So to get a substandard Falmouth which can be sold by existing existing by the results of next like this is not the problem we want to solve so I want to look through a well hyperplanes satisfying these constraints and from these hyperplanes satisfies constraints we want to take the 1 that has the minimum value he of this next much and either plan that so far only to get a simpler presentation re could also combine these 2 constraints into a singer 1 of with simply could put that by here as the fact are and don't need to be to distinguish between 2 cases but the negative and for the next but because when we do this is to use for the mind as 1 example of negative Exxon this we have minus 1 W times why by the call units of the highest rates on the rise the minus 1 great of an early crew to the role and is simply become minus W timelines as the last 1 is so great that the crew to the wrong then we could move the 1 on this side if minus 1 So we want to write we want to arrive here are in me them this strange how the size the are so he has apparently this year this must be the and thank you for the and of and the and represented multiply though thing with minus 1 and forget W multiplied by what I've lost be less than what he could to minus 1 and that is exactly what we get here and the same is true for the politics of the of just offensive way of expressing his distinction of 2 cases sold this not are highly Optimization problem we need to solve when we want to find the maximum much intensified given some training said and just constraints it consists of a single constraint for each training so that looks pretty simple but as it seen in the last 13 slides duration is is a but complicated but every step is really really symbol of and is just a way of busiest but on the other hand if will start with this X person I would have never know of doing at the time Alpino no early Seventies rugged doing it a again dissolved Asian Hull Kennedy's also will not now we need some kind of new medical Optimization on tourism so affectionately this discipline and mathematics by which gives with so called quadratic Programming programs Huppi for salt and there are many many algorithms to find the 2 most solution of problems that lookalike this is also the reason why we added 0 1 5 year that cause all the people in this week you Huppi off area just defined the problems this way became so that we could find the maxim much not playing using some some underwritten sales of the books on this how this can be done this won't be the topic of his lecture just use some ivory facades come from and what you have some kind of an American competition lecture they should do was that is anyone 1 of you then who has some knowledge 1 kewpie problems and just 1st Melo adaptive selective
It is quite a complicated stuff but these problems can be solved without OK let's go on and have a right to know that they to have a break now we will see began in his and 5 minutes of locating and let's go on sale for whom provide a arrived at some part of the motivation problem which we can solve and when we saw that we find the maximum mountain classified which is the Linear board victim machine would use to classify density and uncertainty that's not the end of the storey because found a that uses are quite and and they found out that if we want to see why this problem but does just seeing a it might be easier to to on some of the different problem which is equivalent to 1 just shown time yet we won't go into details see its it just just seen it and I knew terms and don't and don't get confused if I read something about it because this is usually the representation of the problems you will find in books details about that the machines are great ideas and you just have to see this neck to make summarisation problems have no idea where all this comes from
So around the trick is cost duality and each Optimization credit Optimization problem has so called humour isn't Asian not which can be derived by introducing a gradual multiply through all the used them and truculence feedback and open was used some some kind of the transformation in all quite complicated and left on this lesser sometimes go and I'm not a meditation and found this really confusing but actually a father Woodward's that you don't need to read it if you want to without the book the thing that really as you should remember that this is some kind of human full of the problem to be sold to fund which looks like this and in the representation we are going to maximise and mayor of all of us that he is a vector consisting of and numbers in renumber so in order in this file relations we wanted to find that the demands of the job representing or like the plane shift and now we want to find out
It all remember and the number of trainee examples now we 1 number training example which usually is much smaller than the number died when the fine too long to to find the demand and the role that the problem is usually simpler when we take the lead when the defined in this for so the temperamentally maximise but this morning and he is so we want to maximise the some of that they are of a mind some kind of strange but here that for where comes from and the constraints to be satisfied with all files on less and greater than early crew to the world and find the training example of this equations and the and the 28 this should be a any ideas of the not so great at that a week grid and the world and also told this time off for should be 0 so of some some constrained on all politics on the other hand he gave to get and some way this would be 0 so you directly arrived this from the initial problem if you use the duality mechanism but it doesn't help that its looks it and it looks a bit more complicated but usually it is easier to solve when made problem in this way so 1 a very pleasant probity of this operation is that we have seen each other from their real corresponds to 1 trading example and and the solution by any optimized Lucian to this Optimization problem has the probity that if for the this solution to 1 of these various his last in the world then the corresponding trade example it is the perfect or so another important thing is that because for no support that vector assault on plans in the training Spaceline talk side and the dead are not really interested party finding the separating heidiklein for these points these are various under the well and so we can't just economic training X under the new not supported vector so because I want the public to have 0 values but we can make Noel at that point that can Rudolf is being supported by the US but also makes diminish from much easier so and that is still somebody usually most rates on the size 0 so I don't have to deal with and training examples usually but does a small fraction of the but also makes holding up problems but not easy but came when you within this do with the presentation we could also give a different representation of training but occasion function so big remember that has vacation saying function simply is the creation of the hyperplanes and it returns in negative value known of minus 1 returns in negative value
The 1 side and negative values called for datapoints lying on the left side lying on the negative side of the space and a positive number for points allowing the right the 2 side of the dead as they sold reviews The Duke of 1 can rise Solidification function which is just this morning I and we take the time off this values of this directly corresponds to to the distant in some way from the separating planes and it for has some de point this distances positive and function returns plus 1 for the the other points but the test occasion function returns minus 1 so that occasion function is used to classify you get up points X is a new day point at put into this function and then calculated this value yesterday are by unknown from a from the solution of Optimization problem with just seeing is allies unknown from the presentation of all supply of that the wives of the Labour off by the public to the political negative X is and that the latest data presentation of on new training example and be there is a constant that can be computed directly from the solution of Optimization problems so before when event found a solution to the duty as case into the Duke of this problem and get all the of as we are able to direct the derive classification function from the south and again the benefit from using the dog has taken is that the only need to look at disappointed because some and that 0 0 or not supposed that do not contribute to are closed occasion function that also they do not contribute for cake lacing policy of constant be so using the durability Asian next as fication a lot easier so of and you should also know that are classification functions and the definition of the also the and the and only depend on a laptop between following should de plants and some supplanted Octo point we don't need to do any other computations was are the points to be appointed because it is a fight that compelling it to a series of superb Victor points by taking this Gaia upright so this year the case and he we don't even have order point so that the crown probity a key feature on which we will use various who so we really need scale approach and beat only need support points a game to get now we know how we solve all my occasion problems which linearly separate and the 1st assumption the beginning but in order to realise is that beautiful that she would like to have it usually found but it might easily happened that some of the point might be located here right in the middle for a positive examples of the negative ExoMars and and they have no chance to drag a separating hyped up playing between the 2 classes of this would be a better place because it is classified as this up so we know we need some way to cope with these exceptions in a reasonable way chaotic and due to the Hindu now also called soft much so we do not assuming that the justification disclosed that O'Hara politics are those on the right side and 1 night at a summit on the left side but we assume that the classified name make some this takes about when going the plane so you don't need to divide space into 2 a crisp costs but there might be traced example it's being on the wrong side of cost when a training example is on the wrong side of the plane this would introduce some some kind of classification costs such as cation which should be used to find the best hyperplane use separating the data looks at the best of occasions and so that the best to the hyperplane separating followed as space and his hyperplane having them not and that has been as big as possible and at the same time makes and makes a slip are also as possible of course that the 2 were to factors you have to have to to wait in some way so that the girls to make a good compromise between with of the mountain and are also in the occasion alright soul and the and simply is the distance of are testified training examples from the hyperplane which would make it correctly classified so of this would introduce Systems some kind of cost which is the summit distance so now weekend extend Optimization problem a by so called selected very able these these but a one two bed and so for each training sound with humour the training example can be shifted a little bit to the left to the right and a chaining example wage missed Getronics under his and shifted into the right space such a we really have to correct the occasion again and the politician issues as follows we now have the status of the area but has a lot to us as the parameters to be optimized so again this all and issue of 2 migration problem and not to do a problem and are allowed to minimize not in which is not at constant see might apply with all or shift constrained of secretary of seat is it is a constant that she was in an advanced and that is used to to wait the mountain with the has the air of make intensification so easy is not than making and in the Kazakh Asian is much more important than having a large large mountains and if he is more than having a large mahjong is more potent than making a also wanted and avoiding are looking and and we have increase all constraints told the Belize all be positive on all the world to be positive shifts and we assuming that the following day since the end of this was the constraints constraints saying that all positive some should be at least 1 away from all separating advocated those directions and now we use this really losing this constraint LittleBig saying that of course on the distant don't have to be has to be 1 but also could be system or not it could be negative and this distance than and his this changed by bad I'm so and if for some trading example go back for some but if this is all I've complained that we would need
So began the or 1 hyperplanes this shift 1 and is also shift 1 we won't be able to get a shift of 1 for this that point because they are ready the distance he was for example 5 than they would need to define if this is all eyes training to define that I'm the crew to fly to allow the match in 1 match and correction he of the size of 5 and now we we assume that these de point is located here we would treat this step point as it would be located at dislocation and introduced at Kennedy shifting the step point and not to use all hyperplane because it may not make the the correct classification because this point is now located here shifted its but such shifting with reduced the cost of flights and almost was happening and so is the highest point gets misclassified with a shift of that are higher than the price we pay for and are having to use this shift is the and the constant see my supplied by the strength of this shift of the said sees some positive constant which regulates pulp expensive Everest be treated in autumn addition public again if he is last than making justification are is a significant factor in on and off value to be minimised so it sees large then we try to envoy it any cost possible so in extreme cases the could she see the crew to influence the and then we would have on the issue of whether to problems and then or problem would follow would only be solver if there is a high plane separating the dead and it is a by introducing a see which is the number of different from in 50 with David to allow for the US and with them the calling the case for the foot and in the case of Siamese training example we have now this constrained by the need this has been 0 before of fall relations and a chaining points that can be classified correctly and and exactly the way we did before of this that would be 0-pc because it doesn't make any sense to to take a lot of the because this would introduce a penalty and for those that points that canopied testified correctly we left to you to take a bath value which is large other 0 and dust reintroduced some kind of energy and and then we have to wait mountain with again Kennedy and arrive some hours solution that compromises those again the the the largest but don't need to assuming the separate separability and more and again 1 can from a for across pointing to a problem which looks simpler and like this so we might remember all Richard were problem simply doesn't had this constrained he had no we simply continues to opt out of the use Liburd weaned 0 and see the CIA's just some kind of up constrained off so it's not going to achieve while this and not the bond and the Duke partner but it simply is the way it is and that is also a positive thing for using the door for accommodation it really stays you easy and does need reduced any more and more parameters is just a slightly change constraint use of much sought and began to for these kind of problems they are under is available that that can find solutions efficiently became not to classify and guess said we have using earlier Classifier and but also can be held for the noise and the death of does situations that are not so clear that you could see was a straight line looking
Expression is some we assuming to the field only to buy a new regasification from saucepan not Bambara rather than what happens if they are more than 2 classes in in Omnes these days for example in the case nearest neighbor it's really easy to with to use different classes for example of user uses space where they have spent and and politics and something out and you just use the classes cells that the machines are now in somewhere bound to abide test occasions but they are methods to to extend them to a 2 might the classes so what ideas to for each classes trained the Classifier and has for each the 4 summary of 3 classes this for this politics and this is science and his unit that each documents belongs to 1 of exactly 1 of these classes and that is a problem I can offer to the public to machine because of Beckham chic and only can only magazines between 2 classes so what can still do is training classified for each of the 3 classes so Roberta classified for that vessels non spent rebuilt as a product of machine for politics that was non politics and bill to machine for science lose non science and then for each new document we want to play as if I'd be which use each of the 3 thousand files and shake up the mountain of the new training point services or space and this is also backed as far as early as bad and he is not spread and on new document around a classifies located then this would be the mountain for this new document which respect that works on the mountain of 6 and and then let's say we have a different as as all politics testified has politics and here is not politics so the state of but differently to the example of this of politics classified he politics and he is non politics than again we can use this as a finite to determine but Alan you documented is politics or not politics and we will find out what sounded as this document is politics but with a much smaller amount in that it is not too far out on the day the same for for Science testified and then we assigned that the document to the class will not India's largest so in this case we would signed a new document to this last because it spreads with the weight of 6 for the might of 6 and it's only politics with a much of 2 to its more it's more likely to be to be the bullets and politics at assuming that the structure and can only be twisting last book became then Rugby can also do is built a 1 rose 1 classified instead of training squad was not spread we would trained classified spot where the politics but where the science and politics where the scientist at the and the again use classified as he as well on to a new training said and car and the number of times an item specified back and and items testified another classes and then simply take the cost chosen by most of these 1 2 1 might of causes of 10 classes you need of 50 million the unique unique its at 50 times 49 no 100 times 1990 but through the number of classes you would need animals above that the machines I would need and and imagination of the large number of large numbers of classes of and this is not a good approach of under which he would stick to this 1 year what sort of a possible so called might class public to machines on the job by complicated expansion of the spine read about victim concept where reuse might at the height planes and wants and combined them in some ways we will not talk about this in this costs around ways to deal with for that to machines in my because setting from their different 1 c of side which 1 you want to to use a Qaeda next powers lecture so called non Linear the product of machine if found the at you could also you could also which ranges board looked victim machine but we each new documentary and because it but by the user that usually take it training said that is large enough uses training said to create your eye to testify to a two year on the plane and then stick to this type of plane took as a sign new documents of cross it it makes sense offers some time to 2 reevaluates from your idea but victim sheen given the new information you have but this is how it usually done and then you can use this information because you don't have any Sunday is a concert hall stuck to answer point to machine which tries to use some the debt to be classified of and that the problem becomes have a training said with limited founder and you have a set of documents from it only nautical adding that and the other ideas to to look at some kind of the space where the whether you use this and you could use of class technique to 2 0 estimated what the correct Labour of training self of these examples could be if I don't know them but rather complicated and that way to well stated Sunday is a little bit better than the number of the big 2 machine that usually you can only use the training the said there has been manually as a step too but you can buy and that the same for types of the occasion because the civilised as occasion he you need a training said consists of a doctor who was patient and fleet document recorked Labour violated known to be correct and the and now it's a different situation I am found dead in a cave Justerini huge we don't have anything against of what what might be might be correct information so 1 could also think of supervised test approach where someone gives you a reference to a string that has been created manually and from this command from discuss and more generally the string of space has to be rifles could be could be a problem that these a different of this being the 1st to link the the 2 weeks ago we we had the distinction into different the 1st occasion on different machine learning to ask 1 must supervised where you a on provides correct information to the system which can be used to to learn something and you have sent me is a semi supervised sending where you give some correct information in some editions information for some but the debt to be classified the don't could be used if you if you at of this debt is located space to look at that as a child in the class real but model and these are not uncivilised occasion we don't have any information which uses these 2 with frustrating because you don't know what should be a correct last you only have some order presentation to documented if no idea what to do with the it can just use some heuristics and assumed that some of simonetta to measure is Scott in some way all Greece and human human celebrity judgement is all you can do sometimes it if you were as document and you want to wanted makers classification you can use a document content for example you want to but if you want a classified UK Politics documents politics of non politics you could to could try to and all of the user could if you some pointed picture of some of politicians minister something else and then you can try generalised using co-occurrence of terms but also could be on the point particular and use this information to to Duke occasion so that the huge range of of populist occasion that can be done and extreme points are just you learn from them and known to be correct and the other extremist you don't have any information you just have to get up and do whatever you like and and high Ohio run but you can do it but there is no guarantee that so long as the most visiting a civilised learning found but this large space in midweek so they are the approaches where the classified is able to ask the was published information books of the year such as a finite identifies the scent of a specially off a specially vague examples of which are which which to be critical and it does seem to be clear whether this would be justified in 1 from the other this could ask you with a full information is also possible to within the range of ways to do it in the to we only dealing with most of the 1 and in my opinion these complicated and not usually so into Solidification are made and a book about machine learning that usually the major Trump spending all these approaches the below the with a lot different or to sort of do this film and machine learning as a way I want to go that some of right again in London yesterday that the machines so we have assumed that there are ways is the said about several of pop or in cases where it is not linearly separately this is because most the dead are also some presentation else but sometimes it might be true that the debt itself is the latest in a long nearest separated of parts of the year it might be perfectly reasonable to assume that 1 topic all 1 class is located in the middle of the stage and 1 that is some the unjust of light so as a way to describe this situation using line so it does make sense to do divide here because they would be and will be missed as occasion he doesn't make sense to do it he will he is the only way to do it would be to have to have to separating the 9th so the whether all site of Qwest this is not a Linear and the question is how to do it so hot do not Alenia justification ideas squads imploded goods from either of the situation then returned FameLab data into a high images based on the decks of the with 1 minute this for each training example is described by a senior value on and on and on the singer lines and if you try found this data to images based so far sombre by a giving giving the values that life on the outside a high the 2nd clad in and around in the middle and the local audience than equal arrived at this debilitation and he a weekend I draw the line to separated the positives from the negative examples of this are the the underlying not long is a bet that the machines that waste a transformation stepped bringing the data into a high demand in the space in which we can used Linear classification of precious higher to do this transformation not as good information will and what is not and how to deal with debt and a very high damages basis or in some cases the spaces might have 10 thousand stunned and has done and what you more doesn't sound to end so he is still some kind of visualization again not his London India are Nonlinear has occasional it works of his it doesn't care for we will open the video or this old works so here in the middle of the of of the politics of the and on the other side we have over the negative examples everyone to do is have a classification so inside well all site and now comes the transformation we are now mapping are time and his based in freedom and space by introducing as demand and and now we can use hyperplane playing in this case industry man days to separated the positive from the negative and the fit again break down this Linear caps in Georgia to limit days than the finely arrived at circle which divides outside from the inside of this sort is the latest step usually but cuts in the price of idea and the good thing is that it stays quite simply because of the good properties of Europe problem retreat just discussed
So of course when we were looking high dimensions spaces and the and reduced information step and computing the transformation and then dwindling act occasion in a very high demand based might be very difficult so it would be very good if we don't have to to do this transformation explicitly we just now we don't so that that this policy is down a training that which is not a several is after and found dead on in the new space which is the several and the supply of victim can only were directly on this understand so what you usually it would do its 1st transfer and the data and the and were in the transfer space with his above the to Machine so but we are going to do because transfer summation might be expensive for large desert and for large and vitamins to work directly with the owner which days doing or computations and if we are working in the transfer of space so looking for some kind of implicit transformation that is computation efficient and a party that is the way to do this and this and this and this at a time again depends on the fact that the only need to deal with scale-out Prolog when redefined are the point that the problem is and Europe problems so we all need to do is get up tracts of are all regional according of all of us about that and we only need to compute scale-out or acts of new de points with with the support of up so we don't have to make any other computation and if we are not able to compute this abstract after transplant spaces directly and we just have to have to change this part of the of the optimized Asian problem and the rest distaste the same this is called the colour of trick with colour some kind of mathematical function some of the special properties have held by a group of Kenyan on of it and we don't we don't go to the top is how this really works the assembly is the if you use colours and then you're are able to compute a laptop in the transfer of space in a very simple way so let's assume that H is some functions that maps are all which the debt of the from Sunday dimensions based in some deep fundamentalist days so the killing the Prime is much Rodgers and the and the and if we want to solve all provision problem we would transform way are that points and or on new points to be classified and and just family laid out of demonisation problem in terms of the new space so why I've becomes becomes 8 of why and or X becomes becomes each of the age of the ex so and again it you can see that we are still need to work only computer scale order of these transform make chaos Scalability Scalability Scalable here and I feel able to compute scale efficiently in the new space with of having to defend the transformation and this country can be done really really quickly following the communication problem so I'm without transformation and that the good thing about it has some of the plays of some special type so that the sulker function so that many many pubs because the fact that about half the has property that you can't computer this game abstract off to a transfer collector of using all the political party that in the in the UK which is based so attacks on the island this summer applauding only colour cancellation of the 2nd degree biologist based is to revenge and we can computer mapping into a 1 2 3 4 5 6 stamina space by saying that the 1st goal in that is all which won the 2nd goal and it is XKR would of 2 times Ulrichen origin of 1st collided and so on and so on and so interesting probity is the following if we want to compute this game Prolog of to transfer director so given to evict as X and ex prime knowledge based and we need to compute scale are products of the sector in the in the transfer and space and this is simply not the case that is which is based might supplied by 1 and a good things at so we don't need to compute the transformation into a new space itself for computing this gap in the transfer space we can just read ironed simple computations involving a rich nickel this is what the country is about time that the 11 year behind it but that essentially the idea computer scale opera in the transfer of space efficiently because that that is where we need to do when dealing with the public to machines came have demonstration of the of the public to machines so that a lot of love for the some job operates and then the weapons Labour all illustrating howls of the commission's work is 1 of them fine current you choose to play around with his told to get a bet on the standing of the this so he a weekend Regan on defined different coloured who want to use of the only because the like some good books on the degree of 5 and Furyk and please Alexei under the so world that is all positive and unfortunately on negative exiled slide just in the middle of all the politics some but so that would be any way to derive Linear that Linear line separating the space and the need to high Adam and on Monday it has occasion in the sound the of foreign only rather which is now computer to and this is what the Green only would do so these of the public to be supervectors on this side 1 No 1 another 1 another 1 5 support that was on the other side the cell is done so again think of this as a transformation from Heinemann's space where I can do pollinia separation and protecting down to do the 2 women based and so the separating hyperplane become some kind of crime is a point only know popular choice of so called radio basis functions and turning examples and again before different ways basis functions usually for some kind of close to close to the coast code like the the 1 he was closed and goes along this way in the Foreign only is setting usually have large area of some the stunning he goes wrong and being opened to the other side is only and integrated basis functions usually only for some close to close the difference between these 2 and a good questioned a this also probity of these found based functions they aren't that is a tough imagined and it is in some ways these these that area was continued somewhere on this site you thought through the ability the transfer space and this was connected to an area lying on this site which can seem the picture not because only early in a very small beer of the of the space but that is some way off being located here which is the same as this money and there for me a few number for public of the need to achieve so that is all was a problem when going these things in the region as a base for purpose of has vacation it works pretty well of cause a problem was within hours that points lying here that likely to be missed off underlying here because it is too could be an area where the big money again to do this and to the club so it is a perfect but usually if you representative sent off your today that the training the and the and the and the public to machines with Colin usually brings them a very good applications for me became this works of works sonatas personal spot that to machines working information retriever followed so furloughs not so some some small examples to to prove his because occasions a quite the problem and it's just applied in information trio of cost 1 1 important area of also application is textures vacation has said politics will also something out of this could be the 1st of the important libraries which to Tuiavii with which the index of classified a new books they get and if it is they have the books in a digital full that could use domestic as occasion systems to Amte found derived some by some classes the but might be long to give some training the and then the band can decide whether this is vacation is the 1 they want to use all of just have to make the changes but does not have to wait to make all the occasion by the scope implications that take justice has also very popular soul and the document recitation you can use the for the public to machines that these are the Sunday that displays has seen it you could also add some addition features some addition dimensions like talks on the document lengths away the which have some reason to think that long documents might be contained in some other club and smaller ones for some believe fewer if you may sell observation that in your collection and about documents tend to be very long only every shot and ending the document lengths to their Tuesday or a presentation might be a good idea of the same is true of other derived features and you could also use undesirable sentation not talk as occasion purposes and is possibly the only thing I you need to have a some kind of future presentation of fuel document so that each document disappoint space and documents belonging to the same class tend to have similar properties as the victim Machine will find out what is really meant Simmons and and derives desiccation from it sold found the damage annuity of course when you that this is quite high because every type then becomes an exodus in yesterday's this usually is not a big problem because the almost documents on the only very few ecstasy and different from 0 so no documents remain contains or terms after collection to usually the each director all played each document is presented by a vector are where there are some numbers in but many many many 0 so this offers iteration westabout about victim machines Skandia is now that can handle the situations where excess containing the euro's just ignore in the UK and is still unable to find up to a solution was found that 2 machines Skandia response data very good they really is a founder of the occasion the those in this file 1990 8 the where some experiments on the right of collective also remember what does collections of a set of new was a of new stretches from the right as company from the end all the and and for for some categories in the desert of positive and negative examples have been collected has occasionally has been trained and the and test of the new documents has been Kazuhide using a rhythm and and it has been evaluated hold with the 1st occasion was in terms of possession and recover in each values he in the table below is the best measure of the for months so 100 per cent means perfect as occasion 0 means they petrification so these are the categories which has been tried and these are the IRA's and so this 19 Disley based is a truck has vacationed these decision trees another way of public as occasions this case nearest neighbor in these different for most of the public to machines to India for a victim machines using to different Kennedy constraints for mystification to and and the victim machines using a renewed basis functions current was the perimeter here on doesn't does not buy the you and so and they found out if you look at the average or where these process is that the justification defendants followed was the board victimage jeans or or is in the media that on average what the want a 68 78 per cent and that the other party was the full not significantly were so rupture has been quite good of calls and a nearest neighbor but support victim machines found after the fall of the everybody in the squad suprising at a time because of a back to machines around 98 has been quite new technique of the community that the only happy to have a technique had really really homes where competitor techniques and can be can be applied of to document collection of cost if you if you look at different Otago worries that might be situations where the board victim before more than other techniques of some 30 year for the interest category of the victim machines here are launch of 70 per cent of 75 best and case whose name is that in on the but all over the world in the area but that to machines have been proved to be that this doesn't have to be or a case of calls it depends on the connexions to have it depends on the her presentation of the documents kind of space to your using usually the about victim machines before very very well but a and and not the case and the public to machines is called learning to to rank is also quite new topic information midfield and here special titles when the computer is used so called code rankings victim a she when again the training said consists of documents that the here and now and again of documents and the idea was that the have a trainee payoff documents why by 1 and a wide eyed what eye and why prime than the payout expresses which documented why for by his prefered to it is better than why crime with his back to some Creery oversaw the if you have the right the baby ranked list of results some create that you might to arrive some pass from its that for Sunday this result is that this month for some if you're looking for the IPO rather than the Wikipedia Reiver intrigue might be better that might be a better result than some spent and to be either a page might be better than the man affected official page about the bride and of course the man affect effect of official page is a better results and some spam page so here you would be payouts agape 80 is better than spam to keep the is better than the man affected page and the manufacturers page is better than the spent the past 3 trading example and again there example is represented as a point in phase and the information that is used to reduce the ranking function and was that at the idea that we are now able to the site for every new Duckham whether it is that lower than any other documented known in advance of the task is to find a ranking function that designs and America's which document and ideas that that the is called 1 document is higher than the score of another document then the 1st document is prefered to abducted his 2nd to the 2nd 1 is that it is better results Sikri back and some way so straightforward approach would be to limit the images to a special kind of ranking functions Linear taking functions they just to escape the modification of the document data presentation by some by some of the victims and their products or is it to do something with the board that the machines and he again 1 can 1 can family this problem as a boy victim ashamed ask again we want to find the hyperplanes with maximum mountain such that this part of the that trading example so scared from Act of the hyperplanes times the presentation of the document is better than the scorer of the 2nd documented and period full system that much and so that if we say that 1 document is better than not than the constrained is that the difference in schools must be accused 1 so again they can find a list of constraints from this this constraints equivalent to this Fabulation I some number to be determined might applied in this case fashion by some vector because the difference of to documents again is a vector space at some point in space and this is exactly the for full we used in nosopoetic to machines original relations but not a trace of that is that they are in each player nuggets treated as a single point by such striking the training part has from each other but not always in the same boat victim she foliation as before and consulted about the way we did before the use of mountains unique using Linear going from functions so and again the weekend uses to increase results quality of a big and the audience was speeches some some supposed victim Machine guide information retriever accused of work there are some also discussed the question where preference payouts come from which the and we really need to learn ranking function and and whose idea was that if you may get to return from a search engine and list of results from users tend to lead the skin through the results from top to bottom and the user click on those results they think they are adamant so far some with the use get this result him and his 1st click is only keep I up H and weekend assumed that big Epi page is that than this page that in this page and bed in this stage in my beetroot that that these 3 pages still Parliament in a by interest and but if the right but the refuge that this is the best ones and beyond and the search engine shops in future could be in Indonesia to retrieve Toscanini huge Creeley's should put this result at the the top because it seems to be more are and then the other 3 were the idea just over other uses during the rankings for culture from the feedback and some other uses off the same coup in this case we are that we can use this ranking functions 2 0 2 optimized the ranking in the future or possible victim machines so again near computer and issues are just let the user click something the ranking function and then use ranking function to create the ranking in the future so that they are only now of across the the board 1 could also use the ranking function to compute the results which were already have feet from other users to the cause we would we represent a result Oasis that already include use became only the at this link fingers a 2nd look at just of this just list of applications of the public to Machine selected the public to machines a used in many many different area of science assault in Biology chemistry and geographic problems sell the barbeque to machines are some kind of universal to from many many different as vacation Thomas this is a page of someone who collected locally largest applications gigolo but it might be interesting gave finally we have a duty to worry about recognising handwritten digits is a very important Fault some of whom may male companies and that they were under the correct so in Germany since the Dutch oppressed Medicaid the correct beliefs with the edges of like this still will any any kind of look distaste company Eton or a begonias but they do have a problem you went to the kerb Honeywell when let us and about the disease clothes are the most important information for distributing the let us because depending on the Zipcar's that goes into this Blue this been knowing on into this track this track and gets distributed in 2 different directions of Germany or lower for the 1st information information 1 needs to know it is difficult to written on the left and crossed a when dealing with the BBC over the to meet the Colts into its in sales of high end written in the 2 find out whether this is really on the high end of something out of this is a 7 or Suozzi and it will be a very good thing if some kind of machine would be able to read the good and translated into a machine was also the budget get usually the spa curbs on the battle of the where Zipcar other information party has been cancelled into a machine to away and the and the Distribution machines in the in the big logistics and those of the many companies just reading the disease when when dealing with a man and distribute the made where the logs to is a problem and this debt has said is is a popular desert in and had a recognition it just this just taken large collection of reusable could numbers of all the good digits which have been handwritten and and some people manually indicated all these numbers and the task is to know what it is to the tree on a classified from the data that is able to decide when you do did about which digits it is still began to weekend directly derived Anastasia presentation from because every digit is to order a mention in which to each big so is he's a 1 0 0 and has caught in its and just simply treat each Pixar as 1 diamond of space and and each digit simply becomes a binary and say these are 100 pixels to these also 100 pixels than the just as the 10 thousand m and the future space of representing are down and they have different classes for some of the last 6 of the last night of 6 of the its last 6 of the 1st 5 could be done with the public to machines but so that he was that kind of the board that the machines using 10 thousand to test X as using using a large training said no idea how large is that the 10 thousand Test exiled to a very late how good the justification and found out that when trying to do is stand classification into or the can possibly digits the and the way it was as though I'd using the board victims she was in the best case using a special gun despite victims sheen by only about 0 point 5 per cent with which is very very good so of course 1 could ask whether it is possible to make it even better if we look at this 65 misclassification these machines made on the stand test examples and you would see that it even difficult for you to reach and what number of this might be so but it is pick you and for each image which could do not less have been provided to the correction number into the number is signed by the IRA as self under and fashion the idea no which number is which for life tried to find out but not so to find out whether this is a human judgement of this is machines judgement risers up the 1st of the year if you look at this this could be a 5 4 9 so that might be people write 5 like this that might possibly people who might not be so these hours situations value of the don't have any chance to determine whether it is a 5 1 9 in most other cases he the machine doesn't have any Shandeen chaos because because even human humans would not be able to do this case correctly so not having a great of the point 5 per cent might be the best you can do because of the strange examples because of reference should be 0 but the bafflement of human specification next public last public for day is over 15 problem from the sold when we used to but they do machines especially when we use not a point victimage ashamed that but you teach I used a transformation into my dimensions that this really a complicated so that we can can that I can make a perfect classification even or 2 of the 3 it is down to summer if we have this day that he would produce and the Auckland occasions and just assuming that the 2 are delighted that should be of taking to shows but we could also see why airport on Thursday said definitely is correct so I use a very complicated cover and then we arrive at this justification boundaries so division which 1 is better than his and I solution is a simple solution that what do we are always want to have a complicated solution that fits the depth perfectly sold obviously we wanted something in between who are disillusioned with the which is 2 0 complicated but is complicated enough to to be able to represent systematic properties of said sold was about earlier this we have the perfect as fication a very complicated under read about the and it could be the case that it fits the Training said very well but what new new debt that it doesn't really work because it is just 3 training exiled it could look like this and then or Bahloo are because fication boundaries for some might be something like this for some reason but the troops could be that this will be a perfect fit because if we would have had more data than if it were it would have looked like this so I tell want examples of solutions to the death of complicated enough to find systematic but he saw what he would do to Edward overfitting some best technique autocrats litigation rear end and the police are randomly splits are training that into 2 top Sokol training said in the so called test said and and we use the training said to learn because I find it odd that the machine to the occasion boundaries and then used the test said which is unknown to the classified to cheque how good the classified really is so and in the you case that is the case of the violence on the training said would be very similar to the occasion performance on the test said because this was would mean that he has a fight that has found where rather information the training said because this information is also and Wednesday said that has used and the properties this her death by by road by random chance in the training said but not in the Test side and then you can use different different colours and different parameters fall for waiting in the south London talks to use it to find ways to find is a public to machines that his equally good on the training and the test said what is just based on the test is also witchetty still owned
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