Latent Semantic Indexing (11.5.2011)

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Latent Semantic Indexing (11.5.2011)
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10.5446/352 (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.
Statistics Multiplication sign Execution unit Special unitary group Theory Independence (probability theory) Information retrieval Mathematics Causality Different (Kate Ryan album) Term (mathematics) Subject indexing Query language Energy level World Wide Web Consortium Area Domain name Focus (optics) Information Computer simulation Bit Term (mathematics) System call Single-precision floating-point format Type theory Computer animation Search engine (computing) Personal digital assistant Mixed reality Website Endliche Modelltheorie Object (grammar) Library (computing) Spacetime
Consistency Cellular automaton Set (mathematics) Bit Term (mathematics) Infinity Special unitary group Area Independence (probability theory) Frequency Computer animation Term (mathematics) Profil (magazine) Information retrieval Query language Dew point Maize Game theory Series (mathematics) System identification Singuläres Integral World Wide Web Consortium
Multiplication sign Decision theory Water vapor Singular value decomposition Special unitary group Prime ideal Singular value decomposition Subject indexing Energy level Spacetime Endliche Modelltheorie Position operator Linear map World Wide Web Consortium Covering space Information management Matching (graph theory) Mereology Degree (graph theory) Subject indexing Type theory Algebra Computer animation Computer science Mathematician Data structure
Point (geometry) Suite (music) Observational study Multiplication sign Insertion loss Singular value decomposition Icosahedron Special unitary group Information retrieval Vector graphics Vector space Subject indexing Representation (politics) Maize Algebra Linear map Physical system World Wide Web Consortium Multiplication Observational study Matching (graph theory) Information Physical law Branch (computer science) Planning Transformation (genetics) Mathematics Algebra Computer animation Phase transition System programming Linearization Computer science Nichtlineares Gleichungssystem Figurate number Linear map Matrix (mathematics) Spacetime Data compression
Point (geometry) Transformation (genetics) Real number Multiplication sign Heat transfer Mereology Special unitary group Field (computer science) Number Information retrieval Mathematics Different (Kate Ryan album) Vector graphics Vector space Matrix (mathematics) Row (database) Spacetime World Wide Web Consortium Matching (graph theory) Point (geometry) Variable (mathematics) Computer animation Personal digital assistant Network topology Matrix (mathematics) Spacetime Row (database)
Point (geometry) Rectangle Building Divisor Multiplication sign Mereology Number Independence (probability theory) Medical imaging Linear independence Web service Vector space Vector graphics Set (mathematics) Electronic visual display Maize Logic gate Linear map Identity management Rhombus Social class World Wide Web Consortium Personal identification number Multiplication Scaling (geometry) Matching (graph theory) Surface Independence (probability theory) Line (geometry) Cartesian coordinate system Number Process (computing) Symmetric matrix Computer animation Vector space Telecommunication Linearization Theorem Diagonal Musical ensemble Metric system Matrix (mathematics) Square number Identity management Spacetime
Point (geometry) Code Line (geometry) Multiplication sign Execution unit Maxima and minima Special unitary group Computer icon Number Goodness of fit Linear subspace Term (mathematics) Single-precision floating-point format Vector graphics Set (mathematics) Hausdorff dimension Binary multiplier Linear map World Wide Web Consortium Theory of relativity Point (geometry) Planning Independence (probability theory) Basis <Mathematik> Plane (geometry) Single-precision floating-point format Computer animation Angle Personal digital assistant Convex hull Linear subspace Spectrum (functional analysis) Spacetime
Point (geometry) Standard deviation Multiplication sign Combinational logic Set (mathematics) Online help Special unitary group Subset Number Goodness of fit Linear subspace Bit rate Different (Kate Ryan album) Vector graphics Maize Lambda calculus World Wide Web Consortium Octahedron Uniqueness quantification Weight Point (geometry) Independence (probability theory) Basis <Mathematik> Subset Computer animation Basis <Mathematik> Linearization Theorem Quicksort Linear subspace Routing Spacetime Row (database)
Point (geometry) Web page Standard deviation Transformation (genetics) State of matter Weight Execution unit Set (mathematics) Mereology Special unitary group Goodness of fit Linear subspace Cross-correlation Different (Kate Ryan album) Uniqueness quantification Physical system World Wide Web Consortium Matching (graph theory) Information Military base Weight Uniqueness quantification Point (geometry) Physical law Moment (mathematics) Counting Basis <Mathematik> Bit Line (geometry) Transformation (genetics) System call Mathematics Arithmetic mean Wave Computer animation Angle Basis <Mathematik> Personal digital assistant Order (biology) Phase transition Theorem Musical ensemble Figurate number Matrix (mathematics) Spacetime
Point (geometry) Transformation (genetics) Code Length Multiplication sign Orthogonality Set (mathematics) Darstellungsmatrix Radon transform Special unitary group Product (business) Number Mathematics Causality Different (Kate Ryan album) Vector space Vector graphics Green's function World Wide Web Consortium Scaling (geometry) Point (geometry) Expression Length Independence (probability theory) Basis <Mathematik> Product (business) Degree (graph theory) Arithmetic mean Computer animation Vector space Angle Scalar field Normed vector space Order (biology) Routing Spectrum (functional analysis) Writing Row (database)
Length Direction (geometry) Multiplication sign Computer-generated imagery 1 (number) Special unitary group Computer icon Number Independence (probability theory) Information retrieval Medical imaging CAN bus Linear independence Term (mathematics) Different (Kate Ryan album) Vector graphics Set (mathematics) Matrix (mathematics) Moving average Hausdorff dimension Row (database) Ranking Algebra Metropolitan area network World Wide Web Consortium Matching (graph theory) Moment (mathematics) Physical law Length Independence (probability theory) Usability Basis <Mathematik> Number Computer animation Personal digital assistant Interpreter (computing) Theorem Website Diagonal Figurate number Ranking Quicksort Metric system Linear map Matrix (mathematics) Curve fitting Spacetime
Eigenvalues and eigenvectors Divisor Length Scaling (geometry) Multiplication sign Correspondence (mathematics) Real number Characteristic polynomial 1 (number) Special unitary group Computer icon Single-precision floating-point format Vector space Row (database) Ranking Position operator World Wide Web Consortium Matching (graph theory) Scaling (geometry) Eigenvalues and eigenvectors Moment (mathematics) Independence (probability theory) Basis <Mathematik> Number Word Computer animation Vector space Physicist Nichtlineares Gleichungssystem Faktorenanalyse Ranking Metric system Mathematician Square number Spectrum (functional analysis) Spacetime
Eigenvalues and eigenvectors Divisor Multiplication sign Computer-generated imagery Execution unit Singular value decomposition Special unitary group Medical imaging Mathematics Different (Kate Ryan album) Vector space Set (mathematics) Subject indexing Matrix (mathematics) Linear map World Wide Web Consortium Source code Execution unit Matching (graph theory) Scaling (geometry) Eigenvalues and eigenvectors Military base Basis <Mathematik> Mathematics Algebra Computer animation Basis <Mathematik> Universe (mathematics) Metric system Freezing
Point (geometry) Rectangle Transformation (genetics) Mathematical singularity Singular value decomposition Special unitary group Graph coloring Element (mathematics) Bit rate Singular value decomposition Vector graphics Subject indexing Matrix (mathematics) Row (database) Ranking Algebra Linear map World Wide Web Consortium Covering space Matching (graph theory) Structural load Physical law Algebra Computer animation Information retrieval Theorem Right angle Diagonal Metric system Matrix (mathematics) Spacetime Row (database)
Web page Metre Divisor Ferry Corsten Texture mapping Weight Multiplication sign Range (statistics) Singular value decomposition Bit Special unitary group Dimensional analysis Number Information retrieval Mathematics Term (mathematics) Different (Kate Ryan album) Vector graphics Row (database) Ranking Spacetime Physical system World Wide Web Consortium Shift operator Scaling (geometry) Matching (graph theory) Interior (topology) Bit Basis <Mathematik> Measurement Degree (graph theory) Subject indexing Type theory Arithmetic mean Computer animation Personal digital assistant Information retrieval Factory (trading post) Order (biology) Video game Right angle Diagonal Linear map Metric system Matrix (mathematics) Resultant Spacetime Row (database)
Point (geometry) Transformation (genetics) Ferry Corsten Weight Scaling (geometry) Mathematical singularity 1 (number) Orthogonality Distance Special unitary group Approximation Rule of inference Term (mathematics) Vector space Ranking Row (database) Right angle Summierbarkeit World Wide Web Consortium Scaling (geometry) Product (business) Process (computing) Computer animation Basis <Mathematik> Mathematical singularity Diagonal Game theory Matrix (mathematics) Spectrum (functional analysis) Spacetime
Point (geometry) Metre Transformation (genetics) Weight Scaling (geometry) Multiplication sign Orthogonality Special unitary group Computer icon Number Cross-correlation Term (mathematics) Different (Kate Ryan album) Matrix (mathematics) Position operator World Wide Web Consortium Area Information management Electronic data interchange Weight Sound effect Basis <Mathematik> Cartesian coordinate system Measurement Product (business) Degree (graph theory) Type theory Word Computer animation Basis <Mathematik> Principal component analysis Information retrieval Bounded variation Spacetime
Addition Weight View (database) Mathematical singularity Control flow Mass Mereology Special unitary group Approximation Perspective (visual) Food energy Number Mathematics Vector space Row (database) Ranking Spacetime Noise Right angle Summierbarkeit World Wide Web Consortium Noise (electronics) Shift operator Matching (graph theory) Information Weight System call Approximation Product (business) Computer animation Basis <Mathematik> Personal digital assistant Mathematical singularity Website Diagonal Linear subspace Metric system Matrix (mathematics) Spectrum (functional analysis) Spacetime
Point (geometry) Frobenius method Computer file Multiplication sign Distance Approximation Special unitary group Food energy Goodness of fit Different (Kate Ryan album) Helmholtz decomposition Matrix (mathematics) Ranking Endliche Modelltheorie Error message World Wide Web Consortium Personal identification number Matching (graph theory) Measurement Distance Uniform boundedness principle Arithmetic mean Error message Computer animation Personal digital assistant Ranking Metric system Matrix (mathematics)
Point (geometry) Ferry Corsten 1 (number) Drop (liquid) Distance Mereology Approximation Special unitary group Food energy Dimensional analysis Computer icon Neuroinformatik Singular value decomposition Different (Kate Ryan album) Ranking Error message Rhombus Capability Maturity Model World Wide Web Consortium Matching (graph theory) Information Projective plane Data storage device Maxima and minima Fourier transform Approximation Computer animation Vector space Ring (mathematics) Personal digital assistant Theorem Ranking Coefficient Mathematical optimization Matrix (mathematics) Spacetime
Point (geometry) Eigenvalues and eigenvectors Multiplication sign Expandierender Graph Singular value decomposition Mereology Special unitary group Approximation Uniformer Raum Helmholtz decomposition Singular value decomposition Matrix (mathematics) Ranking Row (database) Identity management World Wide Web Consortium Matching (graph theory) Information Eigenvalues and eigenvectors Projective plane Moment (mathematics) Type theory Curvature Computer animation Information retrieval Theorem Video game Metric system Matrix (mathematics) Resultant
Point (geometry) Context awareness Divisor Multiplication sign Gene cluster Singular value decomposition Approximation Special unitary group Cross-correlation Singular value decomposition Term (mathematics) Different (Kate Ryan album) Helmholtz decomposition Subject indexing Ranking Noise Algebra Proxy server Metropolitan area network Linear map Rhombus World Wide Web Consortium Noise (electronics) Matching (graph theory) Information Key (cryptography) Dimensional analysis Line (geometry) Term (mathematics) Rectangle Approximation Algebra Computer animation Personal digital assistant Network topology Spacetime Directed graph
Algorithm INTEGRAL Mathematical singularity Combinational logic Maxima and minima Singular value decomposition Nonlinear system Term (mathematics) Different (Kate Ryan album) Electronic meeting system Aerodynamics Integral equation Position operator Social class Window Algorithm Differential (mechanical device) INTEGRAL Algebraic number Theory Dimensional analysis Term (mathematics) Algebra Computer animation Basis <Mathematik> Computer cluster System programming Partial derivative Nichtlineares Gleichungssystem Ideal (ethics) Matrix (mathematics) Spacetime
Implementation Context awareness Personal identification number Differential (mechanical device) INTEGRAL Multiplication sign Mathematical singularity Similarity (geometry) Ordinary differential equation Coordinate system Food energy Arm Dimensional analysis Knapsack problem Neuroinformatik Nonlinear system Arithmetic mean Term (mathematics) Different (Kate Ryan album) Aerodynamics Sinc function Algorithm Differential (mechanical device) INTEGRAL Algebraic number Physical law Dimensional analysis Theory Coma Berenices Term (mathematics) Cartesian coordinate system Knapsack problem Convolution Arithmetic mean Stochastic Algebra Computer animation Doubling the cube Basis <Mathematik> Intrusion detection system System programming Convex hull Nichtlineares Gleichungssystem Ideal (ethics) Spacetime Geometry
Context awareness MUD Scaling (geometry) Equals sign Mathematical singularity Maxima and minima Coordinate system Mereology Neuroinformatik Information retrieval Nonlinear system Term (mathematics) Different (Kate Ryan album) Singular value decomposition Operator (mathematics) Spacetime Row (database) Aerodynamics Nichtlineares Gleichungssystem Sinc function World Wide Web Consortium Covering space Metropolitan area network Hamiltonian (quantum mechanics) Differential (mechanical device) INTEGRAL Information Algebraic number Dimensional analysis Theory Coma Berenices Term (mathematics) Knapsack problem Word Arithmetic mean Root Algebra Computer animation Basis <Mathematik> System programming Faktorenanalyse Nichtlineares Gleichungssystem Metric system Matrix (mathematics) Square number Spacetime
Divisor Scaling (geometry) Mathematical singularity Maxima and minima Singular value decomposition Coordinate system Information retrieval Root Term (mathematics) Helmholtz decomposition Oval Single-precision floating-point format Matrix (mathematics) Spacetime Row (database) Information World Wide Web Consortium Matching (graph theory) Scaling (geometry) Dimensional analysis Coordinate system Term (mathematics) Flow separation Type theory Stochastic differential equation Root Computer animation Basis <Mathematik> Faktorenanalyse Ranking Metric system Routing Matrix (mathematics) Square number Abstraction
Transformation (genetics) Scaling (geometry) Mathematical singularity Singular value decomposition Information retrieval Causality Term (mathematics) Vector space Vector graphics Query language Spacetime Row (database) Process (computing) World Wide Web Consortium Matching (graph theory) Term (mathematics) Stochastic differential equation Root Computer animation Vector space Faktorenanalyse Musical ensemble Matrix (mathematics) Square number Row (database) Spacetime
Group action Transformation (genetics) Insertion loss Heat transfer Inverse element Mereology Theory Area Prime ideal Mathematics Query language Process (computing) Capability Maturity Model Physical system Area Theory Complete metric space Cartesian coordinate system Measurement Similarity (geometry) Computer animation Partial derivative Nichtlineares Gleichungssystem Right angle Spacetime
Convolution Email Context awareness State of matter Equals sign Mountain pass Mathematical singularity Singular value decomposition Special unitary group Area Neuroinformatik Information retrieval Vector space Electronic meeting system Query language Process (computing) Aerodynamics Sinc function Metropolitan area network Algorithm Differential (mechanical device) Algebraic number Term (mathematics) Knapsack problem Commutative algebra Computer cluster System programming Nichtlineares Gleichungssystem Personal area network Convex hull Ideal (ethics) Geometry MUD Line (geometry) Maxima and minima Coordinate system Vector graphics Ideal (ethics) Spacetime Linear map World Wide Web Consortium Hamiltonian (quantum mechanics) Information management INTEGRAL Dimensional analysis Theory Core dump Cartesian coordinate system Similarity (geometry) Punched card Algebra Stochastic Computer animation Basis <Mathematik> Synchronization Partial derivative
Point (geometry) Group action Scaling (geometry) Mathematical singularity 3 (number) Singular value decomposition Area Number Information retrieval Term (mathematics) Vector space Vector graphics Query language Matrix (mathematics) Spacetime Row (database) Process (computing) Maize Data structure World Wide Web Consortium Area Theory Total S.A. Term (mathematics) Limit (category theory) Computer graphics (computer science) Similarity (geometry) Arithmetic mean Root Computer animation Compilation album Faktorenanalyse Nichtlineares Gleichungssystem Matrix (mathematics) Square number
Point (geometry) Context awareness Eigenvalues and eigenvectors Multiplication sign Maxima and minima Similarity (geometry) Online help Mass Shape (magazine) Mereology Special unitary group Cross-correlation Term (mathematics) Different (Kate Ryan album) Office suite Position operator World Wide Web Consortium Area Execution unit Distribution (mathematics) Matching (graph theory) Eigenvalues and eigenvectors Computer graphics (computer science) Process (computing) Computer animation Mathematical singularity 9 (number) Capability Maturity Model Spacetime
Point (geometry) Classical physics Context awareness Group action Functional (mathematics) Eigenvalues and eigenvectors Multiplication sign Control flow Special unitary group Semantics (computer science) Term (mathematics) Row (database) Software testing Endliche Modelltheorie Message passing Metropolitan area network World Wide Web Consortium Information management Algorithm Matching (graph theory) Information Structural load Electronic program guide Water vapor Term (mathematics) Mathematics Category of being Subject indexing Message passing Computer animation Physicist Information retrieval Compilation album Resultant Spacetime
Point (geometry) View (database) Decision theory Multiplication sign Direction (geometry) Maxima and minima Online help Singular value decomposition Special unitary group Number Data model Roundness (object) Labour Party (Malta) Different (Kate Ryan album) Term (mathematics) Bus (computing) Matrix (mathematics) Representation (politics) Ranking Position operator World Wide Web Consortium Addition View (database) Weight Bit Similarity (geometry) Degree (graph theory) Computer animation Software Angle Different (Kate Ryan album) Video game Ranking Game theory Representation (politics) Thermal conductivity Row (database)
Point (geometry) Presentation of a group Information overload Multiplication sign Real number Correspondence (mathematics) Mereology Special unitary group Number Arithmetic mean Term (mathematics) Matrix (mathematics) Representation (politics) Multiplication Position operator World Wide Web Consortium View (database) Weight Total S.A. Line (geometry) Term (mathematics) Subject indexing Wave Error message Computer animation Software Order (biology) Different (Kate Ryan album) Arithmetic progression Matrix (mathematics) Row (database)
Laptop Algorithm Gradient Multiplication sign Singular value decomposition Approximation Intermediate value theorem Field (computer science) 2 (number) Neuroinformatik Mathematics Read-only memory Term (mathematics) Semiconductor memory Helmholtz decomposition Bubble memory Operator (mathematics) Matrix (mathematics) Representation (politics) Software testing Gradient descent Position operator Physical system World Wide Web Consortium View (database) Projective plane Sampling (statistics) Physicalism Total S.A. Line (geometry) Term (mathematics) Approximation Subset Process (computing) Computer animation Software Order (biology) Different (Kate Ryan album) MiniDisc Quicksort Matrix (mathematics) Near-ring Resultant
Point (geometry) Group action 1 (number) Intermediate value theorem Computer icon Dimensional analysis Number Neuroinformatik Information retrieval Goodness of fit Type theory Different (Kate Ryan album) Matrix (mathematics) Hausdorff dimension Software testing Noise Metropolitan area network Physical system World Wide Web Consortium Area Noise (electronics) World Wide Web Consortium Physical law Dimensional analysis System call Approximation Number Arithmetic mean Word Computer animation Personal digital assistant Function (mathematics) Network topology Order (biology) Software testing Right angle Landau theory Thermal conductivity Bounded variation Resultant
Multiplication sign Parameter (computer programming) Special unitary group Event horizon Formal language Information retrieval Computational physics Different (Kate Ryan album) Energy level Maize Endliche Modelltheorie Scale (map) Information Structural load Physical law Dimensional analysis Coma Berenices Basis <Mathematik> Line (geometry) Cartesian coordinate system Symbol table Demoscene Performance appraisal Population density Arithmetic mean Computer animation Estimation Personal digital assistant Web service Information retrieval Network topology Different (Kate Ryan album) Summierbarkeit Heuristic Matrix (mathematics) Task (computing) Resultant Spacetime
Adventure game Menu (computing) Singular value decomposition Group action Special unitary group Formal language Information retrieval Performance appraisal Computer animation Contrast (vision) Endliche Modelltheorie Quicksort Matrix (mathematics) World Wide Web Consortium Family Scalable Coherent Interface
Some of don't have again welcome to the new simulator of information retrieve and Web search engines and they want to talk a little bit about what we at what can we do to them to the term space where the documents are represented to get them that the feeling of what the document actually describing what the topic of the document was the main purpose of the document and and before the domain technique is called late amantadine mixing and this is what we will be doing today and as a motivation time which was assuming that many of the access in the term space citing about this 2 terms mean exactly the same and document on different access could actually be about the the same type of strike the same thing and this is 1 of the notion that became very well as the well that she was in the 19th so it was not very early fall for information or to tough but in in but that she was very clear that some bubbles wanted was not really and that the focus of whom on all on the single terms but rather the focus on top of what topics off things related to the case and what I need to do that is actually you need to relate single terms each individual terms to some top and you need a need to do to relate the collections of the documents to the top and then off calls on the IRA site you a need to related data to top up a we we know from from but this search and statistics that most theories about 2 to 3 Keywords that up to use the phrase of causes much more difficult to get a topic from 3 individual work than from a whole Texas where we get many whose what the textbook so of this different topics that the different techniques and we want to go into some of them up to see how can we do better so the and that even profits when dealing with topics is is basically we did where the easiest now like and think about the library of an exam Maria on Friday of 300 before Christel something like that but based on the big venture out library that contained so many believe that it took to to the club after the destruction of the library took until the 20th century until we had a single library that again about as many Williams and a library of sounds how did they manage that had been not where each local role as it was in those turned out work with a will located called what was that about and actually during this time that the 1st idea that you need people know about the stuff in the library in all like library who had a first classification system of this is history the SAS and the with this is that I'm a book about Apotek Charil's thought mathematics of something even on a very simple top level just describing the area where the 2 of them were actually something that was investigated and used before crisis in the that when I believe what they are basically David is that they looked Sir some of strolls and and and found out what will be the main topic were library and they separated the growth from each other and the way that they put the object of the end of the mathematics here and there some guy and will just knows what what going on unit and he identifies the topix and assigned document new incoming document which topic in now and then you go like OK if it's about politics at
And document about all the Nike and just assigned a wait for a negative because and the mobile politics but it goes to get the best of the game so something like that maybe the politics called for it a little bit higher but also the implications and the and the and the and the kind of manually assigned and and Rome than you can use the British based retrieval like we did based on these on these value based on the longest public schools And then you have to are find a method to transform the series over turns into the topic of the many in the faces today like like of prostitutes Search intellect where just 6 some books saying no I'm interested in politics so I'm interested biology and and set of basic of the brought topic found but if you just do it by the terms themselves can be pretty difficult because they are likely to face general about what the looking for looking for an animal looking for a new car depends on many things and how often these terms are used and maybe the profile of the person posing the period Wallabies audience that could lead to getting the topic but of course this method really depends on how good the Libor and the work and and it depends on home and documents to so signing the score in the rather consistent with to a few document might work out actually Doing it for millions of billions of books tedious you will get inconsistencies and the death of something that something And that is something you don't want and this is why there should be across now that we cell basically
Once you have found out about found out of the water they document is about what was good about you can do do that rather rather easy but that are making the telescope topics centred document wondering what human indexing that is really something that we had to look into it is the the and that he is
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So what a collection trying victors but if I'd have and M times and match and the respective singular value decomposition than if I'd look at the the map tricks times the transposed matches The end came by re The different majesty psychic after the decomposition such that the Beeston go together But Since there are also Mama their anger is perpendicular and the scale of public 0 So everything perpendicular is 0 and the Rose that corresponds to write column in the central become 1 So actually this is the identity matches And off by discussed this away to be identity Ikon look at what happened here for basically since this is a badge lamented the transposed of the Maddox's exactly the same as a metrics itself and so this is the squalor of the match and the squalor of the dead were metrics dinner like a take every grow and every column assesses quail for the entries of the regional again so this is all that happens but still a diet and looking at you And this Degen match by 1 can show that the columns of you are the eigenvectors It off 18 times chance for the can't to post match the and The metric Cimillo just contains the corresponding like the UK and so this actually 8 decomposition into I'd values and eigenvectors Yes and if you do as a different way around if you take the transposed Maddox time for the Origin Match expand of peace rose are the eigenvectors and Esquel still contains But we just different than the also Momo the column off moment useful on the Flat the result and the and the identity of the with a collection to of eigenvectors said it something as they very a similar to eigenvectors I'm and a singular values just very similar to the UK But
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Everybody still remember long term document magic All basically of all the terms of the and so on and I of all the documents of the collection and so on and in the match exceeding note course in some terms of 1st in some document of Kent The term document much and This is usually a rectangular metric depending where you more document was small real more terms with a small document collection rectangular bomb and if you apply the sinking of the decomposition then you create some intermediate engines which of those with the highest singular values That could be seen as topics basically what it does is it shows correlation in the terms which If somebody topic of some some some terms in the origins of some of the most based their way soakers in the same context as some of the tree the of occurrence of the terms correlated That can be exchanged suspect so probably cinema This correlation will be shown by the singular valued composition because it gives a large senior value to some exodus along the line of correlation as we just soul with the agent and I'd Excel Kent and it gives a very smoke Becta or for along to you to the follow on but it has caught the basic IOMI does not at much information to discriminating between 2 documents that just differ in cinemas is impossible with respect for the new because discuss the difference between the 2 way the case of this we doing we are kind of like bomb But Put together synonymous with a handful of and and if terms that about the same term so basically in the term space her on the same access to Duberry of smokers in different context It is not possible to just over 1 excess showing a correlation because there is not It would be rather like in Why should be way of the points here Where Linear said that approximation was 1 X is the make any sensible enough if these different proxy of this different Clusters and you try to figure out how to discriminate those points with a singer access adjustable work you need to access to distinguish between this is what we call the the police and the request Uk set up by the man described the diamond having slow singular values and would like adjusted during approximation it removes the noise from the data so it actually does not losing 4 major about the term document but at the same time it makes term document metric smaller more compact and remove some noise that comes through the usage of synonyms for different context and APEC so you can show that a key factor in terms of quality and the original
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I have nothing to do with the way this is the kind of information that taking up and where these terms that are underlined are basically the terms of the Her for political party We can also do it all on my own on the cover of means that they don't add much information in a way of cutting the mob before the end of making the being singular value decomposition which very expensive operation on a huge metrics and then cutting the mob after words doesn't make much difference only after computer more of So just focusing on the interesting terms and higher they are crew which was picked to each other in the documents and the every every book is a document of that is the interesting part that we want to focus on Good
But well had we met the document and terms and until late stage but we had this idea of the scale wrangle rank Kate abstract timation and what we do is a week on of get rid of the scaling back of of the single ability I'm so we split up this match eggs and put half ordered into the you and the other half into the
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But we can computed By she was a newer The Metrix transforming the terms on this Coleman to get the origin of term back up again And Niall If we are given the term vector and we know the match you We just can't arrived A private acute crime By inverting the match fixed Phuket crime and multiplying from the left and on 2 C and
This is the new damaged some what we can do this kind of like we have this week they use new book and we solve the facing the suspect to Hugh prime we might declined by the transfer those of far formal the awful MoMA actually pictures of the inverse is the We might apply from the left And basically end up with the rest of the senior value to completion which began my ply by the rest If you want to get the inverse of the of Bajan emetics just take the group reciprocal values of the of the deadline for the UK and so if you have an entry 80 in the dead of after multiplied 1 divided by 80 to get 1 of Kent So if I've Metrix the sea and along and the Rose here and that want the inverse off that the worst is just 1 divided by 1 divided by the And so on Again with the US the UK and this will give me the and matter so I'd take this inverse maturate and multiplied again from the right side of Kent and then and The transformation of The back to queue to get Hugh prime And these are all part of an hour And no you pay prime Another trend and and all the singular acute compositional the recipe for soap
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Well it would take another example of here we have the documents from the area of and new groups actually from used postings in the area of computer graphics selfless but the Hawking and religious texts And we have the terms here so like about 12 thousand terms in total earning in the document published removed and we just take the documents which can see that document term Matrics in doesn't seem to have good structure that some Obviously Some document containing almost all terms the same year And this goes for every area of also and and OR talking about documents that contains a lot of terms all the different and and but there are some document that are based Boston terms for example document here on the few points for the different terms and whenever there is a point it just means that the and of this term is contained in this document document numbers the of 3 And as you can see we basically see nothing at all like a mean this term document that metric Zameen very much of this week re look at at the different documents and the different
Terms taken from some well basically taken from them The other documents so we want to see what happens in computer graphics will find that many of the computer graphics document what kind of similar and the Spice Of the other parts shows that that kind of December With the other documents still come to consider in the for example here the terms of the computer graphics with the terms of the British and document it's rather also not to too much point concerning the hockey document place they seem to be very similar to each other the loss through the and of course we can also see that there some kind of correlation because this area seems to be very crowded and the area Ovadia seems to be very spouse so maybe shifting the matches would be a good idea shifting the basic was exactly what we did and if we take the
3 eigenvectors him The blatant to them and shape time we can see the difference documents up last In different puff office space a pick Classified them according to where they came from the can see that the singular Babycham position The good job Indiscriminating between we can also see that are So there are some help you documents Trying to be computer graphics of talking about the context as computer graphics documents usually to have put my point the finger on on 1 day she said but that still there are some that have interesting on or off the book's context but for the masses of the distribution seems to work quite well And unlike the 12 thousand will unlike the 12th thousand terms that before
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Good yet another example of of the right erotic collection 1 of the classical collections of for testing and load information retrieval algorithms which basically consists of the 20 thousand Musuem messages on taking from from 19 70 87 the talks results and being for the terms taxes and Dragon who was the president of the point of using the late semantic indexing time is fit for the Test Oregan strongly and tax hike are so all Pizzi the this is the a perfect match because reckons that something about Texas The 2nd 1 Rostenkowski says says with big you as text high about it but all credit for point and so this is document where not ready and said something about the taxes but it contains it talks about reckons and need principle And surprise really interesting because it does talk about Texas but it does not talk about reckons It does however have a talk about White House Whitehouse's it or post tax increases unnecessary and you can see this is the 3rd want to the physicist Search match of 20 Feltham's but you definitely contained Sommeil information about taxes and about right Which we could not see from the From from the original term but the match was over and that kind of puts White House and breaking into the the same category They are all open as the message that exchange the terms White House break And for every man Message for for for many messages which has oregano this all that there is a simpler message Saying the White House does this all too apparent And this is kind of like the the beauty of the Lake semantic and index does not directly from that of the term Whether they occur on not like of actress based model like William retrieval like probabilistic between But it tries to forget about what the context of terms on and groups together for those of documents containing the same Walker in the same context while the at the same time making the damage in that he of all the much smaller and and This fund and function across Intel's quality and engine It actually is good to use because the space is a small and what more can you expect to get
And also to give you a different view on Monday side can be seen in a different way this all next the to bomb so on duty on the stood at the side of very easy to see it from a new angle he of just laid back critics and bits and let you up and take you to the beauty of the side again but it was different with the troops to be your network for patient who funeral self new work He's 1 game that describes similar in a if there are no good Like this 1 and connexions between notes about the presentation with with no notes and so on and if you have Matrix that we have with the conduct and Matrix and their risk to value the composition of the side that we have read and heard of columns and each entry can be seen as the ranks of the connexions between the rope and column for Fox or the 2nd round and the 3rd column are connected with the degree of 7 in the sound and the higher the number of those from the connexion so and because in the Travis Matrixes a representation yet for each where with And for each because we also have a note of Assembly bread and the connexion between each row and column knowledge and assigned a wage to each connexion that corresponds to the weight and the respect made sauntered world we have found trials by connected to and looks for a confusing so what can we do Hawkins as by bus in the Mehdi composition help
So in medical decision essentially introduces a New Labour into this network creating to addition and notes are which a used to connect the rose to columns so from now on the roads and cars are not connected directly by just not anywhere but not or connexions on direct through this into intermediate laity so again his like some Matrix and if we do a singer medical position we get paid he could you time as times the and the late that it turned out by Crestmead these on view it as the best regatta from the same date from position so and now we can do the same connexion trick to get in the way of his life now the 1st role is connected to the 1st topic so I remember the columns and new you on topics P Troops and also the roles of the on topics The American seeing that the 1st role is connected to the 1st typikka with a degree of off point to and the 1st public is connected to the 1st column He and his degree of point fall so and As goes directly into the intermediate layout in terms of weight so on this intermediate not are also get the weight of 95 point for the 2nd note gets getaway of 0 at 1 point said So and now we can Wigan on reconstruct all originated from this representation
Progressed of prolific solver and He a look at the entry in the 2nd row and the 1st time the world 1st column the 5 feet 2nd Royal 1st first-come than the order to the connexion between them and the original picture of 5 FIA but not with his immediately that we can reconstruct this 5 from the topic reputation so on 2 it is connected to bowl wrote to is connected to the 1st public with a weight of point by this collection and to cut and won the connexion goes this way and are so that this can connexion along with a 2nd topic going this way now week and we can just the reconstruct origin value by just a them following both part through the network and any not all when the waves with kind sulphoxide on the bomb this year we have 0 points 5 times the weight of the 1st public richest 25 9 points from 4 times the connexion strength to the respective column which is point that and we get it are due to the way it's corresponding to the way off for the 2nd public knowledge this point lead To which I was 1 point 7 times weight on his mind this point have the total we get 5 points away to minus point 3 5 7 and ignoring running at this is about the size is about you would expect the by introducing a new low in the network weekend we can avoid all direct connexions and simplified on the index and the Greek islands and real was and it so if you think of a very large network with every many roles and Collins There would be a number of columns my NYTimes number froze connexions in the region the presentation and usually if introduced this Somali immediately after all with a lot less connexions overload on and we have in the region representations so that this This is representation with intermediate layaway able to find systematic correspondents East between Real's and Collins and into across public's sell them look at the time but when Matrix on the non example it might look like this man's with many nearest in it and that might have this club
Strong line means that there is a strong connexion In this example found so 1 documents contained the 2nd term While documents that are connected to this term in the new network of the CIA the sound 3 documents connected to the time and again weekend we can introduce intermediate their presentation with the ability medical position
And here we can see the topics every year 3 constructed Holland little singer medical position with a total of all 3 intermediate topics and it's a crack confusing Matrix but as it seemed if we did not Alpine of the topics sexy those topics which are really important so that this is only weight off you point 5 about and is much less and point and and the other 2 topics wickets simplifying this new network and this is the system that what I'm not tries to try to on more clear picture of how the connexions are between terms and documents so that the 1st time and that sample does look really really more simpler than what was on the region representations but if you think of really not stand up and make this is an intermediate layout with only connexions with and between terms and and immediately and and documents and and immediately that much less connexions than you would have been enough to hold network by every time is connected to every day
Oh and it's a different way to think that some null began on I would go near found another question is how we can compute the as the sort on received some example and and example the issues some Matrix a competition and ask you to trust us that this will be the right decomposition and that is how to be computers and we weren't going to be tested the lecture because this is really all mathematics and abundant literature hot to compute as we do and what I did wrote the probity it has found In general you could say that this computing the its computer computer computer near expensive so it is that in the operation need you off in income seconds for really not stop document collections it can take hours of days of some of the writers collection of these 20 thousand documented the Physics on the computing the as he died on a notebook computer takes about 19 seconds so and not thinking about all document collections containing millions of the billions of documents and the testing the is is UJT ask and requires Massively Parallel Computation on its it's not never really do and 1 problem is found that many traditional under rhythms for computing the deal that have been developed in the field of mathematics require that followed that the time dopamine Matrix an almighty you as the and all intermediate value to be kept in May and memory to be to be found house so of course you will not be able to apply order job document Matrix the 1st bonding to the worldwide web contributed from the main memory even if you have very big computer because that that it is many many solve gigabytes of them you would need and tackled in computer which could do with the efficiently So and because of this on the are some specialized was available at the time able to to blow summit immediate results not disc with all the adults in the UK on time penalties and how and that it seems still to be researched topic on how to compute the line on the document collection so with looking into the literature and it is up to now there has been any researchers who published their work pound fund as by using more than 1 million documents maybe some guys who will follow the do this efficiently but obviously when no finding out how these different difficult things work than it it is a becomes a trade secrets and become ponies and not interested in publishing called into a lack of competition with very difficult but somehow or you can manage it usually cries of hot and some of tricks may be distributed by picture and no idea So in recent research that means some ideas on how to how to use some some cuts and that the nation on tourism to come up with and approximation off the of the as he died on sold them based on some great into sent of imitation techniques under quite simple to with 2 on to implement currently but it said it research project and open the way to go
A Case found that when you want to compute days but be use some kind of a guy read that is all that many many on my Rossi can download on the Web or use his to with such as method on the bill with the the way from most Document collection of medium size of exercise was the Kate hominy I tell picks order engines should be should be take the and likes of that we had to do it to them engines and the and the and the religions and on the Web expect some of its freedom and on but we have to find out there the correct number so and usually found that the fate of involved on a free kick to many demands and then of course not but we have a better approximation of homage No 10 recommend Matrix that we have not demand we have to to compute on so computation is getting more noise and and of calls for months on the grid in the tree the when are the effect of of contending that the conduct of and Matrix into smaller ones that can be achieved so too many commented that on the other hand too few them engines are thought that aren't because we simply don't pulled topics of cost of iconic and computer as the deal large document collections and people I though the most significant topic but the Emery this would be would be a topic where we lasted tool to launch groups of documents that we won't be able to want to differentiate between the a smaller smaller topic variations in the collection so essentially using too few them engines are not want away with but also to a full man's so people with simply not be able to find with the looking for because they are not able to defend to differentiate between different documents so the momentum of that you demands also bad The finding the right here down usually Wolves just trying on different values And of course depends on all specialized the document collection is so it is that many many different area in the collection for some collection about owners of all different area in in science works on both the new would lead with the 2 law topics that this is because of the collection bombs that contains almost same document and not not many many different topics as more like a good the could be better so you just have to to try out usually found and and where maiden made and experiment where the used to the different different K case on the excess
And Dame concept at some kind of synonyms test vetted their checked Powell many system and them have correctly being group into the same public bombs and higher many words that have different meanings has been put into different topics at that point out that their collection using an intermediate value for cases of about 200 300 you that the best results of began to smile number of demand that such a large number of dimensions also bed on finding the right 1 usually is difficult so that are some some values from experience so sold some people say they are appalled 200 500 solvent public is a good value for Kate
But you need to find out his collective What are the pros and cons of side so we are seeing frostbite usually that the tree quality is quite as it seems with the White House and some no other to method is scenes of law would be a good to retrieve this document but has identified all of that wise White House and red essentially the same as collect so you are able to retrieve rather than documents that accounted for with any other men that definitely a big pro so on their own or also is that the design of the rest on the very strong mathematical foundations so we have seen the other methods where many heuristics reduced the thing think of the violin and the 3rd for you to make some very strange assumptions and in the end it just works but nobody knows why bound for you can explain why you expected as a way but also So from another pro-Iraq as eyes a technique is that you can apply designed to other other kind of on problems not only from the major trio but you can also use it on with the disease in the to in the next week you can also apply to are finding Simenon movies for example so if you try to find out what what movies are similar to ramp and but as I'd techniques you are able to find the house without asking asking people what a symbol of the city tour so that is why this is just a good thing in general selected from its benefits and many different feuds so it's also a good thing too used in information The now also sums on this but it is only as if he or pictures and that some of the by and so that they can turn engines to get such a very difficult to to understand You know they have no idea what he did demand means but you can be sure that documents on times that have similar coordinate in the latest based on cement can that's all I know but you can't say that the 1st excess means Texas where the something I've had no idea of on another Kaunas found that committees competition requirements are really really high as said of can easily take days all week computed iFilm medium sized document collection and ideas and his thing you won't do in a day by day basis 3 all this have to do is off line and definitely not a good time And that on the right case quite how to find just the try out far different K use some Exxon decrease in cheque whether the results are accepted for your application so at this information retriever but we can only provide you with some method some ideas of how to use the NYT this method halted human the parameters Owais dependent on the collection of the problem you have to solve Indeed this the will be done in the next week because of the time the interesting and and the next week we will talk about language model is also load of Thailand last model on all to do with a major review of how to search for and documents and we come to the question What rather than 3 is so railways said that events yet reunited when you see it as a day something really about rather than send them different levels of what relevance really is Andrew would take a look at this and finally below discuss Fault 1 can only evaluate hold but and information extremists and really is so with this ideas we will be able to compel some space between the and by an independent review and see what what works spent on most collection of that it for 2 days ago much weight and