Document Sample

Chapter 2 Modeling Hsin-Hsi Chen Department of Computer Science and Information Engineering National Taiwan University Hsin-Hsi Chen 1 Indexing Hsin-Hsi Chen 2 Indexing • indexing: assign identifiers to text items. • assign: manual vs. automatic indexing • identifiers: – objective vs. nonobjective text identifiers cataloging rules define, e.g., author names, publisher names, dates of publications, … – controlled vs. uncontrolled vocabularies instruction manuals, terminological schedules, … – single-term vs. term phrase Hsin-Hsi Chen 3 Two Issues • Issue 1: indexing exhaustivity – exhaustive: assign a large number of terms – nonexhaustive • Issue 2: term specificity – broad terms (generic) cannot distinguish relevant from nonrelevant items – narrow terms (specific) retrieve relatively fewer items, but most of them are relevant Hsin-Hsi Chen 4 Parameters of retrieval effectiveness • Recall Number of relevant items retrieved R Total number of relevant items in collection • Precision Number of relevant items retrieved P Total number of items retrieved • Goal high recall and high precision Hsin-Hsi Chen 5 Retrieved b a Part Nonrelevant Relevant Items Items c d a a Recall Precision a +d a+b Hsin-Hsi Chen 6 A Joint Measure • F-score ( 1) P R 2 F PR 2 – is a parameter that encode the importance of recall and procedure. – =1: equal weight – >1: precision is more important – <1: recall is more important Hsin-Hsi Chen 7 Choices of Recall and Precision • Both recall and precision vary from 0 to 1. • In principle, the average user wants to achieve both high recall and high precision. • In practice, a compromise must be reached because simultaneously optimizing recall and precision is not normally achievable. Hsin-Hsi Chen 8 Choices of Recall and Precision (Continued) • Particular choices of indexing and search policies have produced variations in performance ranging from 0.8 precision and 0.2 recall to 0.1 precision and 0.8 recall. • In many circumstance, both the recall and the precision varying between 0.5 and 0.6 are more satisfactory for the average users. Hsin-Hsi Chen 9 Term-Frequency Consideration • Function words – for example, "and", "or", "of", "but", … – the frequencies of these words are high in all texts • Content words – words that actually relate to document content – varying frequencies in the different texts of a collect – indicate term importance for content Hsin-Hsi Chen 10 A Frequency-Based Indexing Method • Eliminate common function words from the document texts by consulting a special dictionary, or stop list, containing a list of high frequency function words. • Compute the term frequency tfij for all remaining terms Tj in each document Di, specifying the number of occurrences of Tj in Di. • Choose a threshold frequency T, and assign to each document Di all term Tj for which tfij > T. Hsin-Hsi Chen 11 Discussions • high-frequency terms favor recall • high precision the ability to distinguish individual documents from each other • high-frequency terms good for precision when its term frequency is not equally high in all documents. Hsin-Hsi Chen 12 Inverse Document Frequency • Inverse Document Frequency (IDF) for term Tj N idf j log df j where dfj (document frequency of term Tj) is number of documents in which Tj occurs. – fulfil both the recall and the precision – occur frequently in individual documents but rarely in the remainder of the collection Hsin-Hsi Chen 13 New Term Importance Indicator • weight wij of a term Tj in a document ti N wij tf ij log df j • Eliminating common function words • Computing the value of wij for each term Tj in each document Di • Assigning to the documents of a collection all terms with sufficiently high (tf x idf) factors Hsin-Hsi Chen 14 Term-discrimination Value • Useful index terms distinguish the documents of a collection from each other • Document Space – two documents are assigned very similar term sets, when the corresponding points in document configuration appear close together – when a high-frequency term without discrimination is assigned, it will increase the document space density Hsin-Hsi Chen 15 A Virtual Document Space Original State After Assignment of After Assignment of good discriminator poor discriminator Hsin-Hsi Chen 16 Good Term Assignment • When a term is assigned to the documents of a collection, the few items to which the term is assigned will be distinguished from the rest of the collection. • This should increase the average distance between the items in the collection and hence produce a document space less dense than before. Hsin-Hsi Chen 17 Poor Term Assignment • A high frequency term is assigned that does not discriminate between the items of a collection. • Its assignment will render the document more similar. • This is reflected in an increase in document space density. Hsin-Hsi Chen 18 Term Discrimination Value • definition dvj = Q - Qj where Q and Qj are space densities before and after the assignments of term Tj. 1 N N Q sim( Di , Dk ) N ( N 1) i 1 k 1 ik • dvj>0, Tj is a good term; dvj<0, Tj is a poor term. Hsin-Hsi Chen 19 Variations of Term-Discrimination Value with Document Frequency Thesaurus Phrase transformation transformation Document Frequency N Low frequency Medium frequency High frequency dvj=0 dvj>0 dvj<0 Hsin-Hsi Chen 20 Another Term Weighting • wij = tfij x dvj N • compared with wij tf ij log df j N – : decrease steadily with increasing document df j frequency – dvj: increase from zero to positive as the document frequency of the term increase, decrease shapely as the document frequency becomes still larger. Hsin-Hsi Chen 21 Term Relationships in Indexing • Single-term indexing – Single terms are often ambiguous. – Many single terms are either too specific or too broad to be useful. • Complex text identifiers – subject experts and trained indexers – linguistic analysis algorithms, e.g., NP chunker – term-grouping or term clustering methods Hsin-Hsi Chen 22 Term Classification (Clustering) T 1 T 2 T 3 Tt D1 d 11 d 12 d 1t D 2 d 21 d 22 d 2 t Dn dn1 dn 2 dnt Hsin-Hsi Chen 23 Term Classification (Clustering) • Column part Group terms whose corresponding column representation reveal similar assignments to the documents of the collection. • Row part Group documents that exhibit sufficiently similar term assignment. Hsin-Hsi Chen 24 Linguistic Methodologies • Indexing phrases: nominal constructions including adjectives and nouns – Assign syntactic class indicators (i.e., part of speech) to the words occurring in document texts. – Construct word phrases from sequences of words exhibiting certain allowed syntactic markers (noun- noun and adjective-noun sequences). Hsin-Hsi Chen 25 Term-Phrase Formation • Term Phrase a sequence of related text words carry a more specific meaning than the single terms e.g., “computer science” vs. computer; Thesaurus Phrase transformation transformation Document Frequency N Low frequency Medium frequency High frequency j=0 dvHsin-Hsi Chen dvj>0 dvj<0 26 Simple Phrase-Formation Process • the principal phrase component (phrase head) a term with a document frequency exceeding a stated threshold, or exhibiting a negative discriminator value • the other components of the phrase medium- or low- frequency terms with stated co- occurrence relationships with the phrase head • common function words not used in the phrase-formation process Hsin-Hsi Chen 27 An Example • Effective retrieval systems are essential for people in need of information. – “are”, “for”, “in” and “of”: common function words – “system”, “people”, and “information”: phrase heads Hsin-Hsi Chen 28 The Formatted Term-Phrases effective retrieval systems essential people need information Phrase Heads and Components Phrase Heads and Components Must Be Adjacent Co-occur in Sentence 1. retrieval system* 6. effective systems 2. systems essential 7. systems need 3. essential people 8. effective people 4. people need 9. retrieval people 5. need information* 10. effective information* 11. retrieval information* 12. essential information* 2/5 5/12 *: phrases assumed to be useful for content identification Hsin-Hsi Chen 29 The Problems • A phrase-formation process controlled only by word co-occurrences and the document frequencies of certain words in not likely to generate a large number of high-quality phrases. • Additional syntactic criteria for phrase heads and phrase components may provide further control in phrase formation. Hsin-Hsi Chen 30 Additional Term-Phrase Formation Steps • Syntactic class indicator are assigned to the terms, and phrase formation is limited to sequences of specified syntactic markers, such as adjective- noun and noun-noun sequences. Adverb-adjective adverb-noun • The phrase elements are all chosen from within the same syntactic unit, such as subject phrase, object phrase, and verb phrase. Hsin-Hsi Chen 31 Consider Syntactic Unit • effective retrieval systems are essential for people in the need of information • subject phrase – effective retrieval systems • verb phrase – are essential • object phrase – people in need of information Hsin-Hsi Chen 32 Phrases within Syntactic Components [subj effective retrieval systems] [vp are essential ] for [obj people need information] • Adjacent phrase heads and components within syntactic components – retrieval systems* – people need 2/3 – need information* • Phrase heads and components co-occur within syntactic components – effective systems Hsin-Hsi Chen 33 Problems • More stringent phrase formation criteria produce fewer phrases, both good and bad, than less stringent methodologies. • Prepositional phrase attachment, e.g., The man saw the girl with the telescope. • Anaphora resolution He dropped the plate on his foot and broke it. Hsin-Hsi Chen 34 Problems (Continued) • Any phrase matching system must be able to deal with the problems of – synonym recognition – differing word orders – intervening extraneous word • Example – retrieval of information vs. information retrieval Hsin-Hsi Chen 35 Equivalent Phrase Formulation • Base form: text analysis system • Variants: – system analyzes the text – text is analyzed by the system – system carries out text analysis – text is subjected to system analysis • Related term substitution – text: documents, information items – analysis: processing, transformation, manipulation – system: program, process Hsin-Hsi Chen 36 Thesaurus-Group Generation • Thesaurus transformation – broadens index terms whose scope is too narrow to be useful in retrieval – a thesaurus must assemble groups of related specific terms under more general, higher-level class indicators Thesaurus Phrase transformation transformation Document Frequency N Low frequency Medium frequency High frequency dvj=0 dvj>0 dvj<0 Hsin-Hsi Chen 37 Sample Classes of Roget‟s Thesaurus Class Indicator Entry Class Indicator Entry permission offer leave presentation 760 sanction tender allowance 763 overture tolerance advance authorization submission prohibition proposal veto proposition 761 disallowance invitation injunction refusal ban declining taboo 764 noncompliance consent rejection acquiescence denial 762 compliance agreement acceptance Hsin-Hsi Chen 38 The Indexing Prescription (1) • Identify the individual words in the document collection. • Use a stop list to delete from the texts the function words. • Use an suffix-stripping routine to reduce each remaining word to word-stem form. • For each remaining word stem Tj in document Di, compute wij. • Represent each document Di by Di=(T1, wi1; T2, wi2; …, Tt, wit) Hsin-Hsi Chen 39 Word Stemming • effectiveness --> effective --> effect • picnicking --> picnic • king -\-> k Hsin-Hsi Chen 40 Some Morphological Rules • Restore a silent e after suffix removal from certain words to produce “hope” from “hoping” rather than “hop” • Delete certain doubled consonants after suffix removal, so as to generate “hop” from “hopping” rather than “hopp”. • Use a final y for an I in forms such as “easier”, so as to generate “easy” instead of “easi”. Hsin-Hsi Chen 41 The Indexing Prescription (2) • Identify individual text words. • Use stop list to delete common function words. • Use automatic suffix stripping to produce word stems. • Compute term-discrimination value for all word stems. • Use thesaurus class replacement for all low-frequency terms with discrimination values near zero. • Use phrase-formation process for all high-frequency terms with negative discrimination values. • Compute weighting factors for complex indexing units. • Assign to each document single term weights, term phrases, and thesaurus classes with weights. Hsin-Hsi Chen 42 Query vs. Document • Differences – Query texts are short. – Fewer terms are assigned to queries. – The occurrence of query terms rarely exceeds 1. Q=(wq1, wq2, …, wqt) where wqj: inverse document frequency Di=(di1, di2, …, dit) where dij: term frequency*inverse document frequency t sim(Q, D) wqj‧dij j 1 Hsin-Hsi Chen 43 Query vs. Document • When non-normalized documents are used, the longer documents with more assigned terms have a greater chance of matching particular query terms than do the shorter document vectors. t w ‧d qj ij sim(Q, Di ) j 1 t or (d ) 2 ij j 1 t w ‧d qj ij sim(Q, Di ) t j 1 t (d ) ‧ ( wqj ) 2 2 ij Hsin-Hsi Chen j 1 j 1 44 Relevance Feedback • Terms present in previously retrieved documents that have been identified as relevant to the user‟s query are added to the original formulations. • The weights of the original query terms are altered by replacing the inverse document frequency portion of the weights with term-relevance weights obtained by using the occurrence characteristics of the terms in the previous retrieved relevant and nonrelevant documents of the collection. Hsin-Hsi Chen 45 Relevance Feedback • Q = (wq1, wq2, ..., wqt) • Di = (di1, di2, ..., dit) • New query may be the following form Q‟ = a{wq1, wq2, ..., wqt}+{w‟qt+1, w‟qt+2, ..., w‟qt+m} • The weights of the newly added terms Tt+1 to Tt+m may consist of a combined term- frequency and term-relevance weight. Hsin-Hsi Chen 46 Final Indexing • Identify individual text words. • Use a stop list to delete common words. • Use suffix stripping to produce word stems. • Replace low-frequency terms with thesaurus classes. • Replace high-frequency terms with phrases. • Compute term weights for all single terms, phrases, and thesaurus classes. • Compare query statements with document vectors. • Identify some retrieved documents as relevant and some as nonrelevant to the query. Hsin-Hsi Chen 47 Final Indexing • Compute term-relevance factors based on available relevance assessments. • Construct new queries with added terms from relevant documents and term weights based on combined frequency and term-relevance weight. • Return to step (7). Compare query statements with document vectors …….. Hsin-Hsi Chen 48 Summary of expected effectiveness of automatic indexing • Basic single-term automatic indexing - • Use of thesaurus to group related terms in the given topic area +10% to +20% • Use of automatically derived term associations obtained from joint term assignments found in sample document collections 0% to -10% • Use of automatically derived term phrases obtained by using co-occurring terms found in the texts of sample collections +5% to +10% • Use of one iteration of relevant feedback to add new query terms extracted from previously retrieved relevant documents +30% to +60% Hsin-Hsi Chen 49 Models Hsin-Hsi Chen 50 Ranking • central problem of IR – Predict which documents are relevant and which are not • Ranking – Establish an ordering of the documents retrieved • IR models – Different model provides distinct sets of premises to deal with document relevance Hsin-Hsi Chen 51 Information Retrieval Models • Classic Models – Boolean model • set theoretic • documents and queries are represented as sets of index terms • compare Boolean query statements with the term sets used to identify document content. – Vector model • algebraic model • documents and queries are represented as vectors in a t- dimensional space • compute global similarities between queries and documents. – Probabilistic model • probabilistic • documents and queries are represented on the basis of probabilistic theory Hsin-Hsi Chen• compute the relevance probabilities for the documents of a 52 collection. Information Retrieval Models (Continued) • Structured Models – reference to the structure present in written text – non-overlapping list model – proximal nodes model • Browsing – flat – structured guided – hypertext Hsin-Hsi Chen 53 Taxonomy of Information Retrieval Models Classic Models Set Theoretic boolean Fuzzy vector Extended Boolean probabilistic U S Retrieval: Algebraic Structured Models E Adhoc Generalized Vector boolean R Filtering Lat. Semantic Index vector probabilistic Neural Network T A S Browsing Browsing Probabilistic K Flat Inference Network Structured Guided Brief Network Hypertext Hsin-Hsi Chen 54 Issues of a retrieval system • Models – boolean – vector – probabilistic • Logical views of documents – full text – set of index terms • User task – retrieval – browsing Hsin-Hsi Chen 55 Combinations of these issues LOGICAL VIEW OF DOCUMENTS Full Text+ Index Terms Full Text Structure U S Classic Classic E Retrieval Set Theoretic Set Theoretic R Structured Algebraic Algebraic Probabilistic Probabilistic T A S Flat Structure Guided Browsing Flat K Hypertext Hypertext Hsin-Hsi Chen 56 Retrieval: Ad hoc and Filtering • Ad hoc retrieval – Documents remain relatively static while new queries are submitted • Filtering – Queries remain relatively static while new documents come into the system • e.g., news wiring services in the stock market – User profile describes the user‟s preferences • Filtering task indicates to the user which document might be interested to him • Which ones are really relevant is fully reserved to the user – Routing: a variation of filtering • Ranking filtered documents and show this ranking to users Hsin-Hsi Chen 57 User profile • Simplistic approach – The profile is described through a set of keywords – The user provides the necessary keywords • Elaborate approach – Collect information from the user – initial profile + relevance feedback (relevant information and nonrelevant information) Hsin-Hsi Chen 58 Formal Definition of IR Models • /D, Q, F, R(qi, dj)/ – D: a set composed of logical views (or representations) for the documents in collection – Q: a set composed of logical views (or representations) for the user information needs query – F: a framework for modeling documents representations, queries, and their relationships – R(qi, dj): a ranking function which associations a real number with qiQ and dj D Hsin-Hsi Chen 59 Formal Definition of IR Models (continued) • classic Boolean model – set of documents – standard operations on sets • classic vector model – t-dimensional vector space – standard linear algebra operations on vector • classic probabilistic model – sets – standard probabilistic operations, and Bayes‟ Hsin-Hsi Chen 60 theorem Basic Concepts of Classic IR • index terms (usually nouns): index and summarize • weight of index terms • Definition – K={k1, …, kt}: a set of all index terms – wi,j: a weight of an index term ki of a document dj – dj=(w1,j, w2,j, …, wt,j): an index term vector for the document dj – gi(dj)= wi,j wi,j associated with (ki,dj) tells us nothing about wi+1,j associated with (ki+1,dj) • assumption – index term weights are mutually independent The terms computer and network in the area of computer networks Hsin-Hsi Chen 61 Boolean Model • The index term weight variables are all binary, i.e., wi,j{0,1} • A query q is a Boolean expression (and, or, not) • qdnf: the disjunctive normal form for q • qcc: conjunctive components of qdnf • sim(dj,q): similarity of dj to q – 1: if qcc | (qcc qdnf(ki, gi(dj)=gi(qcc)) – 0: otherwise dj is relevant to q Hsin-Hsi Chen 62 Boolean Model (Continued) (ka kb) (ka kc) = (ka kb kc) (ka kb kc) (ka kb kc) (ka kb kc) • Example = (ka kb kc) (ka kb kc) – q=ka (kb kc) (ka kb kc) – qdnf=(1,1,1) (1,1,0) (1,0,0) (1,1,0) ka (1,0,0) kb (1,1,1) Hsin-Hsi Chen kc 63 Boolean Model (Continued) • advantage: simple • disadvantage – binary decision (relevant or non-relevant) without grading scale – exact match (no partial match) • e.g., dj=(0,1,0) is non-relevant to q=(ka (kb kc) – retrieve too few or too many documents Hsin-Hsi Chen 64 Basic Vector Space Model • Term vector representation of documents Di=(ai1, ai2, …, ait) queries Qj=(qj1, qj2, …, qjt) • t distinct terms are used to characterize content. • Each term is identified with a term vector T. • t vectors are linearly independent. • Any vector is represented as a linear combination of the t term vectors. • The rth document Dr can be represented as a document vector, written as t Dr a r T i i i 1 Hsin-Hsi Chen 65 Document representation in vector space a document vector in a two-dimensional vector space Hsin-Hsi Chen 66 Similarity Measure • measure by product of two vectors x • y = |x| |y| cosa • document-query similarity document vector: term vector: t t Dr a r T i i Qs qsjTj i 1 t j 1 Dr‧Qs a q T ‧T i , j 1 ri sj i j • how to determine the vector components and term correlations? Hsin-Hsi Chen 67 Similarity Measure (Continued) • vector components T 1 T 2 T 3 Tt D1 a 11 a 12 a 1t D2 a 21 a 22 a 2 t A Hsin-Hsi Chen Dn an1 an 2 ant 68 Similarity Measure (Continued) • term correlations Ti • Tj are not available assumption: term vectors are orthogonal Ti • Tj =0 (ij) Ti • Tj =1 (i=j) • Assume that terms are uncorrelated. t sim( Dr , Qs) a q i , j 1 ri sj • Similarity measurement between documents t sim( Dr , Ds) a a i , j 1 ri sj Hsin-Hsi Chen 69 Sample query-document similarity computation • D1=2T1+3T2+5T3 D2=3T1+7T2+1T3 Q=0T1+0T2+2T3 • similarity computations for uncorrelated terms sim(D1,Q)=2•0+3 •0+5 •2=10 sim(D2,Q)=3•0+7 •0+1 •2=2 • D1 is preferred Hsin-Hsi Chen 70 Sample query-document similarity computation (Continued) • T1 T2 T3 T1 1 0.5 0 T2 0.5 1 -0.2 T3 0 -0.2 1 • similarity computations for correlated terms sim(D1,Q)=(2T1+3T2+5T3) • (0T1+0T2+2T3 ) =4T1•T3+6T2 •T3 +10T3 •T3 =-6*0.2+10*1=8.8 sim(D2,Q)=(3T1+7T2+1T3) • (0T1+0T2+2T3 ) =6T1•T3+14T2 •T3 +2T3 •T3 =-14*0.2+2*1=-0.8 • D1 is preferred Hsin-Hsi Chen 71 Vector Model • wi,j: a positive, non-binary weight for (ki,dj) • wi,q: a positive, non-binary weight for (ki,q) • q=(w1,q, w2,q, …, wt,q): a query vector, where t is the total number of index terms in the system • dj= (w1,j, w2,j, …, wt,j): a document vector Hsin-Hsi Chen 72 Similarity of document dj w.r.t. query q • The correlation between vectors dj and q dj d j q sim(d j , q) | d j || q | cos(dj,q) ti 1 wi, j wi,q ti 1 wi2, j tj 1 wi2,q Q • | q | does not affect the ranking • | dj | provides a normalization Hsin-Hsi Chen 73 document ranking • Similarity (i.e., sim(q, dj)) varies from 0 to 1. • Retrieve the documents with a degree of similarity above a predefined threshold (allow partial matching) Hsin-Hsi Chen 74 term weighting techniques • IR problem: one of clustering – user query: a specification of a set A of objects – clustering problem: determine which documents are in the set A (relevant), which ones are not (non-relevant) – intra-cluster similarity • the features better describe the objects in the set A • tf factor in vector model the raw frequency of a term ki inside a document dj – inter-cluster similarity • the features better distinguish the the objects in the set A from the remaining objects in the collection C • idf factor (inverse document frequency) in vector model the inverse of the frequency of a term ki among the documents Hsin-Hsi Chen in the collection 75 Definition of tf • N: total number of documents in the system • ni: the number of documents in which the index term ki appears • freqi,j: the raw frequency of term ki in the document dj (0~1) • fi,j: the normalized frequency of term ki in document dj freqi , j fi, j max l freql , j Term t has maximum frequency l Hsin-Hsi Chen in the document dj 76 Definition of idf and tf-idf scheme • idfi: inverse document frequency for ki N idf i log ni • wi,j: term-weighting by tf-idf scheme N wi, j fi , j log ni • query term weight (Salton and Buckley) 0.5 freqi ,q N wi ,q (0.5 ) log max l freqi ,q ni freqi,q: the raw frequency of the term ki in q Hsin-Hsi Chen 77 Analysis of vector model • advantages – its term-weighting scheme improves retrieval performance – its partial matching strategy allows retrieval of documents that approximate the query conditions – its cosine ranking formula sorts the documents according to their degree of similarity to the query • disadvantages – indexed terms are assumed to be mutually independently Hsin-Hsi Chen 78 Probabilistic Model • Given a query, there is an ideal answer set – a set of documents which contains exactly the relevant documents and no other • query process – a process of specifying the properties of an ideal answer set • problem: what are the properties? Hsin-Hsi Chen 79 Probabilistic Model (Continued) • Generate a preliminary probabilistic description of the ideal answer set • Initiate an interaction with the user – User looks at the retrieved documents and decide which ones are relevant and which ones are not – System uses this information to refine the description of the ideal answer set – Repeat the process many times. Hsin-Hsi Chen 80 Probabilistic Principle • Given a user query q and a document dj in the collection, the probabilistic model estimates the probability that user will find dj relevant • assumptions – The probability of relevance depends on query and document representations only – There is a subset of all documents which the user prefers as the answer set for the query q • Given a query, the probabilistic model assigns to each document dj a measure of its similarity to the query P(d j relevant to q) Hsin-Hsi Chen P(d j nonrelevant to q) 81 Probabilistic Principle • wi,j{0,1}, wi,q{0,1}: the index term weight variables are all binary non-relevant • q: a query which is a subset of index terms • R: the set of documents known to be relevant • R (complement of R): the set of documents • P(R|dj): the probability that the document dj is relevant to the query q • P(R|dj): the probability that dj is non-relevant to q Hsin-Hsi Chen 82 similarity • sim(dj,q): the similarity of the document dj to the query q P( R | d j ) sim(d j , q ) (by definition) P( R | d j ) P(d j | R) P( R) sim(d j , q ) (Bayes‟ rule) P(d j | R) P( R) P(d j | R) sim(d j , q ) (P(R) and P(R) are the P(d j | R) same for all documents) P( d j | R ) : the probability of randomly selecting the document dj from the set of R of relevant documents P(R): the probability that a document randomly selected from Hsin-Hsi Chen 83 the entire collection is relevant P(d j | R) P(ki|R): the probability that the index sim(d j , q ) P(d j | R) term ki is present in a document randomly selected from the set R. t gi ( d j ) 1 gi ( d j ) ( P(ki | R)) ( P (k i | R )) P(ki|R): the probability that the index log i 1 t gi ( d j ) 1 gi ( d j ) term ki is not present in a document ( P(ki | R)) ( P (k i | R )) randomly selected from the set R. i 1 gi ( d j ) 1 gi ( d j ) t ( P (ki | R )) ( P (k i | R )) log independence assumption of gi ( d j ) 1 gi ( d j ) i 1 ( P (ki | R )) ( P (k i | R )) index terms gi ( d j ) t ( P (ki | R ) P (k i | R )) ( P (k i | R )) log gi ( d j ) i 1 ( P (ki | R ) P (k i | R )) ( P (k i | R )) t P ( ki | R ) P ( k i | R ) t P ( k i | R ) gi (d j ) log i 1 P (ki | R ) P (k i | R ) i 1 P (k i | R ) t P (ki | R ) (1 P (ki | R )) t P (k i | R ) gi (d j ) log i 1 P (ki | R ) (1 P (ki | R )) i 1 P (k i | R ) Hsin-Hsi Chen 84 P(d j | R) sim(d j , q ) P(d j | R) t P (ki | R ) (1 P (ki | R )) t P (k i | R ) gi (d j ) log i 1 P (ki | R ) (1 P (ki | R )) i 1 P (k i | R ) t P ( ki | R ) (1 P (ki | R )) t P(k | R) gi (d j ) (log ) i ) log i 1 (1 P (ki | R )) P ( ki | R ) i 1 P ( k i | R ) t P ( ki | R ) (1 P (ki | R )) gi (d j ) (log ) log ) i 1 (1 P (ki | R )) P ( ki | R ) Problem: where is the set R? Hsin-Hsi Chen 85 Initial guess • P(ki|R) is constant for all index terms ki. p(ki | R) 0.5 • The distribution of index terms among the non-relevant documents can be approximated by the distribution of index terms among all the documents in the collection. ni P ( ki | R ) N (假設N>>|R|,N|R|) Hsin-Hsi Chen 86 Initial ranking • V: a subset of the documents initially retrieved and ranked by the probabilistic model (top r documents) • Vi: subset of V composed of documents which contain the index term ki • Approximate P(ki|R) by the distribution of the index term ki among the documents retrieved so far. V P ( ki | R ) i V • Approximate P(ki|R) by considering that all the non-retrieved documents are not relevant. ni Vi Hsin-Hsi Chen P(ki | R) 87 N V Small values of V and Vi Vi P ( ki | R ) V a problem when V=1 and Vi=0 ni Vi P(ki | R) • alternative 1 N V V 0.5 P ( ki | R ) i V 1 ni Vi 0.5 P ( ki | R ) N V 1 • alternative 2 n Vi i P ( ki | R ) N V 1 n ni Vi i P ( ki | R ) N Hsin-Hsi Chen N V 1 88 Analysis of Probabilistic Model • advantage – documents are ranked in decreasing order of their probability of being relevant • disadvantages – the need to guess the initial separation of documents into relevant and non-relevant sets – do not consider the frequency with which an index terms occurs inside a document – the independence assumption for index terms Hsin-Hsi Chen 89 Comparison of classic models • Boolean model: the weakest classic model • Vector model is expected to outperform the probabilistic model with general collections (Salton and Buckley) Hsin-Hsi Chen 90 Alternative Set Theoretic Models -Fuzzy Set Model • Model – a query term: a fuzzy set – a document: degree of membership in this set – membership function • Associate membership function with the elements of the class • 0: no membership in the set • 1: full membership documents • 0~1: marginal elements of the set Hsin-Hsi Chen 91 Fuzzy Set Theory a class • A fuzzy subset A of a universe of discourse U is characterized by a membership function µA: U[0,1] which associates with each element u of U a number µA(u) in the interval [0,1] a document – complement: A (u) 1 A (u) – union: AB (u) max( A (u), B (u)) – intersection: AB (u) min( A (u), B (u)) Hsin-Hsi Chen 92 Examples • Assume U={d1, d2, d3, d4, d5, d6} • Let A and B be {d1, d2, d3} and {d2, d3, d4}, respectively. • Assume A={d1:0.8, d2:0.7, d3:0.6, d4:0, d5:0, d6:0} and B={d1:0, d2:0.6, d3:0.8, d4:0.9, d5:0, d6:0} • A (u) 1 A (u) ={d1:0.2, d2:0.3, d3:0.4, d4:1, d5:1, d6:1} • AB (u) max( A (u), B (u))={d1:0.8, d2:0.7, d3:0.8, d4:9, d5:0, d6:0} • AB (u) min( A (u), B (u))={d1:0.2, d2:0.6, d3:0.6, d4:0, Hsin-Hsi Chen 93 d5:0, d6:0} Fuzzy Information Retrieval • basic idea – Expand the set of index terms in the query with related terms (from the thesaurus) such that additional relevant documents can be retrieved – A thesaurus can be constructed by defining a term-term correlation matrix c whose rows and columns are associated to the index terms in the document collection keyword connection matrix Hsin-Hsi Chen 94 Fuzzy Information Retrieval (Continued) • normalized correlation factor ci,l between two terms ki and kl (0~1) ni,l ni is # of documents containing term ki ci,l where nl is # of documents containing term kl ni nl ni,l ni,l is # of documents containing ki and kl • In the fuzzy set associated to each index term ki, a document dj has a degree of membership µi,j i, j 1 (1 ci,l ) Hsin-Hsi Chen kl d j 95 Fuzzy Information Retrieval (Continued) • physical meaning – A document dj belongs to the fuzzy set associated to the term ki if its own terms are related to ki, i.e., i,j=1. – If there is at least one index term kl of dj which is strongly related to the index ki, then i,j1. ki is a good fuzzy index – When all index terms of dj are only loosely related to ki, i,j0. ki is not a good fuzzy index Hsin-Hsi Chen 96 Example • q=(ka (kb kc) =(ka kb kc) (ka kb kc) (ka kb kc) =cc1+cc2+cc3 Da: the fuzzy set of documents Da cc3 cc2 associated to the index ka cc1 djDa has a degree of membership a,j > a predefined threshold K Db Da: the fuzzy set of documents associated to the index ka Dc (the negation of index term ka) Hsin-Hsi Chen 97 Example Query q=ka (kb kc) disjunctive normal form qdnf=(1,1,1) (1,1,0) (1,0,0) (1) the degree of membership in a disjunctive fuzzy set is computed using an algebraic sum (instead of max function) more smoothly (2) the degree of membership in a conjunctive fuzzy set is computed using an algebraic product (instead of min function) q, j cc1 cc2 cc3, j 3 Recall A (u) 1 A (u) 1 (1 cci , j ) i 1 1 (1 a, j b, j c, j ) (1 a, j b, j (1 c, j )) (1 a, j (1 b, j )(1 c, j )) Hsin-Hsi Chen 98 Alternative Algebraic Model: Generalized Vector Space Model • independence of index terms – ki: a vector associated with the index term ki – the set of vectors {k1, k2, …, kt} is linearly independent • orthogonal: ki k j 0 for ij – The index term vectors are assumed linearly independent but are not pairwise orthogonal in generalized vector space model – The index term vectors, which are not seen as the basis of the space, are composed of smaller components derived from the particular collection. Hsin-Hsi Chen 99 Generalized Vector Space Model • {k1, k2, …, kt}: index terms in a collection • wi,j: binary weights associated with the term-document pair {ki, dj} • The patterns of term co-occurrence (inside documents) can be represented by a set of 2t minterms m1=(0, 0, …, 0): point to documents containing none of index terms m2=(1, 0, …, 0): point to documents containing the index term k1 only m3=(0,1,…,0): point to documents containing the index term k2 only m4=(1,1,…,0): point to documents containing the index terms k1 and k2 … m2t=(1, 1, …, 1): point to documents containing all the index terms • gi(mj): return the weight {0,1} of the index term ki in the minterm mj (1 i t) Hsin-Hsi Chen 100 Generalized Vector Space Model (Continued) m1 (1,0,...,0,0) m 2 (0,1,...,0,0) ... m i m j 0 for i j m t (0,0,...,0,1) (the set of mi are pairwise orthogonal) 2 • mi (2t-tuple vector) is associated with minterm mi (t-tuple vector) • e.g., m4 is associated with m4 containing k1 and k2, and no others • co-occurrence of index terms inside documents: dependencies among index terms Hsin-Hsi Chen 101 minterm mr mr vector d1 (t1) d11 (t1 t2) m1=(0,0,0) m1=(1,0,0,0,0,0,0,0)d2 (t3) d12 (t1 t3) m2=(0,0,1) m2=(0,1,0,0,0,0,0,0)d3 (t3) d13 (t1 t2) m3=(0,1,0) m3=(0,0,1,0,0,0,0,0)d4 (t1) d14 (t1 t2) t=3 m =(0,1,1) m4=(0,0,0,1,0,0,0,0)d5 (t2) d15 (t1 t2 t3) 4 m5=(1,0,0) m5=(0,0,0,0,1,0,0,0)d6 (t2) d16 (t1 t2) m6=(1,0,1) m6=(0,0,0,0,0,1,0,0)d7 (t2 t3) d17 (t1 t2) m7=(1,1,0) m7=(0,0,0,0,0,0,1,0)d8 (t2 t3) d18 (t1 t2) m8=(1,1,1) m8=(0,0,0,0,0,0,0,1)d9 (t2) d19 (t1 t2 t3) d10 (t2 t3) d20 (t1 t2) c1,5 m5 c1,6 m6 c1,7 m7 c1,8 m8 k1 c1,52 c1,6 2 c1,7 2 c1,82 c1,5 w1,1 w1,4 c1,6 w1,12 c1,7 w1,11 w1,13 w1,14 w1,16 w1,17 w1,18 w1,20 c1,8 Chen1,15 w1,19 Hsin-Hsi w 102 minterm mr mr vector d1 (t1) d11 (t1 t2) m1=(0,0,0) d2 (t3) m1=(1,0,0,0,0,0,0,0) d12 (t1 t3) m2=(0,0,1) d3 (t3) m2=(0,1,0,0,0,0,0,0) d13 (t1 t2) m3=(0,1,0) d4 (t1) m3=(0,0,1,0,0,0,0,0) d14 (t1 t2) t=3 m =(0,1,1) d5 (t2) m4=(0,0,0,1,0,0,0,0) d15 (t1 t2 t3) 4 m5=(1,0,0) d6 (t2) m5=(0,0,0,0,1,0,0,0) d16 (t1 t2) m6=(1,0,1) d7 (t2 t3) m6=(0,0,0,0,0,1,0,0) d17 (t1 t2) m7=(1,1,0) d8 (t2 t3) m7=(0,0,0,0,0,0,1,0) d18 (t1 t2) m8=(1,1,1) d9 (t2) m8=(0,0,0,0,0,0,0,1) d19 (t1 t2 t3) d10 (t2 t3) d20 (t1 t2) c2,3 m3 c2,4 m4 c2,7 m 7 c2,8 m8 k2 c2,32 c2,4 2 c2,7 2 c2,82 c2,3 w2,5 w2,6 w2,9 c2,4 w2,7 w2,8 w2,10 c2,7 w2,11 w2,13 w2,14 w2,16 w2,17 w2,18 w2,20 Chen c2Hsin-Hsiw2,15 w2,19 ,8 103 minterm mr mr vector d1 (t1) d11 (t1 t2) m1=(0,0,0) m1=(1,0,0,0,0,0,0,0) d2 (t3) d12 (t1 t3) m2=(0,0,1) m2=(0,1,0,0,0,0,0,0) d3 (t3) d13 (t1 t2) m3=(0,1,0) m3=(0,0,1,0,0,0,0,0) d4 (t1) d14 (t1 t2) t=3 m =(0,1,1) m4=(0,0,0,1,0,0,0,0) d5 (t2) d15 (t1 t2 t3) 4 m5=(1,0,0) m5=(0,0,0,0,1,0,0,0) d6 (t2) d16 (t1 t2) m6=(1,0,1) m6=(0,0,0,0,0,1,0,0) d7 (t2 t3) d17 (t1 t2) m7=(1,1,0) m7=(0,0,0,0,0,0,1,0) d8 (t2 t3) d18 (t1 t2) m8=(1,1,1) m8=(0,0,0,0,0,0,0,1) d9 (t2) d19 (t1 t2 t3) d10 (t2 t3) d20 (t1 t2) c3,2 m 2 c3,4 m4 c3,6 m 6 c3,8 m8 k3 c3,2 2 c3,4 2 c3,6 2 c3,82 c3,2 w3,2 w3,3 c3,4 w3,7 w3,8 w3,10 c3,6 w3,12 Hsin-Hsi Chen c3,8 w3,15 w3,19 104 Generalized Vector Space Model (Continued) • Determine the index vector ki associated with the index term ki ki r, gi (mr )1ci,r mr Collect all the vectors mr in which the index term ki is in r, gi (mr )1 i,r c2 state 1. ci ,r w Sum up wi,j associated with the index term ki and document i, j dj whose term occurrence d j |gl ( d j ) gl ( mr ) for all l pattern coincides with minterm mr Hsin-Hsi Chen 105 Generalized Vector Space Model (Continued) • kikj quantifies a degree of correlation between ki and kj ki k j ci,r c j,r r | gi ( mr ) 1 gj ( mr ) 1 • standard cosine similarity is adopted d j i wi , j k i q i wi ,q k i ki r, gi (mr )1ci,r mr Hsin-Hsi Chen r, gi (mr )1 i,r c2 106 c1,5 m5 c1,6 m6 c1,7 m7 c1,8 m8 k1 c1,52 c1,6 2 c1,7 2 c1,82 c2,3 m3 c2,4 m4 c2,7 m 7 c2,8 m8 k2 c2,32 c2,4 2 c2,7 2 c2,82 c3,2 m 2 c3,4 m4 c3,6 m6 c3,8 m8 k3 c3,2 2 c3,4 2 c3,6 2 c3,82 k 1 k 2 c1,7 c2,7 c1,8 c2,8 k 1 k 3 c1,6 c3,6 c1,8 c3,8 Hsin-Hsi Chen k 2 k 3 c2,4 c3,4 c2,8 c3,8 107 Comparison with Standard Vector Space Model d1 (t1): (w1,1,0,0) d11 (t1 t2) d2 (t3): (0,0,w3,2) d12 (t1 t3) d3 (t3): (0,0,w3,3) d13 (t1 t2) d4 (t1): (w1,4,0,0) d14 (t1 t2) d5 (t2): (0,w2,5,0) d15 (t1 t2 t3) d6 (t2): (0,w2,6,0) d16 (t1 t2) d7 (t2 t3): (0,w2,7,w3,7) d17 (t1 t2) d8 (t2 t3): (0,w2,8,w3,8) d18 (t1 t2) d9 (t2): (0,w2,9,0) d19 (t1 t2 t3) d10 (t2 t3): (0,w2,10,w3,10) d20 (t1 t2) Hsin-Hsi Chen 108 Latent Semantic Indexing Model • representation of documents and queries by index terms – problem 1: many unrelated documents might be included in the answer set – problem 2: relevant documents which are not indexed by any of the query keywords are not retrieved • possible solution: concept matching instead of index term matching – application in cross-language information retrieval Hsin-Hsi Chen 109 basic idea • Map each document and query vector into a lower dimensional space which is associated with concepts • Retrieval in the reduced space may be superior to retrieval in the space of index terms Hsin-Hsi Chen 110 Definition • t: the number of index terms in the collection • N: the total number of documents • M=(Mij): a term-document association matrix with t rows and N columns • Mij: a weight wi,j associated with the term- document pair [ki, dj] (e.g., using tf-idf) Hsin-Hsi Chen 111 Singular Value Decomposition A R nn (1) A AT Q R nn st QQT I {QT Q I } orthogonal sin gular value decomposition : A QDQT { AT (QDQT )T (QT )T DT QT QDQT A} 1 2 0 where D = . diagonal matrix . 0 . n Hsin-Hsi Chen 112 1 2 … n 0 A R nn (2) A AT U , V R nn st U T U I , V T V I orthogonal sin gular value decomposition : (AB)T= BT AT A UDV T AAT (UDV T )(UDV T )T (UDV T )(VDU T ) UD 2U T 1 2 0 where D = . diagonal matrix . 0 . n Hsin-Hsi Chen 1 2 … n 0 113 A QDQT AQ QDQT Q QD where Q [q1 q2 qn ], qi : a column vector 1 2 0 A[q1 q2 qn ] [q1 q2 qn ] . . . n [ Aq1 Aq2 Aqn ] [1q1 2 q2 n qn ] Aq1 1q1 Aq2 2 q2 Aqn n qn 1, 2, …, n 為A之eigenvalues， qk為A相對於k之eigenvector Hsin-Hsi Chen 114 Singular Value Decomposition M : a term document matrix with t rows and N columns t M KSD t M M : a N N document to document matrix t M M : a t t term to term matrix According to M Rt N t t K : the matrix of eigenvectors derived from M M K KI t t D : the matrix of eigenvectors derived from M M D D I t M KSD Hsin-Hsi Chen 115 t M M : document to document matrix t t ( K S D )t ( K S D ) 對照A=QDQT t t t ( D S K )( K S D ) Q is matrix of eigenvectors of A 2 t D is diagonal matrix of singular values DS D 得到 t D : the matrix of eigenvectors M M : term to term matrix t t t t derived from M M ( K S D )( K S D ) K : the matrix of eigenvectors t t t ( K S D )( D S K ) t derived from M M 2 t KS K S : r r diagonal matrix of sin gular values, where r min( t , N ) Hsin-Hsi Chen 116 s < r (Concept space is reduced) Consider only the s largest singular values of S 1 2 0 . . 0 . n 1 2 … n 0 The resultant Ms matrix is the matrix of rank s which is closest to the original matrix M in the least square sense. t M s Ks Ss D s (s<<t, s<<N) Hsin-Hsi Chen 117 Ranking in LSI • query: a pseudo-document in the original M term-document – query is modeled as the document with number 0 – MstMs: the ranks of all documents w.r.t this query Hsin-Hsi Chen 118 Structured Text Retrieval Models • Definition – Combine information on text content with information on the document structure – e.g., same-page(near(„atomic holocaust‟, Figure(label(„earth‟)))) • Expressive power vs. evaluation efficiency – a model based on non-overlapping lists – a model based on proximal nodes • Terminology – match point: position in the text of a sequence of words that matches the user query – region: a contiguous portion of the text – node: a structural component of the document (chap, sec, …) Hsin-Hsi Chen 119 Non-Overlapping Lists • divide the whole text of each document in non- overlapping text regions (lists) • example 1 Chapter 1 5000 L0 Chapter a list of all chapters in the document 1 1.1 3000 3001 1.2 5000 L1 Sections indexing 1a list of all sections in the document 1.1.1 1000 1001 3000 3001 1.2.1 5000 1.1.2 lists L2 Subsections a list of all subsections in the document 1 500 501 1000 1001 L3 Subsubsections a list all subsubsections in the document • Text regions from distinct lists might overlap Hsin-Hsi Chen 120 Non-Overlapping Lists (Continued) • Data structure Recall that there is another inverted – a single inverted file file for the words in the text – each structural component stands as an entry – for each entry, there is a list of text regions as a list occurrences • Operations – Select a region which contains a given word – Select a region A which does not contain any other region B (where B belongs to a list distinct from the list for A) – Select a region not contained within any other region – … Hsin-Hsi Chen 121 Inverted Files • File is represented as an array of indexed records. Term 1 Term 2 Term 3 Term 4 Record 1 1 1 0 1 Record 2 0 1 1 1 Record 3 1 0 1 1 Record 4 0 0 1 1 Hsin-Hsi Chen 122 Inverted-file process • The record-term array is inverted (transposed). Record 1 Record 2 Record 3 Record 4 Term 1 1 0 1 0 Term 2 1 1 0 0 Term 3 0 1 1 1 Term 4 1 1 1 1 Hsin-Hsi Chen 123 Inverted-file process (Continued) • Take two or more rows of an inverted term-record array, and produce a single combined list of record identifiers. Query (term2 and term3) 1 1 0 0 0 1 1 1 --------------------------------- 1 <-- R2 Hsin-Hsi Chen 124 Extensions of Inverted Index Operations (Distance Constraints) • Distance Constraints – (A within sentence B) terms A and B must co-occur in a common sentence – (A adjacent B) terms A and B must occur adjacently in the text Hsin-Hsi Chen 125 Extensions of Inverted Index Operations (Distance Constraints) • Implementation – include term-location in the inverted indexes information: {R345, R348, R350, …} retrieval: {R123, R128, R345, …} – include sentence-location in the indexes information: {R345, 25; R345, 37; R348, 10; R350, 8; …} retrieval: {R123, 5; R128, 25; R345, 37; R345, 40; …} Hsin-Hsi Chen 126 Extensions of Inverted Index Operations (Distance Constraints) – include paragraph numbers in the indexes sentence numbers within paragraphs word numbers within sentences information: {R345, 2, 3, 5; …} retrieval: {R345, 2, 3, 6; …} – query examples (information adjacent retrieval) (information within five words retrieval) – cost: the size of indexes Hsin-Hsi Chen 127 Model Based on Proximal Nodes • hierarchical vs. flat indexing structures nodes: position in the text Chapter Sections hierarchical index Subsections Subsubsections flat index paragraphs, pages, lines an inverted list for holocaust … holocaust 10 256 … 48,324 Hsin-Hsi Chen 128 … entries: positions in the text Model Based on Proximal Nodes (Continued) • query language – Specification of regular expressions – Reference to structural components by name – Combination – Example • Search for sections, subsections, or subsubsections which contain the word „holocaust‟ • [(*section) with („holocaust‟)] Hsin-Hsi Chen 129 Model Based on Proximal Nodes (Continued) • Basic algorithm – Traverse the inverted list for the term „holocaust‟ – For each entry in the list (i.e., an occurrence), search the hierarchical index looking for sections, subsections, and sub-subsections • Revised algorithm – For the first entry, search as before – Let the last matching structural component be the innermost matching component nearby nodes – Verify the innermost matching component also matches the second entry. • Hsin-Hsi Chen If it does, the larger structural components above it also do. 130 Models for Browsing • Browsing vs. searching – The goal of a searching task is clearer in the mind of the user than the goal of a browsing task • Models – Flat browsing – Structure guided browsing – The hypertext model Hsin-Hsi Chen 131 Models for Browsing • Flat organization – Documents are represented as dots in a 2-D plan – Documents are represented as elements in a 1-D list, e.g., the results of search engine • Structure guided browsing – Documents are organized in a directory, which group documents covering related topics • Hypertext model – Navigating the hypertext: a traversal of a directed graph Hsin-Hsi Chen 132 Trends and Research Issues • Library systems – Cognitive and behavioral issues oriented particularly at a better understanding of which criteria the users adopt to judge relevance • Specialized retrieval systems – e.g., legal and business documents – how to retrieve all relevant documents without retrieving a large number of unrelated documents • The Web – User does not know what he wants or has great difficulty in formulating his request – How the paradigm adopted for the user interface affects the ranking – The indexes maintained by various Web search engine133 Hsin-Hsi Chen are almost disjoint

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