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Information Retrieval Models 1 Retrieval Models • A retrieval model specifies the details of: 1. Document representation 2. Query representation 3. Retrieval function • Determines a notion of relevance. • Notion of relevance can be binary or continuous (i.e. ranked retrieval). 2 Classes of Retrieval Models • Boolean models (set theoretic) • Statistical (Probabilistic) models • Vector space models (statistical/algebraic) – Generalized VS • Extended Boolean Models 3 Other Model Dimensions • Logical View of Documents – Index terms – Full text – Full text + Structure (e.g. hypertext) • User Task – Retrieval – Browsing 4 Retrieval Tasks • Ad hoc retrieval: Fixed document corpus, varied queries. • Filtering: Fixed query, continuous document stream. – Binary decision of relevant/not-relevant. • Routing: Same as filtering but continuously supply ranked lists rather than binary filtering. 5 Common Preprocessing Steps • Strip unwanted characters/markup (e.g. HTML tags, punctuation, numbers, etc.). • Break into tokens (keywords) on whitespace. • Stem tokens to “root” words – computational comput • Remove common stopwords (e.g. a, the, it, etc.). • Detect common phrases (possibly using a domain specific dictionary). • Build inverted index (keyword list of docs containing it). 6 Boolean Model • A document is represented as a set of keywords. • Queries are Boolean expressions of keywords, connected by AND, OR, and NOT, including the use of brackets to indicate scope. – ((Rio AND Brazil) OR (Hilo AND Hawaii)) AND hotel AND NOT Hilton) • Output: Document is relevant or not. No partial matches or ranking. 7 Exact Match - Boolean Search • You retrieve exactly what you ask for in the query: – all documents that have the term(s) with logical connection(s), as stated in the query – exactly: nothing less, nothing more • Based on matching following rules of Boolean algebra, or algebra of sets – ‘new algebra’ – presented by circles in Venn diagrams 8 Boolean Algebra • Operates on sets – e.g. set of documents • Has four operations (like in algebra): 1. A: retrieve set A • I want documents that have the term programming 2. A AND B: retrieve set that has A and B • often called intersection & labeled A B • I want documents that have both terms programming and language some place within 9 Boolean algebra 3. A OR B: retrieve set that has either A or B • often called union and labeled A B • I want documents that have either term programming or term language someplace within 4. A NOT B: retrieve set A but not B • often called negation and labeled A – B • I want documents that have term programming but if they also have term language I do not want those 10 Potential problems • But beware: – programming AND language will retrieve documents that have programming language (together as a phrase) but also documents that have language in the first paragraph and programming in the third section, 5 pages later, and it does not deal with programming language at all – thus in Google you will ask for “programming language” and in DIALOG for programming language to retrieve the exact phrase programming language 11 Potential problems – programming NOT language will retrieve documents that have programming and suppress those that along with programming also have language, but sometimes those suppressed may very well be relevant. Thus, NOT is also known as the “dangerous operator “ 12 Boolean algebra depicted in Venn diagrams Four basic operations: e.g. A = programming B= language A B A alone. All documents that have A. Shade 1 & 2. 1 2 3 programming A B 1 2 3 A AND B. Shade 2 programming AND language A B 1 2 3 A OR B. Shade 1, 2, 3 programming OR language A B A NOT B. Shade 1 1 2 3 programming NOT language 13 Venn diagrams … cont. Complex statements allowed e.g (A OR B) AND C A B Shade 4,5,6 2 1 3 (programming OR language) AND 4 5 6 visual 7 C (A OR B) NOT C Shade what? (programming OR language) NOT visual 14 Boolean Retrieval Model • Popular retrieval model because: – Easy to understand for simple queries. – Clean formalism. • Reasonably efficient implementations possible for normal queries. 15 Boolean Models Problems • Very rigid: AND means all; OR means any. • Difficult to express complex user requests. • Difficult to control the number of documents retrieved. – All matched documents will be returned. • Difficult to rank output. – All matched documents logically satisfy the query. • Difficult to perform relevance feedback. – If a document is identified by the user as relevant or irrelevant, how should the query be modified? 16 Statistical Models • A document is typically represented by a bag of words (unordered words with frequencies). • Bag = set that allows multiple occurrences of the same element. • User specifies a set of desired terms with optional weights: – Weighted query terms: Q = < database 0.5; text 0.8; information 0.2 > – Unweighted query terms: Q = < database; text; information > – No Boolean conditions specified in the query. 17 Statistical Retrieval • Retrieval based on similarity between query and documents. • Output documents are ranked according to similarity to query. • Similarity based on occurrence frequencies of keywords in query and document. • Automatic relevance feedback can be supported. 18 Issues for Vector Space Model • How to determine important words in a document? – Word sense? – Word n-grams (and phrases,…) terms • How to determine the degree of importance of a term within a document and within the entire collection? • How to determine the degree of similarity between a document and the query? • In the case of the web, what is a collection and what are the effects of links, formatting information, etc.? 19 The Vector-Space Model • Assume t distinct terms remain after preprocessing; call them index terms or the vocabulary. • These “orthogonal” terms form a vector space. Dimension = t = |vocabulary| • Each term, i, in a document or query, j, is given a real-valued weight, wij. • Both documents and queries are expressed as t-dimensional vectors: dj = (w1j, w2j, …, wtj) 20 Graphic Representation Example: D1 = 2T1 + 3T2 + 5T3 T3 D2 = 3T1 + 7T2 + T3 Q = 0T1 + 0T2 + 2T3 5 D1 = 2T1+ 3T2 + 5T3 Q = 0T1 + 0T2 + 2T3 2 3 T1 D2 = 3T1 + 7T2 + T3 • Is D1 or D2 more similar to Q? • How to measure the degree of 7 T2 similarity? Distance? Angle? Projection? 21 Document Collection • A collection of n documents can be represented in the vector space model by a Term-Document Matrix. • An entry in the matrix corresponds to the “weight” of a term in the document; zero means the term has no significance in the document or it simply doesn’t exist in the document. T1 T2 …. Tt D1 w11 w21 … wt1 D2 w12 w22 … wt2 : : : : : : : : Dn w1n w2n … wtn 22 Term Weights: Term Frequency • More frequent terms in a document are more important, i.e. more indicative of the topic. fij = frequency of term i in document j • May want to normalize term frequency (tf) across the entire document: tfij = fij / max{fij} 23 Term Weights: Inverse Document Frequency • Terms that appear in many different documents are less indicative of overall topic. df i = document frequency of term i = number of documents containing term i idfi = inverse document frequency of term i, = log2 (N/ df i) (N: total number of documents) • An indication of a term’s discrimination power. • Log used to dampen the effect relative to tf. 24 TF-IDF Weighting • A typical combined term importance indicator is tf-idf weighting: wij = tfij idfi = tfij log2 (N/ dfi) • A term occurring frequently in the document but rarely in the rest of the collection is given high weight. • Many other ways of determining term weights have been proposed. • Experimentally, tf-idf has been found to work well. 25 Computing TF-IDF -- An Example -Given a document containing terms with given frequencies: A(3), B(2), C(2), D(1) -Assume collection contains 10,000 documents and document frequencies of these terms are: A(50), B(1300), C(250), D(20) -Then: A: tf = 3/3; idf = log(10000/50) = 7.6; tf-idf = 7.6 B: tf = 2/3; idf = log(10000/1300) = 2.9; tf-idf = 1.9 C: tf = 2/3; idf = log(10000/250) = 5.3; tf-idf = 3.5 D: tf = 1/3; idf = log(10000/20) = 8.9 tf-idf = 2.9 26 Query Vector • Query vector is typically treated as a document and also tf-idf weighted. • Alternative is for the user to supply weights for the given query terms. 27 Similarity Measure • A similarity measure is a function that computes the degree of similarity between two vectors. • Using a similarity measure between the query and each document: – It is possible to rank the retrieved documents in the order of presumed relevance. – It is possible to enforce a certain threshold so that the size of the retrieved set can be controlled. 28 Similarity Measure - Inner Product • Similarity between vectors for the document di and query q can be computed as the vector inner product: t sim(dj,q) = dj•q = w ·w i 1 ij iq where wij is the weight of term i in document j and wiq is the weight of term i in the query • For binary vectors, the inner product is the number of matched query terms in the document (size of intersection). • For weighted term vectors, it is the sum of the products of the weights of the matched terms. 29 Inner Product -- Examples Binary: – D = 1, 1, 1, 0, 1, 1, 0 Size of vector = size of vocabulary = 7 – Q = 1, 0 , 1, 0, 0, 1, 1 0 means corresponding term not found in document or query sim(D, Q) = 3 Weighted: D1 = 2T1 + 3T2 + 5T3 D2 = 3T1 + 7T2 + 1T3 Q = 0T1 + 0T2 + 2T3 sim(D1 , Q) = 2*0 + 3*0 + 5*2 = 10 sim(D2 , Q) = 3*0 + 7*0 + 1*2 = 2 30 Properties of Inner Product • The inner product is unbounded. • Favors long documents with a large number of unique terms. • Measures how many terms are matched but NOT how many terms are not matched. 31 Cosine Similarity Measure • Cosine similarity measures the cosine of t3 the angle between two vectors. • Inner product normalized by the vector 1 lengths. t D1 dj q ( wij wiq) Q CosSim(dj, q) = i 1 t t 2 t1 wij wiq 2 2 dj q i 1 i 1 t2 D2 D1 = 2T1 + 3T2 + 5T3 CosSim(D1 , Q) = 10 / (4+9+25)(0+0+4) = 0.81 D2 = 3T1 + 7T2 + 1T3 CosSim(D2 , Q) = 2 / (9+49+1)(0+0+4) = 0.13 Q = 0T1 + 0T2 + 2T3 D1 is 6 times better than D2 using cosine similarity but only 5 times better using inner product. 32 Naïve Implementation -Convert all documents in collection D to tf-idf weighted vectors, dj, for keyword vocabulary V. -Convert query to a tf-idf-weighted vector q. -For each dj in D do Compute score sj = cosSim(dj, q) -Sort documents by decreasing score. -Present top ranked documents to the user. Time complexity: O(|V|·|D|) Bad for large V & D ! |V| = 10,000; |D| = 100,000; |V|·|D| = 1,000,000,000 33 Comments on Vector Space Models • Simple, mathematically based approach. • Considers both local (tf) and global (idf) word occurrence frequencies. • Provides partial matching and ranked results. • Tends to work quite well in practice despite obvious weaknesses. • Allows efficient implementation for large document collections. 34 Problems with Vector Space Model • Missing semantic information (e.g. word sense). • Missing syntactic information (e.g. phrase structure, word order, proximity information). • Assumption of term independence (e.g. ignores synonomy). • Lacks the control of a Boolean model (e.g., requiring a term to appear in a document). – Given a two-term query “A B”, may prefer a document containing A frequently but not B, over a document that contains both A and B, but both less frequently. 35 Extended Boolean Model • Disadvantages of “Boolean Model” : • No term weight is used • Counter example: query q=Kx AND Ky. Documents containing just one term, e,g, Kx is considered as irrelevant as another document containing none of these terms. 36 Extended Boolean Model: • The Extended Boolean model was introduced in 1983 by Salton, Fox, and Wu • The idea is to make use of term weight as vector space model. • Strategy: Combine Boolean query with vector space model. • Advantages: It is easy for user to provide query. 37 Extended Boolean Model • Each document is represented by a vector (similar to vector space model.) wx , j tf norm x , j * idf norm x , j tf x , j idf x tf norm x , j and idf norm x , j tf m axx , j idf m ax • Query is in terms of Boolean formula. 38 The Idea qand = kx AND ky; x=wxj and y= wyj ky (1,1) dj y = wyj AND dj+1 (0,0) x = wxj kx We want a document to be as close as possible to (1,1) 39 AND query • For query q=Kx AND Ky, (1,1) is the most desirable point. We use to rank the documents (1 x) (1 y) 2 2 sim(qand , d ) 1 2 • The bigger the better. 40 The Idea qor = kx OR ky; x= wxjand y=wyj ky (1,1) y = wyj dj OR dj+1 (0,0) x = wxj kx We want a document to be as far as possible from (0,0) 41 OR query • For query q=Kx OR Ky, (0,0) is the point we try to avoid. We can use to rank the documents 2 x y 2 sim(qor , d ) 2 • The bigger the better. 42 Weights and Euclidean Distances Maximum Euclidean Distance, dmax, in a two-dimensional term space. 43 AND query "AND" Euclidean Distance in a two-dimensional term space. 44 OR query The Euclidean distance of a document at (x, y) must be d < 1.41 45 Normalized Similarity Scores • To compare similarity scores for a variety of scenarios we need to normalize all distances by dividing by dmax. Thus, for OR and AND queries we obtain 46 Extend the idea to m terms • qor=k1 k2 … Km x x ... x ) p p p 1/ p ,d ) ( 1 2 m sim(qor j m • qand=k1 k2 … km 1/ p (1 x ) (1 x ) ...(1 x ) p p p sim(qand , dj ) 1 ( 1 2 m ) m 47 Example: • For instance, consider the query q=(k1 AND k2) OR k3. The similarity sim(q,dj) between a document dj and this query is then computed as p 1 p 1 x1 1 x2 p p xp p 2 3 sim(q, d j ) 2 • Any boolean can be expressed as a numeral formula. 48 Exercise • Rank the following by decreasing cosine similarity: – Two documents that have only frequent words (the, a, an, of) in common. – Two documents that have no words in common. – Two documents that have many rare words in common (wingspan, tailfin). 49 Exercise • Consider three Documents: Austen's Sense and Sensibility(SaS), Pride and Prejudice(PaP); Bronte's Wuthering Heights (WH) SaS PaP WH affection 115 58 20 jealous 10 7 11 gossip 2 0 6 SaS PaP WH affection 0.996 0.993 0.847 jealous 0.087 0.120 0.466 gossip 0.017 0.000 0.254 • Calculate cos(SAS, PAP) and cos(SAS, WH) 50 Exercise: 1. Give the numeral formula for extended Boolean model of the query q=(k1 or k2 or k3)and (not k4 or k5). (assume that there are 5 terms in total.) 2. Assume that the document is represented by the vector (0.8, 0.1, 0.0, 0.0, 1.0). What is sim(q, d) for extended Boolean model? 51

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Information Retrievaland Web Search lecture

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