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Information Retrieval

Information Retrieval. CSE 8337 (Part B) Spring 2009 Some Material for these slides obtained from: Modern Information Retrieval by Ricardo Baeza -Yates and Berthier Ribeiro-Neto http://www.sims.berkeley.edu/~hearst/irbook/

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Information Retrieval

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  1. Information Retrieval CSE 8337 (Part B) Spring 2009 Some Material for these slides obtained from: Modern Information Retrieval by Ricardo Baeza-Yates and BerthierRibeiro-Netohttp://www.sims.berkeley.edu/~hearst/irbook/ Data Mining Introductory and Advanced Topics by Margaret H. Dunham http://www.engr.smu.edu/~mhd/book Introduction to Information Retrieval by Christopher D. Manning, PrabhakarRaghavan, and HinrichSchutze http://informationretrieval.org

  2. CSE 8337 Outline • Introduction • Simple Text Processing • Boolean Queries • Web Searching/Crawling • Indexes • Vector Space Model • Matching • Evaluation

  3. CSE 8337 Outline • Introduction • Simple Text Processing • Boolean Queries • Web Searching/Crawling • Indexes • Vector Space Model • Matching • Evaluation

  4. Modeling TOC(Vector Space and Other Models) • Introduction • Classic IR Models • Boolean Model • Vector Model • Probabilistic Model • Extended Boolean Model • Vector Space Scoring • Vector Model and Web Search

  5. Algebraic Set Theoretic Generalized Vector Lat. Semantic Index Neural Networks Structured Models Fuzzy Extended Boolean Non-Overlapping Lists Proximal Nodes Classic Models Probabilistic boolean vector probabilistic Inference Network Belief Network Browsing Flat Structure Guided Hypertext IR Models U s e r T a s k Retrieval: Adhoc Filtering Browsing

  6. The Boolean Model • Simple model based on set theory • Queries specified as boolean expressions • precise semantics and neat formalism • Terms are either present or absent. Thus, wij  {0,1} • Consider • q = ka  (kb  kc) • qdnf = (1,1,1)  (1,1,0)  (1,0,0) • qcc= (1,1,0) is a conjunctive component

  7. Ka Kb (1,1,0) (1,0,0) (1,1,1) Kc The Boolean Model • q = ka  (kb kc) • sim(q,dj) = 1 if  qcc| (qcc  qdnf)  (ki, gi(dj)= gi(qcc)) 0 otherwise

  8. Drawbacks of the Boolean Model • Retrieval based on binary decision criteria with no notion of partial matching • No ranking of the documents is provided • Information need has to be translated into a Boolean expression • The Boolean queries formulated by the users are most often too simplistic • As a consequence, the Boolean model frequently returns either too few or too many documents in response to a user query

  9. The Vector Model • Use of binary weights is too limiting • Non-binary weights provide consideration for partial matches • These term weights are used to compute a degree of similarity between a query and each document • Ranked set of documents provides for better matching

  10. The Vector Model • wij > 0 whenever ki appears in dj • wiq >= 0 associated with the pair (ki,q) • dj = (w1j, w2j, ..., wtj) • q = (w1q, w2q, ..., wtq) • To each term ki is associated a unitary vector i • The unitary vectors i and j are assumed to be orthonormal (i.e., index terms are assumed to occur independently within the documents) • The t unitary vectors i form an orthonormal basis for a t-dimensional space where queries and documents are represented as weighted vectors

  11. The Vector Model j dj  q i • Sim(q,dj) = cos() = [dj  q] / |dj| * |q| = [ wij * wiq] / |dj| * |q| • Since wij > 0 and wiq > 0, 0 <= sim(q,dj) <=1 • A document is retrieved even if it matches the query terms only partially

  12. Weights wij and wiq ? • One approach is to examine the frequency of the occurence of a word in a document: • Absolute frequency: • tf factor, the term frequency within a document • freqi,j - raw frequency of ki within dj • Both high-frequency and low-frequency terms may not actually be significant • Relative frequency: tf divided by number of words in document • Normalized frequency: fi,j = (freqi,j)/(maxl freql,j)

  13. Inverse Document Frequency • Importance of term may depend more on how it can distinguish between documents. • Quantification of inter-documents separation • Dissimilarity not similarity • idf factor, the inverse document frequency

  14. IDF • N be the total number of docs in the collection • ni be the number of docs which contain ki • The idf factor is computed as • idfi = log (N/ni) • the log is used to make the values of tf and idf comparable. It can also be interpreted as the amount of information associated with the term ki. • IDF Ex: • N=1000, n1=100, n2=500, n3=800 • idf1= 3 - 2 = 1 • idf2= 3 – 2.7 = 0.3 • idf3 = 3 – 2.9 = 0.1

  15. The Vector Model • The best term-weighting schemes take both into account. • wij = fi,j * log(N/ni) • This strategy is called a tf-idf weighting scheme

  16. The Vector Model • For the query term weights, a suggestion is • wiq = (0.5 + [0.5 * freqi,q / max(freql,q]) * log(N/ni) • The vector model with tf-idf weights is a good ranking strategy with general collections • The vector model is usually as good as any known ranking alternatives. • It is also simple and fast to compute.

  17. The Vector Model • Advantages: • term-weighting improves quality of the answer set • partial matching allows retrieval of docs that approximate the query conditions • cosine ranking formula sorts documents according to degree of similarity to the query • Disadvantages: • Assumes independence of index terms (??); not clear that this is bad though

  18. k2 k1 d7 d6 d2 d4 d5 d3 d1 k3 The Vector Model: Example I

  19. k2 k1 d7 d6 d2 d4 d5 d3 d1 k3 The Vector Model: Example II

  20. k2 k1 d7 d6 d2 d4 d5 d3 d1 k3 The Vector Model: Example III

  21. Probabilistic Model • Objective: to capture the IR problem using a probabilistic framework • Given a user query, there is an ideal answer set • Querying as specification of the properties of this ideal answer set (clustering) • But, what are these properties? • Guess at the beginning what they could be (i.e., guess initial description of ideal answer set) • Improve by iteration

  22. Probabilistic Model • An initial set of documents is retrieved somehow • User inspects these docs looking for the relevant ones (in truth, only top 10-20 need to be inspected) • IR system uses this information to refine description of ideal answer set • By repeating this process, it is expected that the description of the ideal answer set will improve • Have always in mind the need to guess at the very beginning the description of the ideal answer set • Description of ideal answer set is modeled in probabilistic terms

  23. Probabilistic Ranking Principle • Given a user query q and a document dj, the probabilistic model tries to estimate the probability that the user will find the document dj interesting (i.e., relevant). Ideal answer set is referred to as R and should maximize the probability of relevance. Documents in the set R are predicted to be relevant. • But, • how to compute probabilities? • what is the sample space?

  24. The Ranking • Probabilistic ranking computed as: • sim(q,dj) = P(dj relevant-to q) / P(dj non-relevant-to q) • This is the odds of the document dj being relevant • Taking the odds minimize the probability of an erroneous judgement • Definition: • wij {0,1} • P(R | dj) :probability that given doc is relevant • P(R | dj) : probability doc is not relevant

  25. The Ranking • sim(dj,q) = P(R | dj) / P(R | dj) = [P(dj | R) * P(R)] [P(dj | R) * P(R)] ~ P(dj | R) P(dj | R) • P(dj | R) : probability of randomly selecting the document dj from the set R of relevant documents

  26. The Ranking • sim(dj,q) ~ P(dj | R) P(dj | R) ~ [  P(ki | R)] * [  P(ki | R)] [  P(ki | R)] * [  P(ki | R)] • P(ki | R) : probability that the index term ki is present in a document randomly selected from the set R of relevant documents

  27. The Ranking • sim(dj,q) ~ log [  P(ki | R)] * [  P(kj | R)] [  P(ki |R)] * [  P(ki | R)] ~ K * [ log  P(ki | R) + log  P(ki | R) ] P(ki | R) P(ki | R) where P(ki | R) = 1 - P(ki | R) P(ki | R) = 1 - P(ki | R)

  28. The Initial Ranking • sim(dj,q) ~  wiq * wij * (log P(ki | R) + log P(ki | R) ) P(ki | R) P(ki | R) • Probabilities P(ki | R) and P(ki | R) ? • Estimates based on assumptions: • P(ki | R) = 0.5 • P(ki | R) = ni N • Use this initial guess to retrieve an initial ranking • Improve upon this initial ranking

  29. Improving the Initial Ranking • Let • V : set of docs initially retrieved • Vi : subset of docs retrieved that contain ki • Reevaluate estimates: • P(ki | R) = Vi V • P(ki | R) = ni - Vi N - V • Repeat recursively

  30. Improving the Initial Ranking • To avoid problems with V=1 and Vi=0: • P(ki | R) = Vi + 0.5 V + 1 • P(ki | R) = ni - Vi + 0.5 N - V + 1 • Also, • P(ki | R) = Vi + ni/N V + 1 • P(ki | R) = ni - Vi + ni/N N - V + 1

  31. Pluses and Minuses • Advantages: • Docs ranked in decreasing order of probability of relevance • Disadvantages: • need to guess initial estimates for P(ki | R) • method does not take into account tf and idf factors

  32. Brief Comparison of Classic Models • Boolean model does not provide for partial matches and is considered to be the weakest classic model • Salton and Buckley did a series of experiments that indicate that, in general, the vector model outperforms the probabilistic model with general collections • This seems also to be the view of the research community

  33. Extended Boolean Model • Boolean model is simple and elegant. • But, no provision for a ranking • As with the fuzzy model, a ranking can be obtained by relaxing the condition on set membership • Extend the Boolean model with the notions of partial matching and term weighting • Combine characteristics of the Vector model with properties of Boolean algebra

  34. The Idea • The Extended Boolean Model (introduced by Salton, Fox, and Wu, 1983) is based on a critique of a basic assumption in Boolean algebra • Let, • q = kx ky • wxj = fxj * idfx associated with [kx,dj] max(idfi) • Further, wxj = x and wyj = y

  35. 2 2 sim(qand,dj) = 1 - sqrt( (1-x) + (1-y) ) 2 The Idea: qand = kx ky; wxj = x and wyj = y (1,1) ky AND y = wyj dj (0,0) x = wxj kx

  36. 2 2 sim(qor,dj) = sqrt( x + y ) 2 The Idea: qor = kx ky; wxj = x and wyj = y (1,1) ky OR dj y = wyj (0,0) x = wxj kx

  37. Generalizing the Idea • We can extend the previous model to consider Euclidean distances in a t-dimensional space • This can be done using p-norms which extend the notion of distance to include p-distances, where 1  p  is a new parameter

  38. Generalizing the Idea 1 1 p p p p p p    p p p    p p • sim(qor,dj) = (x1 + x2 + . . . + xm ) m p p p • sim(qand,dj)=1 - ((1-x1) + (1-x2) + . . . + (1-xm) ) m • A generalized disjunctive query is given by • qor = k1 k2 . . . kt • A generalized conjunctive query is given by • qand = k1 k2 . . . kt

  39. Properties • If p = 1 then (Vector like) • sim(qor,dj) = sim(qand,dj) = x1 + . . . + xm m • If p =  then (Fuzzy like) • sim(qor,dj) = max (wxj) • sim(qand,dj) = min (wxj) • By varying p, we can make the model behave as a vector, as a fuzzy, or as an intermediary model

  40. Properties 2    • This is quite powerful and is a good argument in favor of the extended Boolean model • q = (k1 k2) k3 k1 and k2 are to be used as in a vector retrieval while the presence of k3 is required. • sim(q,dj) = ( (1 - ( (1-x1) + (1-x2) ) ) + x3 ) 2 ______ 2

  41. Conclusions • Model is quite powerful • Properties are interesting and might be useful • Computation is somewhat complex • However, distributivity operation does not hold for ranking computation: • q1 = (k1  k2)  k3 • q2 = (k1  k3)  (k2  k3) • sim(q1,dj)  sim(q2,dj)

  42. Vector Space Scoring • First cut: distance between two points • ( = distance between the end points of the two vectors) • Euclidean distance? • Euclidean distance is a bad idea . . . • . . . because Euclidean distance is large for vectors of different lengths.

  43. Why distance is a bad idea The Euclidean distance between q and d2 is large even though the distribution of terms in the query qand the distribution of terms in the document d2 are very similar.

  44. Use angle instead of distance • Thought experiment: take a document d and append it to itself. Call this document d′. • “Semantically” d and d′ have the same content • The Euclidean distance between the two documents can be quite large • The angle between the two documents is 0, corresponding to maximal similarity. • Key idea: Rank documents according to angle with query.

  45. From angles to cosines • The following two notions are equivalent. • Rank documents in decreasing order of the angle between query and document • Rank documents in increasing order of cosine(query,document) • Cosine is a monotonically decreasing function for the interval [0o, 180o]

  46. Length normalization • A vector can be (length-) normalized by dividing each of its components by its length – for this we use the L2 norm: • Dividing a vector by its L2 norm makes it a unit (length) vector • Effect on the two documents d and d′ (d appended to itself) from earlier slide: they have identical vectors after length-normalization.

  47. cosine(query,document) Dot product Unit vectors qi is the tf-idf weight of term i in the query di is the tf-idf weight of term i in the document cos(q,d) is the cosine similarity of q and d … or, equivalently, the cosine of the angle between q and d.

  48. Cosine similarity amongst 3 documents How similar are the novels SaS: Sense and Sensibility PaP: Pride and Prejudice, and WH: Wuthering Heights? Term frequencies (counts)

  49. 3 documents example contd. Log frequency weighting After normalization cos(SaS,PaP) ≈ 0.789 ∗ 0.832 + 0.515 ∗ 0.555 + 0.335 ∗ 0.0 + 0.0 ∗ 0.0 ≈ 0.94 cos(SaS,WH) ≈ 0.79 cos(PaP,WH) ≈ 0.69 Why do we have cos(SaS,PaP) > cos(SAS,WH)?

  50. tf-idf weighting has many variants Columns headed ‘n’ are acronyms for weight schemes. Why is the base of the log in idf immaterial?

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