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Basic IR: Modeling Basic IR Task: Match a subset of documents to the user’s query Slightly more complex: and rank the resulting documents by predicted relevance The derivation of relevance leads to different IR models.

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Concepts: Term-Document Incidence Imagine matrix of terms X documents with 1 when the term appears in the document and 0 otherwise. Queries satisfied how? Problems? searchsegmentselectsemantic… MIR1011 AI1101 …

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Concepts: Term Frequency To support document ranking, need more than just term incidence. Term frequency records number of times a given term appears in each document. Intuition: More times a term appears in a document the more central it is to the topic of the document.

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Concept: Term Weight Weights represent the importance of a given term for characterizing a document. w ij is a weight for term i in document j.

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Mapping Task and Document Type to Model Index Terms Full Text Full Text + Structure Searching (Retrieval) Classic Structured Surfing (Browsing) Flat Hypertext Structure Guided Hypertext

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

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Classic Models: Basic Concepts Ki is an index term dj is a document t is the total number of docs K = (k1, k2, …, kt) is the set of all index terms wij >= 0 is a weight associated with (ki,dj) wij = 0 indicates that term does not belong to doc vec(dj) = (w1j, w2j, …, wtj) is a weighted vector associated with the document dj gi(vec(dj)) = wij is a function which returns the weight associated with pair (ki,dj)

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Classic: Boolean Model Based on set theory: map queries with Boolean operations to set operations Select documents from term-document incidence matrix Pros: Cons:

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Exact Matching Ignores… term frequency in document term scarcity in corpus size of document ranking

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Vector Model Vector of term weights based on term frequency Compute similarity between query and document where both are vectors vec(dj) = (w1j, w2j,..., wtj) vec(q) = (w1q, w2q,..., wtq) Similarity is the cosine of the angle between the vectors.

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Cosine Measure Since wij > 0 and wiq > 0, 0 <= sim(q,dj) <=1 j dj q from MIR notes

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How to Set Wij Weights? TF-IDF Within document: Term-Frequency tf measures term density within a document Across document: Inverse Document Frequency idf measures informativeness or rarity of term across corpus.

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TF * IDF Computation What happens as number of occurrences in a document increases? What happens as term becomes more rare?

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TF * IDF TF may be normalized. tf(i,d) = freq(i,d) / max(freq(l,d)) IDF is computed normalized to size of corpus as log to make TF and IDF values comparable IDF requires a static corpus.

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How to Set W i,q Weights? 1.Create Vector directly from query 2.Use modified tf-idf

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d1 d2 d3 d4d5 d6 d7 k1 k2 k3 from MIR notes The Vector Model: Example

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d1 d2 d3 d4d5 d6 d7 k1 k2 k3 from MIR notes The Vector Model: Example (cont.) 1.Compute Tf-IDF Vector for each document For first document: K1: ((2/2)*(log (7/5))=.33 K2: (0*(log (7/4))) = 0 K3: ((1/2)*(log (7/3))) =.42 for rest: [ ], [ ], [ ], [ ], [ ], [0.56 0]

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The Vector Model: Example (cont.) 2. Compute the Tf-IDF for the query [1 2 3]: K1: (.5 + ((.5 * 1)/3))*(log (7/5))) K2: (.5 + ((.5 * 2)/3))*(log (7/4))) K3: (.5 + ((.5 * 3)/3))*(log (7/3))) which is: [ ] d1 d2 d3 d4d5 d6 d7 k1 k2 k3

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The Vector Model: Example (cont.) 3. Compute the Sim for each document: D1: D1*q = (.33 *.22) + (0 *.47) + (.42 *.85) =.43 |D1| = sqrt((.33^2) + (.42^2)) =.53 |q| = sqrt((.22^2) + (.47^2) + (.85^2)) = 1.0 sim =.43 / (.53 * 1.0) =.81 D2:.22 D3:.93 D4:.23 D5:.97 D6:.51 D7:.47 d1 d2 d3 d4d5 d6 d7 k1 k2 k3

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Vector Model Implementation Issues Sparse TermXDocument matrix Store term count, term weight, or weighted by idf i ? What if the corpus is not fixed (e.g., the Web)? What happens to IDF? How to efficiently compute Cosine for large index?

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Heuristics for Computing Cosine for Large Index Select from only non-zero cosines Focus on non-zero cosines for rare (high idf) words Pre-compute document adjacency for each term, pre-compute k nearest docs for a t term query, compute cosines from query to union of t pre-computed lists, choose top k

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Pros: term-weighting improves quality cosine ranking formula sorts documents according to degree of similarity to the query Cons: assumes independence of index terms The TFIDF Vector Model: Pros/Cons

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