Basic IR: Modeling Basic IR Task: Slightly more complex: 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.

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? search segment select semantic … MIR 1 AI

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.

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

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

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

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)

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

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

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.

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

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.

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

TF * IDF TF may be normalized. IDF is computed 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.

How to Set Wi,q Weights? Create Vector directly from query Use modified tf-idf

The Vector Model: Example k1 k2 k3 Which document seems to best match the query? What would we expect the ranking to be? from MIR notes

The Vector Model: Example (cont.) k1 k2 k3 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: [.34 0 0], [0 .19 .85], [.34 0 0], [.08 .28 .85], [.17 .56 0], [0 .56 0] TF-IDF for first document… k1 is 2* log(7/5)=.67, k2 is 0 * log(7/4)=0, k3 is 1 * log(7/3)=.84 [.67 0 .84] normalized it is k1= (2/2)*log(7/5)=.33, k2=0, k3=(1/4)*log(7/3)=.21 To match query, from MIR notes

The Vector Model: Example (cont.) k1 k2 k3 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: [.22 .47 .85]

The Vector Model: Example (cont.) k1 k2 k3 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

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

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

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