Vector Space Model

1. Vector Space Model CS 652 Information Extraction and Integration

2. Introduction Docs Index Terms doc match Ranking Information Need query

3. Introduction • A ranking is an ordering of the documents retrieved that (hopefully) reflects the relevance of the documents to the user query • A ranking is based on fundamental premises regarding the notion of relevance, such as: • common sets of index terms • sharing of weighted terms • likelihood of relevance • Eachset of premises leads to a distinct IR model

4. Algebraic Set Theoretic Generalized Vector (Space) Latent Semantic Index Neural Networks Structured Models Fuzzy Extended Boolean Non-Overlapping Lists Proximal Nodes Classic Models Probabilistic Boolean Vector (Space) Probabilistic Inference Network Belief Network Browsing Flat Structure Guided Hypertext IR Models U s e r T a s k Retrieval Browsing

5. Basic Concepts Each document is described by a set of representative keywords or index terms Index terms are document words (i.e. nouns), which have meaning by themselves for remembering the main themes of a document However, search engines assume that all words are index terms (full text representation)

6. Basic Concepts • Not all terms are equally useful for representing the document contents • The importance of the index terms is represented by weights associated to them • Let • kibe an index term • djbe a document • wij is a weight associated with (ki,dj ),which quantifies the importance of ki for describing the contents of dj

7. The Vector (Space) Model • Define: • wij > 0 whenever ki dj • wiq>= 0 associated with the pair (ki,q) • vec(dj ) = (w1j, w2j, ..., wtj),document vectorof dj • vec(q) = (w1q, w2q, ..., wtq),query vectorof q • The unitary vectors vec(di) and vec(qj) are assumed to be orthonormal (i.e., index terms are assumed to occur independently within the documents) • Queries and documents are represented as weighted vectors

8. The Vector (Space) Model j dj q  i Sim(q,dj ) = cos() = [vec(dj) vec(q)] / |dj |  |q| = [ti=1wij wiq ] /  ti=1wij2   ti=1wiq2 where  is the inner product operator & |q| is the length of q Since wij0and wiq 0, 1 sim(q, dj )  0 A document is retrieved even if it matches the query terms only partially

9. The Vector (Space) Model • Sim(q, dj ) = [ti=1 wij wiq ] / |dj |  |q| • How to compute the weights wijand wiq? • A good weight must take into account two effects: quantification of intra-document contents (similarity) • tf factor, the term frequency within a document quantification of inter-documents separation (dissi- milarity) • idf factor, the inverse document frequency • wij = tf(i, j)  idf(i)

10. The Vector (Space) Model • Let, • N be the total number of documents in the collection • nibe the number of documents which containki • freq(i, j), theraw frequency of kiwithin dj • A normalizedtf factor is given by • f(i, j) = freq(i, j) / max(freq(l, j)), • where the maximum is computed over all terms which occur within the document dj • The inverse document frequency (idf)factor is • idf(i) = 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 term ki.

11. The Vector (Space) Model • The best term-weighting schemes use weights which are give by • wij = f(i, j) log(N / ni) • the strategy is called a tf-idf weighting scheme • For the query term weights, a suggestion is • Wiq = (0.5 + [0.5 freq(i, q) / max(freq(l, q))])  log(N/ni) • The vector model with tf-idf weights is a good ranking strategy with general collections • The VSM is usually as good as the known ranking alternatives. It is also simple and fast to compute

12. The Vector (Space) Model • Advantages: • term-weighting improves quality of the answer set • partial matching allows retrieval of documents that approximate the query conditions • cosine ranking formula sorts documents according to degree of similarity to the query • A popular IR model because of its simplicity & speed • Disadvantages: • assumes mutuallyindependence of index terms (??); • not clear that this is bad though

13. Naïve Bayes Classifier CS 652 Information Extraction and Integration

14. Bayes Theorem The basic starting point for inference problems using probability theory as logic

15. Bayes Theorem .008 .992 .98 .02 .03 .97 P(+|cancer)P(cancer)=(.98).008=.0078 P(+|~cancer)P(~cancer)=(.03).992=.0298

16. Basic Formulas for Probabilities

17. Naïve Bayes Classifier

18. Naïve Bayes Classifier

19. Naïve Bayes Classifier

20. Naïve Bayes Algorithm

21. Naïve Bayes Subtleties

22. Naïve Bayes Subtleties m-estimate of probability

23. Learning to Classify Text • Classify text into manually defined groups • Estimate probability of class membership • Rank by relevance • Discover grouping, relationships • Between texts • Between real-world entities mentioned in text

24. Learn_Naïve_Bayes_Text(Example, V)

25. Calculate_Probability_Terms

26. Classify_Naïve_Bayes_Text(Doc)

27. How to Improve • More training data • Better training data • Better text representation • Usual IR tricks (term weighting, etc.) • Manually construct good predictor features • Hand off hard cases to human being