Retrieval by Content. Part 2: Text Retrieval Term Frequency and Inverse Document Frequency. Srihari: CSE 626 1

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Edgar Holt
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1 Retrieval by Content Part 2: Text Retrieval Term Frequency and Inverse Document Frequency Srihari: CSE 626 1

2 Text Retrieval Retrieval of text-based information is referred to as Information Retrieval (IR) Used by text search engines over the internet Text is composed of two fundamental units documents and terms Document: journal paper, book, messages, source code, web pages Term: word, word-pair, phrase within a document Srihari: CSE 626 2

3 Representation of Text Capability to retain as much of the semantic content of the data as possible Computation of distance measures between queries and documents efficiently Natural language processing is difficult, e.g., Polysemy (same word with different meanings) Synonymy (several different ways to describe the same thing) IR systems is use today do not rely on NLP techniques Instead rely on vector of term occurrences Srihari: CSE 626 3

4 Vector Space Representation Document-Term Matrix t1 t2 t3 t4 t5 t6 D D D D D D D D D D Terms used In Database Related t1 t2 t3 t4 t5 t6 database SQL index regression likelihood linear Regression Terms d ij represents number of times that term appears in that document Srihari: CSE 626 4

5 Cosine Distance between Document Vectors Document-Term Matrix t1 t2 t3 t4 t5 t6 D D D D D D D D D D d c Cosine Distance ( D, D i j ) = T k = 1 d ik d jk T T 2 dik k = 1 k = 1 Cosine of the angle between two vectors Equivalent to their inner product after each has been normalized to have unit Higher values for more similar vectors Reflects similarity in terms of relative distributions of components d 2 jk Cosine is not influenced by one document being small compared Srihari: CSE to the other (as in the case of Euclidean)

Euclidean vs Cosine Distance Database Regression Document-Term Matrix t1 t2 t3 t4 t5 t6 D1 24 21 9 0 0 3

0 0 22 4 2 D9 1 0 0 34 27 25 D10 6 0 0 17 4 23 Document Document Euclidean White = 0 Black = max distance

Document (database documents and regression documents) Euclidean: 3,4 closer to 6-9 than to 5 since 3,4,

6 Euclidean vs Cosine Distance Database Regression Document-Term Matrix t1 t2 t3 t4 t5 t6 D D D D D D D D D D Document Document Euclidean White = 0 Black = max distance Document Number Cosine White = LargerCosine (or smaller angle) Both show two clusters of light sub-blocks Document (database documents and regression documents) Euclidean: 3,4 closer to 6-9 than to 5 since 3,4, 6-9 are closer to origin than 5 Cosine emphasizes relative contributions of individual terms Srihari: CSE 626 6

7 Properties of Document-Term Matrix Each vector D i is a surrogate document for the original document Entire document-term matrix (N x T) is sparse, with only 0.03% of cells being non-zero in TREC collection Each document is a vector in terms-space Due to sparsity, original text documents are represented as an inverted file structure (rather than matrix directly) Each term t j points to a list of N numbers describing term occurrences for each document Generating document-term matix is non-trivial Are plural and singular terms counted? Are very common words used as terms? Srihari: CSE 626 7

8 Vector Space Representation of Queries Queries Expressed using same term-based representation as documents Query is a document with very few terms Vector space representation of queries t1 database = (1,0,0,0,0,0) t2 SQL = (0,1,0,0,0,0) t3 regression = (0,0,0,1,0,0) t4 Terms database SQL index regression t5 t6 likelihood linear Srihari: CSE 626 8

9 Query match against database using cosine distance database SQL index regression likelihood linear D D D D D D D D D D database = (1,0,0,0,0,0) closest match is D2 SQL = (0,1,0,0,0,0) closest match is D3 regression = (0,0,0,1,0,0) closest match is D9 Use of cosine distance results in D2, D3 and D9 ranked as closest Srihari: CSE 626 9

10 Weights in Vector Space Model d ik is the weight for the k th term Many different choices for weights in IR literature Boolean approach of setting weights to 1 if term occurs and 0 if it doesn t favors larger documents since larger document is more likely to include query term somewhere TF-IDF weighting scheme is popular TF (term frequency) is same as seen earlier IDF (inverse document frequency) favors terms that occur in relatively few documents database SQL index regression likelihood linear D D D D D D D D D D Srihari: CSE

11 Inverse Document Frequency of a Term Definition log( N N = total number of documents n j = number of documents containing term j ( / N) is n j the fraction of / n j ) documents containing term j IDF favors terms that occur in relatively few documents Example of IDF IDF weights of terms (using natural logs): 0.105,0.693,0.511,0.693,0.357,0.69 Term database occurs in many documents and is given least weight regression occurs in fewest documents and given highest weight database SQL index regression likelihood linear D D D D D D D D D Srihari: CSE D

12 TF-IDF Weighting of Terms TF-IDF weighting scheme TF = term frequency, denoted TF(d,t) IDF = inverse document frequency, IDF(t) TF-IDF weight is the product of TF and IDF for a particular term in a particular document TF(d,t)IDF(t) Example is given next Srihari: CSE

13 TF-IDF Document Matrix TF (d,t) Document Matrix database SQL index regression likelihood linear D D D D D D D D D D IDF (t) weights (using natural logs): 0.105,0.693,0.511,0.693,0.357,0.69 TF-IDF Document Matrix Srihari: CSE

14 Classic Approach to Matching Queries to Documents Represent queries as term vectors 1s for terms occurring in the query and 0s everywhere else Represent term vectors for documents using TF- IDF for the vector components Use the cosine distance measure to rank the documents in terms of distance to query Has disadvantage that shorter documents have a better match with query terms Srihari: CSE

15 Document Retrieval with TF and TF-IDF TF: Document Term Matrix database SQL index regression likelihood linear D D D D D D D D D D Query contains both database and index Q=(1,0,1,0,0,0) TF-IDF Document Matrix Document TF distance TF-IDF distance D D D D D D D D D D Max values for query (1,0,1,0,0,0) Cosine distance is high when there is a better match TF-IDF chooses D2 while TF chooses D5 Unclear why D5 is a better choice Cosine distance favors shorter documents Srihari: CSE (a disadvantage)

16 Comments on TF-IDF Method TF-IDF-based IR system first builds an inverted index with TF and IDF information Given a query (vector) lists some number of document vectors that are most similar to the query TF-IDF is superior in precision-recall compared to other weighting schemes Default baseline method for comparing performance Srihari: CSE

Boolean and Vector Space Retrieval Models

Boolean and Vector Space Retrieval Models Many slides in this section are adapted from Prof. Joydeep Ghosh (UT ECE) who in turn adapted them from Prof. Dik Lee (Univ. of Science and Tech, Hong Kong) 1