The vector space model
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The document discusses the vector space model for representing text documents and queries in information retrieval systems. It describes how documents and queries are represented as vectors of term weights, with each term being assigned a weight based on its frequency in the document or query. The vector space model allows documents and queries to be compared by calculating the similarity between their vector representations. Terms that are more frequent in a document and less frequent overall are given higher weights through techniques like TF-IDF weighting. This vector representation enables efficient retrieval of documents ranked by similarity to the query.
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The vector space model
- 1. The Vector space model Submitted By – Deeksha Agarwal Semester 5th University of Allahabad
- 2. Boolean Model Disadvantages • Similarity function is boolean ⁻ Exact-match only, no partial matches ⁻ Retrieved documents not ranked • All terms are equally important – Boolean operator usage has much more influence than a critical word • Query language is expressive but complicated
- 3. Statistical Models • A document is typically represented by a bag of words (unordered words with frequencies). • Bag = set that allows multiple occurrences of the same element.
- 4. 4 Statistical Retrieval • Retrieval based on similarity between query and documents. • Output documents are ranked according to similarity to query. • Similarity based on occurrence frequencies of keywords in query and document. • Automatic relevance feedback can be supported: – Relevant documents “added” to query. – Irrelevant documents “subtracted” from query.
- 5. 5 The Vector-Space Model • Documents and queries are both vectors • Each term, i, in a document or query, j, is given a real-valued weight, wij. • Both documents and queries are expressed as t- dimensional vectors: dj = (w1j, w2j, …, wtj)
- 6. 6 Graphic Representation Example: D1 = 2T1 + 3T2 + 5T3 D2 = 3T1 + 7T2 + T3 Q = 0T1 + 0T2 + 2T3 T3 T1 T2 D1 = 2T1+ 3T2 + 5T3 D2 = 3T1 + 7T2 + T3 Q = 0T1 + 0T2 + 2T3 7 32 5
- 7. 7 Document Collection • A collection of n documents can be represented in the vector space model by a term-document matrix. • An entry in the matrix corresponds to the “weight” of a term in the document; zero means the term has no significance in the document or it simply doesn’t exist in the document. T1 T2 …. Tt D1 w11 w21 … wt1 D2 w12 w22 … wt2 : : : : : : : : Dn w1n w2n … wtn
- 8. 8 Term Weights: Term Frequency • More frequent terms in a document are more important, i.e. more indicative of the topic. fij = frequency of term i in document j • May want to normalize term frequency (tf) by dividing by the frequency of the most common term in the document: tfij = fij / maxi{fij}
- 9. 9 Term Weights: Inverse Document Frequency • Terms that appear in many different documents are less indicative of overall topic. df i = document frequency of term i = number of documents containing term i idfi = inverse document frequency of term i, = log2 (N/ df i) (N: total number of documents)
- 10. 10 TF-IDF Weighting • A typical combined term importance indicator is tf-idf weighting: wij = tfij idfi = tfij log2 (N/ dfi) • A term occurring frequently in the document but rarely in the rest of the collection is given high weight. • Many other ways of determining term weights have been proposed. • Experimentally, tf-idf has been found to work well.
- 11. 11 Computing TF-IDF -- An Example Given a document containing terms with given frequencies: A(3), B(2), C(1) Assume collection contains 10,000 documents and document frequencies of these terms are: A(50), B(1300), C(250) Then: A: tf = 3/3; idf = log2(10000/50) = 7.6; tf-idf = 7.6 B: tf = 2/3; idf = log2 (10000/1300) = 2.9; tf-idf = 2.0 C: tf = 1/3; idf = log2 (10000/250) = 5.3; tf-idf = 1.8
- 12. THANKYOU
Editor's Notes
- #3: 1.Very rigid: AND means all; OR means any. 2.Difficult to express complex user requests. 3.Difficult to control the number of documents retrieved-All matched documents will be returned.5.Difficult to rank output-All matched documents logically satisfy the query. 7.Difficult to perform relevance feedback-a document is identified by the user as relevant or irrelevant, how should the query how should the query be modified?
- #9: if a term t appears often in a document, then a query containing t should retrieve that document. Zipf’s law: term frequency » 1/rank importance is inversely proportional to frequency of occurrence.
- #12: tfij = fij / maxi{fij}