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Ranking models in IR

Ranking models in IR. Key idea: We wish to return in order the documents most likely to be useful to the searcher To do this, we want to know which documents best satisfy a query If a document talks about a topic more than another, then it is a better match

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Ranking models in IR

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  1. Ranking models in IR • Key idea: • We wish to return in order the documents most likely to be useful to the searcher • To do this, we want to know which documents best satisfy a query • If a document talks about a topic more than another,then it is a better match • A query should then just specify terms that are relevant to the information need, without requiring that all of them must be present • Document relevant if it has a lot of the terms

  2. Binary term presence matrices • Record whether a document contains a word: document is binary vector in {0,1}v • What we have mainly assumed so far • Idea: Query satisfaction = overlap measure =

  3. Problems with overlap measure? • It doesn’t consider: • Term frequency (count) in document • Term scarcity in collection (document mention frequency) • Length of documents • (And queries: score not normalized)

  4. Digression: terminology • WARNING: In a lot of IR literature, “frequency” is used to mean “count” • Thus term frequency in IR literature is used to mean number of occurrences in a doc • Not divided by document length (which would actually make it a frequency) • We will conform to this misnomer • In saying term frequency we mean the number of occurrences of a term in a document.

  5. Overlap matching: Normalization • One can normalize in various ways: • Jaccard coefficient: • Cosine measure: • Questions: • What documents would score best using Jaccard against a typical query? • Does the cosine measure fix this problem?

  6. Count term-document matrices • We haven’t considered frequency of a word • Count of a word in a document: • Bag of words model • Document is a vector in ℕv • Raw frequencies below

  7. Bag of words view of a doc • Thus the doc • John is quicker than Mary. is indistinguishable from the doc • Mary is quicker than John. Which of the indexes discussed so far distinguish these two docs?

  8. Weighting term frequency: tf • What is the relative importance of • 0 vs. 1 occurrence of a term in a doc • 1 vs. 2 occurrences • 2 vs. 3 occurrences … • It seems that more is better, but a lot isn’t necessarily better than a few • Can just use raw score • Another option commonly used in practice:

  9. Score computation • Score for a query q = sum over terms t in q: • [Note: 0 if no query terms in document] • Can use wf instead of tf in the above • Still doesn’t consider term scarcity in collection • Does not consider length of document yet

  10. Weighting should depend on the term overall • Which of these tells you more about a doc? • 10 occurrences of hernia? • 10 occurrences of the? • Suggest looking at collection frequency (cf) • But document frequency (df) may be better: Word cf df ferrari 10422 17 insurance 10440 3997 Both “ferrari” and “insurance” occur the same # of time in corpus, but” insurance” occurs in far fewer documents! • Document frequency weighting is only possible in we know (static) collection frequency.

  11. tf x idf term weights • tf x idf measure combines: • term frequency (tf) • measure of term density in a doc • inverse document frequency (idf) • measure of discriminating power of term: its rarity across the whole corpus • could just be raw count of number of documents the term occurs in (idfi = 1/dfi) • but by far the most commonly used version is:

  12. Term Weight:= tf x idf (or tf.idf) • Assign a tf.idf weight to each term i in each document d • Increases with the number of occurrences withina doc • Increases with the rarity of the term acrossthe whole corpus What is the weight of a term that occurs in all of the docs?

  13. Real-valued term-document matrices • Function (scaling) of count of a word in a document: • Bag of words model • Each is a vector in ℝv • Here log-scaled tf.idf Note can be >1!

  14. Review • We compute tf.idf values for each term-doc pair • A doc can be viewed as a vector of tf.idf values • Dimensions = number of terms in lexicon • Thus far, documents either match a query or do not. • But how well does a document match a query? • How can we measure similarity between a query and document? • Gives rise to ranking and scoring • Vector space models • Relevance ranking

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