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![Answers to query
Antony and Cleopatra, Act III, Scene ii
Agrippa [Aside to DOMITIUS ENOBARBUS]: Why, Enobarbus,
When Antony found Julius Caesar dead,
He cried almost to roaring; and he wept
When at Philippi he found Brutus slain.
Hamlet, Act III, Scene ii
Lord Polonius: I did enact Julius Caesar I was killed i' the
Capitol; Brutus killed me.
8
Sec. 1.1
Brutus AND Caesar but NOT Calpurnia](https://image.slidesharecdn.com/booleanirandindexing-230520190147-2c0d37b3/85/Boolean-IR-and-Indexing-pptx-8-320.jpg)
![A naïve dictionary
An array of struct:
char[20] int Postings *
Sec. 3.1
18](https://image.slidesharecdn.com/booleanirandindexing-230520190147-2c0d37b3/85/Boolean-IR-and-Indexing-pptx-18-320.jpg)
Boolean IR and Indexing.pptx
- 1. Boolean retrieval &basics of indexing Modern Information Retrieval University of Qom Z. Imanimehr Spring 2023
- 2. Boolean retrieval model 2 Query: Boolean expressions Boolean queries use AND, OR and NOT to join query terms Views each doc as a set of words Term-incidence matrix is sufficient Shows presence or absence of terms in each doc Perhaps the simplest model to build an IR system on
- 3. Boolean queries: Exactmatch In pure Boolean model, retrieved docs are not ranked Result is a set of docs. It is precise or exact match (docs match condition or not). Primary commercial retrieval tool for 3 decades (Until 1990’s). Many search systems you still use are Boolean: Email, library catalog, Mac OS X Spotlight 3 Sec. 1.3
- 4. The classic searchmodel Task Info Need Query Results SEARCH ENGINE Query Refinement Get rid of mice in a politically correct way Info about removing mice without killing them mouse trap Misconception? Misformulation? Corpus 4
- 5. Example: Plays ofShakespeare Which plays of Shakespeare contain the words Brutus AND Caesar but NOT Calpurnia? scanning all of Shakespeare’s plays for Brutus and Caesar, then strip out those containing Calpurnia? The above solution cannot be the answer for large corpora (computationally expensive) Efficiency is also an important issue (along with the effectiveness) Index: data structure built on the text to speed up the searches 5 Sec. 1.1
- 6. Example: Plays ofShakespeare Term-document incidence matrix Antony and Cleopatra Julius Caesar The Tempest Hamlet Othello Macbeth Antony 1 1 0 0 0 1 Brutus 1 1 0 1 0 0 Caesar 1 1 0 1 1 1 Calpurnia 0 1 0 0 0 0 Cleopatra 1 0 0 0 0 0 mercy 1 0 1 1 1 1 worser 1 0 1 1 1 0 1 if play contains word, 0 otherwise Sec. 1.1 6
- 7. Incidence vectors Sowe have a 0/1 vector for each term. Brutus AND Caesar but NOT Calpurnia To answer query: take the vectors for Brutus, Caesar and Calpurnia (complemented) bitwise AND. 110100 AND 110111 AND 101111 = 100100. 7 Sec. 1.1 Antony and Cleopatra Julius Caesar The Tempest Hamlet Othello Macbeth Antony 1 1 0 0 0 1 Brutus 1 1 0 1 0 0 Caesar 1 1 0 1 1 1 Calpurnia 0 1 0 0 0 0 Cleopatra 1 0 0 0 0 0 mercy 1 0 1 1 1 1 worser 1 0 1 1 1 0
- 8. Answers to query Antony and Cleopatra, Act III, Scene ii Agrippa [Aside to DOMITIUS ENOBARBUS]: Why, Enobarbus, When Antony found Julius Caesar dead, He cried almost to roaring; and he wept When at Philippi he found Brutus slain. Hamlet, Act III, Scene ii Lord Polonius: I did enact Julius Caesar I was killed i' the Capitol; Brutus killed me. 8 Sec. 1.1 Brutus AND Caesar but NOT Calpurnia
- 9. Bigger collections Numberof docs: N = 106 Average length of a doc≈ 1000 words No. of distinct terms: M = 500,000 Average length of a word ≈ 6 bytes including spaces/punctuation 6GB of data 9 Sec. 1.1
- 10. Sparsity of Term-documentincidence matrix 500K x 1M matrix has half-a-trillion 0’s and 1’s. But it has no more than one billion 1’s. matrix is extremely sparse. so a minimum of 99.8% of the cells are zero. What’s a better representation? We only record the 1 positions. 10 Why? Sec. 1.1
- 11. Inverted index Foreach term t, store a list of all docs that contain t. Identify each by a docID, a document serial number Can we use fixed-size arrays for this? 11 Brutus Calpurnia Caesar 1 2 4 5 6 16 57 132 1 2 4 11 31 45 173 2 31 What happens if the word Caesar is added to doc 14? Sec. 1.2 174 54 101
- 12. Inverted index Weneed variable-size postings lists On disk, a continuous run of postings is normal and best In memory, can use linked lists or variable length arrays Some tradeoffs in size/ease of insertion 12 Dictionary Postings Sorted by docID Posting Sec. 1.2 Brutus Calpurnia Caesar 1 2 4 5 6 16 57 132 1 2 4 11 31 45 173 2 31 174 54 101
- 13. Tokenizer Token stream FriendsRomans Countrymen Inverted index construction Linguistic modules Modified tokens friend roman countryman Indexer Inverted index friend roman countryman 2 4 2 13 16 1 We will see more on these later. Docs to be indexed Friends, Romans, countrymen. Sec. 1.2 13
- 14. Indexer steps: Tokensequence Sequence of (Modified token, Document ID) pairs. I did enact Julius Caesar I was killed i' the Capitol; Brutus killed me. Doc 1 So let it be with Caesar. The noble Brutus hath told you Caesar was ambitious Doc 2 Sec. 1.2 14
- 15. Indexer steps: Sort Sort by terms And then docID Core indexing step Sec. 1.2 15
- 16. Indexer steps: Dictionary& Postings Multiple term entries in a single doc are merged. Split into Dictionary and Postings Document frequency information is added. Why frequency? Will discuss later. Sec. 1.2 16
- 17. Where do wepay in storage? 17 Pointers Terms and counts Sec. 1.2 Lists of docIDs
- 18. A naïve dictionary An array of struct: char[20] int Postings * Sec. 3.1 18
- 19. Query processing: AND Consider processing the query: Brutus AND Caesar Locate Brutus in the dictionary; Retrieve its postings. Locate Caesar in the dictionary; Retrieve its postings. “Merge” (intersect) the two postings: 19 128 34 2 4 8 16 32 64 1 2 3 5 8 13 21 Brutus Caesar Sec. 1.3
- 20. The merge Walkthrough the two postings simultaneously, in time linear in the total number of postings entries 20 If list lengths are x and y, merge takes O(x+y) operations. Crucial: postings sorted by docID. Sec. 1.3 128 31 2 4 8 41 48 64 1 2 3 8 11 17 21 Brutus Caesar 2 8
- 21. Intersecting two postingslists (a “merge” algorithm) 21
- 22. Boolean queries: Moregeneral merges Exercise: Adapt the merge for the queries: Brutus AND NOT Caesar Brutus OR NOT Caesar Can we still run through the merge in time 𝑂(𝑥 + 𝑦)? 22 Sec. 1.3
- 23. Merging What about anarbitrary Boolean formula? (Brutus OR Caesar) AND NOT (Antony OR Cleopatra) Can we merge in “linear” time for general Boolean queries? Linear in what? Can we do better? 23 Sec. 1.3
- 24. Query optimization Whatis the best order for query processing? Consider a query that is an AND of 𝑛 terms. For each of the 𝑛 terms, get its postings, then AND them together. Brutus Caesar Calpurnia 1 2 3 5 8 16 21 34 2 4 8 16 32 64 128 13 16 Query: Brutus AND Calpurnia AND Caesar 24 Sec. 1.3 24
- 25. Query optimization example Process in order of increasing freq: start with smallest set, then keep cutting further. 25 This is why we kept document freq. in dictionary Execute the query as (Calpurnia AND Brutus) AND Caesar. Sec. 1.3 Brutus Caesar Calpurnia 1 2 3 5 8 16 21 34 2 4 8 16 32 64 128 13 16
- 26. More general optimization Example: (madding OR crowd) AND (ignoble OR strife) Get doc frequencies for all terms. Estimate the size of each OR by the sum of its doc. freq.’s (conservative). Process in increasing order of OR sizes. 26 Sec. 1.3
- 27. Exercise 27 Recommend aquery processing order for (tangerine OR trees) AND (marmalade OR skies) AND (kaleidoscope OR eyes) Which two terms should we process first? Term Freq eyes 213312 kaleidoscope 87009 marmalade 107913 skies 271658 tangerine 46653 trees 316812
- 28. Summary of BooleanIR: Advantages of exact match 28 It can be implemented very efficiently Predictable, easy to explain precise semantics Structured queries for pinpointing precise docs neat formalism Work well when you know exactly (or roughly) what the collection contains and what you’re looking for
- 29. Summary of BooleanIR: Disadvantages of the Boolean Model 29 Query formulation (Boolean expression) is difficult for most users Too simplistic Boolean queries by most users AND, OR as opposite extremes in a precision/recall tradeoff Usually either too few or too many docs in response to a user query Retrieval based on binary decision criteria No ranking of the docs is provided Difficulty increases with collection size
- 30. Ranking results inadvanced IR models Boolean queries give inclusion or exclusion of docs. Results of queries in Boolean model as a set Modern information retrieval systems are no longer based on the Boolean model Often we want to rank/group results Need to measure proximity from query to each doc. Index term weighting can provide a substantial improvement 30
- 31. 31 Phrase and proximityqueries: positional indexes
- 32. Phrase queries Example:“stanford university” “I went to university at Stanford” is not a match. Easily understood by users One of the few “advanced search” ideas that works At least 10% of web queries are phrase queries Many more queries are implicit phrase queries such as person names entered without use of double quotes. It is not sufficient to store only the doc IDs in the posting lists Sec. 2.4 32
- 33. Approaches for phrasequeries 33 Indexing bi-words (two word phrases) Positional indexes Full inverted index
- 34. Biword indexes Indexevery consecutive pair of terms in the text as a phrase E.g., doc :“Friends, Romans, Countrymen” would generate these biwords: “friends romans” , “romans countrymen” Each of these biwords is now a dictionary term Two-word phrase query-processing is now immediate. Sec. 2.4.1 34
- 35. Biword indexes: Longerphrase queries Longer phrases are processed as conjunction of biwords Query: “stanford university palo alto” can be broken into the Boolean query on biwords: “stanford university” AND “university palo” AND “palo alto” Can have false positives! Without the docs, we cannot verify that the docs matching the above Boolean query do contain the phrase. Sec. 2.4.1 35
- 36. Issues for biwordindexes False positives (for phrases with more than two words) Index blowup due to bigger dictionary Infeasible for more than biwords, big even for biwords Biword indexes are not the standard solution (for all biwords) but can be part of a compound strategy Sec. 2.4.1 36
- 37. Positional index Inthe postings, store for each term the position(s) in which tokens of it appear: <term, doc freq.; doc1: position1, position2 … ; doc2: position1, position2 … ; …> Sec. 2.4.2 37 <be: 993427; 1: 7, 18, 33, 72, 86, 231; 2: 3, 149; 4: 17, 191, 291, 430, 434; 5: 363, 367, …> Which of docs 1,2,4,5 could contain “to be or not to be”?
- 38. Positional index Forphrase queries, we use a merge algorithm recursively at the doc level We need to deal with more than just equality of docIDs: Phrase query: find places where all the words appear in sequence Proximity query: to find places where all the words close enough Sec. 2.4.2 38
- 39. Processing a phrasequery: Example Query: “to be or not to be” Extract inverted index entries for: to, be, or, not Merge: find all positions of “to”, i, i+4, “be”, i+1, i+5, “or”, i+2, “not”, i+3. to: <2:1,17,74,222,551>; <4:8,16,190,429,433, 512>; <7:13,23,191>; ... be: <1:17,19>; <4:17,191,291,430,434>; <5:14,19,101>; ... or: <3:5,15,19>; <4:5,100,251,431,438>; <7:17,52,121>; ... not: <4:71,432>; <6:20,85>; ... Sec. 2.4.2 39
- 40. Positional index: Proximityqueries k word proximity searches Find places where the words are within k proximity Positional indexes can be used for such queries as opposed to biword indexes Exercise: Adapt the linear merge of postings to handle proximity queries. Can you make it work for any value of k? Sec. 2.4.2 40
- 41.
- 42. Positional index: size You can compress position values/offsets Nevertheless, a positional index expands postings storage substantially Positional index is now standardly used because of the power and usefulness of phrase and proximity queries … used explicitly or implicitly in a ranking retrieval system. Sec. 2.4.2 42
- 43. Positional index: size Need an entry for each occurrence, not just once per doc Index size depends on average doc size Average web page has <1000 terms SEC filings, books, even some epic poems … easily 100,000 terms Consider a term with frequency 0.1% Why? 100 1 100,000 1 1 1000 Expected entries in Positional postings Expected Postings Doc size (# of terms) Sec. 2.4.2 43
- 44. Positional index: size(rules of thumb) A positional index is usually 2–4 as large as a non- positional index Positional index size 35–50% of volume of original text Caveat: all of this holds for “English-like” languages Sec. 2.4.2 44
- 45. Phrase queries: Combinationschemes Combining two approaches For queries like “Michael Jordan”, it is inefficient to merge positional postings lists Good queries to include in the phrase index: common queries based on recent querying behavior. and also for phrases whose individual words are common but the phrase is not such common Example: “The Who” Sec. 2.4.3 45
- 46. Phrase queries: Combinationschemes 46 Williams et al. (2004) evaluate a more sophisticated mixed indexing scheme needs (in average) ¼ of the time of using just a positional index needs 26% more space than having a positional index alone