Boolean retrieval & basics of indexing CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2014 Most slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276, Stanford)
Boolean retrieval model 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 2
Sec. 1.3 Boolean queries: Exact match 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. 1.1 Example: Plays of Shakespeare 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 4
Example: Plays of Shakespeare Term-document incidence matrix 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 1 if play contains word, 0 otherwise 5
Sec. 1.1 Incidence vectors So we 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. 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 6 worser 1 0 1 1 1 0
Sec. 1.1 Answers to query Brutus AND Caesar but NOT Calpurnia 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. 7
Sec. 1.1 Bigger collections Number of docs: N = 10 6 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 8
Sec. 1.1 Can t build the 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. Why? What s a better representation? We only record the 1 positions. 9
Sec. 1.2 Inverted index For each 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? 1 2 4 11 31 45 173174 1 2 4 5 6 16 57 132 2 31 54 101 What happens if the word is added to doc 14? 10
Sec. 1.2 Inverted index We need 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 Posting Brutus 1 2 4 11 31 45 173174 Caesar 1 2 4 5 6 16 57 132 Calpurnia 2 31 54 101 Dictionary Postings Sorted by docid 11
Sec. 1.2 Inverted index construction Docs to be indexed Friends, Romans, countrymen. Tokenizer Token stream Friends Romans Countrymen More on these later. Linguistic modules 12 Modified tokens Inverted index Indexer friend roman countryman friend roman countryman 2 4 1 2 13 16
Sec. 1.2 Indexer steps: Token sequence Sequence of (Modified token, Document ID) pairs. Doc 1 Doc 2 I did enact Julius Caesar I was killed i' the Capitol; Brutus killed me. So let it be with Caesar. The noble Brutus hath told you Caesar was ambitious 13
Sec. 1.2 Indexer steps: Sort Sort by terms And then docid Core indexing step 14
Sec. 1.2 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. 15
Sec. 1.2 Where do we pay in storage? Lists of docids Terms and counts 16 Pointers
Sec. 3.1 A naïve dictionary An array of structure: char[20] int Postings * 17
Sec. 3.1 Dictionary data structures Two main choices: Hashtables Search trees Some IR systems use hashtables, some trees 18
Sec. 3.1 Hashtables Each vocabulary term is hashed to an integer Pros: Lookup is faster than for a tree: O(1) Cons: No easy way to find minor variants: judgment/judgement No prefix search tolerant retrieval If vocabulary keeps growing, need to occasionally rehash everything 19
Sec. 3.1 Binary tree a-m Root n-z a-hu hy-m n-sh si-z 20
Sec. 5.2 Binary tree Terms Freq. Postings ptr. a 656,265 aachen 65.. zulu 221 Dictionary search structure 21
Sec. 3.1 Trees Simplest: binary tree More usual: B-trees Pros: Solves the prefix problem (terms starting with hyp) Cons: Slower: O(log M) [and this requires balanced tree] Rebalancing binary trees is expensive But B-trees mitigate the rebalancing problem 22
Sec. 1.3 The index we just built So far, we built the index How do we process a query? What kinds of queries can we process? 23
Sec. 1.3 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: Brutus Caesar 2 4 8 16 32 64 1 2 3 5 8 13 21 128 34 24
Sec. 1.3 The merge Walk through the two postings simultaneously, in time linear in the total number of postings entries 2 4 8 41 48 64 128 1 2 3 8 11 17 21 31 2 8 If list lengths are x and y, merge takes O(x+y) operations. Crucial: postings sorted by docid. 25
Intersecting two postings lists (a merge algorithm) 26
Sec. 1.3 Boolean queries: More general 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)? 27
Sec. 1.3 Merging What about an arbitrary 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? 28
Sec. 1.3 Query optimization What is 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 2 4 8 16 32 64 128 1 2 3 5 8 16 21 34 13 16 Query: Brutus AND Calpurnia AND Caesar 29 29
Sec. 1.3 Query optimization example Process in order of increasing freq: start with smallest set, then keep cutting further. This is why we kept document freq. in dictionary Brutus Caesar Calpurnia 2 4 8 16 32 64 128 1 2 3 5 8 16 21 34 13 16 Execute the query as (Calpurnia AND Brutus) AND Caesar. 30
Sec. 1.3 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. 31
Exercise Recommend a query processing order for (tangerine OR trees) AND (marmalade OR skies) AND (kaleidoscope OR eyes) Term Freq eyes 213312 kaleidoscope 87009 marmalade 107913 skies 271658 tangerine 46653 trees 316812 32
Query processing exercises Exercise: If the query is friends AND romans AND (NOT countrymen), how could we use the freq of countrymen? Exercise: Extend the merge to an arbitrary Boolean query. Can we always guarantee execution in time linear in the total postings size? Hint: Begin with the case of a Boolean formula query where each term appears only once in the query. 33
Example of extended Boolean model: WestLaw http://www.westlaw.com/ Sec. 1.4 Largest commercial (paying subscribers) legal search service (started 1975; ranking added 1992) Tens of terabytes of data; 700,000 users Majority of users still use boolean queries Example query: What is the statute of limitations in cases involving the federal tort claims act? LIMIT! /3 STATUTE ACTION /S FEDERAL /2 TORT /3 CLAIM /k = within k words, /S = in same sentence 34
Advantages of exact match 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 36
Disadvantages of the Boolean Model 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 As a consequence, frequently returns either too few or too many docs in response to a user query Difficulty increases with collection size Retrieval based on binary decision criteria No ranking of the docs is provided (absence of a grading scale) Index term weighting can provide a substantial improvement 37
Ranking results in advanced 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. 38
39 Text operations
Recall the basic indexing pipeline Document Friends, Romans, countrymen. Tokenizer Token stream Friends Romans Countrymen Linguistic modules Modified tokens friend roman countryman Indexer Inverted index friend roman countryman 40 2 4 1 2 13 16
Text operations Tokenization Stop word removal Normalization Stemming or lemmatization Equivalence classes Example1: case folding Example2: using thesauri (or Soundex) to find equivalence classes of synonyms and homonyms [later lectures] 41
Sec. 2.1 Parsing a document What format is it in? pdf/word/excel/html? What language is it in? What character set is in use? Each of these is a classification problem, which we will study later in the course. But these tasks are often done heuristically 42
Sec. 2.1 Complications: Format/language Corpus can include docs from different languages A single index may have to contain terms of several languages. Sometimes a doc or its components can contain multiple languages/formats French email with a German pdf attachment. What is a unit document? (indexing granularity) A file? An email? (Perhaps one of many in an mbox.) An email with 5 attachments? A group of files (PPT or LaTeX as HTML pages) 43
Sec. 2.2.1 Tokenization Input: Friends, Romans, Countrymen Output: Tokens Friends Romans Countrymen Each such token is now a candidate for an index entry, after further processing 44
Sec. 2.2.1 Tokenization Issues in tokenization: Finland s capital Finland? Finlands? Finland s? Hewlett-Packard Hewlett and Packard as two tokens? co-education lower-case state-of-the-art: break up hyphenated sequence. It can be effective to get the user to put in possible hyphens San Francisco: one token or two? How do you decide it is one token? 45
Sec. 2.2.1 Tokenization: Numbers Examples 3/12/91 Mar. 12, 1991 12/3/91 55 B.C. B-52 My PGP key is 324a3df234cb23e (800) 234-2333 Often have embedded spaces Older IR systems may not index numbers But often very useful e.g., looking up error codes/stack traces on the web Will often index meta-data separately Creation date, format, etc. 46
Sec. 2.2.1 Tokenization: Language issues French L'ensemble: one token or two? L? L? Le? German noun compounds are not segmented Lebensversicherungsgesellschaftsangestellter life insurance company employee German retrieval systems benefit greatly from a compound splitter module Can give a 15% performance boost for German 47
Sec. 2.2.1 Tokenization: Language issues Chinese and Japanese have no spaces between words: 莎拉波娃现在居住在美国东南部的佛罗里达 Not always guaranteed a unique tokenization Further complicated in Japanese, with multiple alphabets intermingled Dates/amounts in multiple formats フォーチュン 500 社は情報不足のため時間あた $500K( 約 6,000 万円 ) Katakana Hiragana Kanji Romaji End-user can express query entirely in hiragana! 48
Sec. 2.2.1 Tokenization: Language issues Arabic (or Hebrew) is basically written right to left, but with certain items like numbers written left to right Words are separated, but letter forms within a word form complex ligatures Algeria achieved its independence in 1962 after 132 years of French occupation. With Unicode, the surface presentation is complex, but the stored form is straightforward 49
Sec. 2.2.2 Stop words Stop list: exclude from dictionary the commonest words. They have little semantic content: the, a, and, to, be There are a lot of them: ~30% of postings for top 30 words But the trend is away from doing this: Good compression techniques (IIR, Chapter 5) the space for including stop words in a system is very small Good query optimization techniques (IIR, Chapter 7) pay little at query time for including stop words. You need them for: Phrase queries: King of Denmark Various song titles, etc.: Let it be, To be or not to be Relational queries: flights to London 50
Sec. 2.2.3 Normalization to terms Normalize words in indexed text (also query) U.S.A. USA Term is a (normalized) word type, which is an entry in our IR system dictionary We most commonly implicitly define equivalence classes of terms by, e.g., deleting periods to form a term U.S.A., USA USA deleting hyphens to form a term anti-discriminatory, antidiscriminatory antidiscriminatory 51
Sec. 2.2.3 Normalization: Other languages Accents: e.g., French résumé vs. resume. Umlauts: e.g., German: Tuebingen vs. Tübingen Should be equivalent Most important criterion: How are your users like to write their queries for these words? Users often may not type them (even in languages that standardly have accents) Often best to normalize to a de-accented term Tuebingen, Tübingen, Tubingen Tubingen 52
Sec. 2.2.3 Normalization: Other languages Normalization of things like date forms 7 月 30 日 vs. 7/30 Japanese use of kana vs. Chinese characters Tokenization and normalization may depend on the language (intertwined with language detection) Crucial: Need to normalize indexed text as well as query terms into the same form Is this German mit? 53
Sec. 2.2.3 Case folding Reduce all letters to lower case exception: upper case in mid-sentence? e.g., General Motors Fed vs. fed SAIL vs. sail Often best to lower case everything, since users will use lowercase regardless of correct capitalization Google example: Query C.A.T. #1 result was for cat not Caterpillar Inc. 54
Sec. 2.2.3 Normalization to terms An alternative to equivalence classing is to do asymmetric expansion An example of where this may be useful Enter: window Search: window, windows Enter: windows Search: Windows, windows, window Enter: Windows Search: Windows Potentially more powerful, but less efficient 55
Thesauri and soundex Do we handle synonyms and homonyms? E.g., by hand-constructed equivalence classes car = automobile color = colour We can rewrite to form equivalence-class terms When the doc contains automobile, index it under car-automobile (and/or vice-versa) Or we can expand a query When the query contains automobile, look under car as well What about spelling mistakes? One approach is soundex, which forms equivalence classes of words based on phonetic heuristics (More Chapter 3 & 9) 56
Sec. 2.2.4 Lemmatization Reduce inflectional/variant forms to base form, e.g., am, are, is be car, cars, car's, cars' car the boy's cars are different colors the boy car be different color Lemmatization implies doing proper reduction to dictionary headword form 57
Sec. 2.2.4 Stemming Reduce terms to their roots before indexing Stemming: crude affix chopping language dependent e.g., automate(s), automatic, automation all reduced to automat. for example compressed and compression are both accepted as equivalent to compress. for exampl compress and compress ar both accept as equival to compress 58
Sec. 2.2.4 Porter s algorithm Commonest algorithm for stemming English Results suggest it s at least as good as other stemming options Conventions + 5 phases of reductions phases applied sequentially each phase consists of a set of commands sample convention: Of the rules in a compound command, select the one that applies to the longest suffix. 59
Sec. 2.2.4 Porter s algorithm: Typical rules sses ss ies i ational ate tional tion Rules sensitive to the measure of words (m>1) EMENT replacement replac cement cement 60
Sec. 2.2.4 Other stemmers Other stemmers exist, e.g., Lovins stemmer http://www.comp.lancs.ac.uk/computing/research/stemming/general/lovins.htm Single-pass, longest suffix removal (about 250 rules) Full morphological analysis at most modest benefits for retrieval Do stemming and other normalizations help? English: very mixed results. Helps recall but harms precision operative (dentistry) oper operational (research) oper operating (systems) oper Definitely useful for Spanish, German, Finnish, 30% performance gains for Finnish! 61
Sec. 2.2.4 Language-specificity Many of the above features embody transformations that are Language-specific Often, application-specific These are plug-in addenda to the indexing process Both open source and commercial plug-ins are available for handling these 62
Sec. 2.2 Dictionary entries first cut 時間 These may be grouped by language (or not ). More on this in ranking/query processing. 63
Resources IIR 1 IIR 2.1-2.2 MIR 9.2 Porter s stemmer: http://www.tartarus.org/~martin/porterstemmer/ 64