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Dictionary data structures for inverted indexes

Dictionary data structures for inverted indexes
Introduction to Information Retrieval Introduction to Information Retrieval Dictionaries and tolerant retrieval www.ThesisScientist.comIntroduction to Information Retrieval Ch. 2 Recap of the previous lecture  The type/token distinction  Terms are normalized types put in the dictionary  Tokenization problems:  Hyphens, apostrophes, compounds, CJK  Term equivalence classing:  Numbers, case folding, stemming, lemmatization  Skip pointers  Encoding a treelike structure in a postings list  Biword indexes for phrases  Positional indexes for phrases/proximity queries www.ThesisScientist.comIntroduction to Information Retrieval Ch. 3 This lecture  Dictionary data structures  “Tolerant” retrieval  Wildcard queries  Spelling correction  Soundex www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Dictionary data structures for inverted indexes  The dictionary data structure stores the term vocabulary, document frequency, pointers to each postings list … in what data structure www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 A naïve dictionary  An array of struct: char20 int Postings 20 bytes 4/8 bytes 4/8 bytes  How do we store a dictionary in memory efficiently  How do we quickly look up elements at query time www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Dictionary data structures  Two main choices:  Hashtables  Trees  Some IR systems use hashtables, some trees www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Hashtables  Each vocabulary term is hashed to an integer  (We assume you’ve seen hashtables before)  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 do the expensive operation of rehashing everything www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Tree: binary tree Root am nz ahu hym nsh siz www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Tree: Btree nz ahu hym  Definition: Every internal nodel has a number of children in the interval a,b where a, b are appropriate natural numbers, e.g., 2,4. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.1 Trees  Simplest: binary tree  More usual: Btrees  Trees require a standard ordering of characters and hence strings … but we typically have one  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 Btrees mitigate the rebalancing problem www.ThesisScientist.comIntroduction to Information Retrieval WILDCARD QUERIES www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2 Wildcard queries:  mon: find all docs containing any word beginning with “mon”.  Easy with binary tree (or Btree) lexicon: retrieve all words in range: mon ≤ w moo  mon: find words ending in “mon”: harder  Maintain an additional Btree for terms backwards. Can retrieve all words in range: nom ≤ w non. Exercise: from this, how can we enumerate all terms meeting the wildcard query procent www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2 Query processing  At this point, we have an enumeration of all terms in the dictionary that match the wildcard query.  We still have to look up the postings for each enumerated term.  E.g., consider the query: seate AND filer This may result in the execution of many Boolean AND queries. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2 Btrees handle ’s at the end of a query term  How can we handle ’s in the middle of query term  cotion  We could look up co AND tion in a Btree and intersect the two term sets  Expensive  The solution: transform wildcard queries so that the ’s occur at the end  This gives rise to the Permuterm Index. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.1 Permuterm index  For term hello, index under:  hello, elloh, llohe, lohel, ohell, hello where is a special symbol.  Queries:  X lookup on X X lookup on X  X lookup on X X lookup on X  XY lookup on YX XYZ Exercise Query = helo X=hel, Y=o Lookup ohel www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.1 Permuterm query processing  Rotate query wildcard to the right  Now use Btree lookup as before.  Permuterm problem: ≈ quadruples lexicon size Empirical observation for English. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.2 Bigram (kgram) indexes  Enumerate all kgrams (sequence of k chars) occurring in any term  e.g., from text “April is the cruelest month” we get the 2grams (bigrams) a,ap,pr,ri,il,l,i,is,s,t,th,he,e,c,cr,ru, ue,el,le,es,st,t, m,mo,on,nt,h  is a special word boundary symbol  Maintain a second inverted index from bigrams to dictionary terms that match each bigram. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.2 Bigram index example  The kgram index finds terms based on a query consisting of kgrams (here k=2). m mace madden mo among amortize on along among www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.2 Processing wildcards  Query mon can now be run as  m AND mo AND on  Gets terms that match AND version of our wildcard query.  But we’d enumerate moon.  Must postfilter these terms against query.  Surviving enumerated terms are then looked up in the termdocument inverted index.  Fast, space efficient (compared to permuterm). www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.2.2 Processing wildcard queries  As before, we must execute a Boolean query for each enumerated, filtered term.  Wildcards can result in expensive query execution (very large disjunctions…)  pyth AND prog  If you encourage “laziness” people will respond Search Type your search terms, use ‘’ if you need to. E.g., Alex will match Alexander. www.ThesisScientist.com  Which web search engines allow wildcard queriesIntroduction to Information Retrieval SPELLING CORRECTION www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3 Spell correction  Two principal uses  Correcting document(s) being indexed  Correcting user queries to retrieve “right” answers  Two main flavors:  Isolated word  Check each word on its own for misspelling  Will not catch typos resulting in correctly spelled words  e.g., from  form  Contextsensitive  Look at surrounding words,  e.g., I flew form Heathrow to Narita. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3 Document correction  Especially needed for OCR’ed documents  Correction algorithms are tuned for this: rn/m  Can use domainspecific knowledge  E.g., OCR can confuse O and D more often than it would confuse O and I (adjacent on the QWERTY keyboard, so more likely interchanged in typing).  But also: web pages and even printed material have typos  Goal: the dictionary contains fewer misspellings  But often we don’t change the documents and instead fix the querydocument mapping www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3 Query misspellings  Our principal focus here  E.g., the query Alanis Morisett  We can either  Retrieve documents indexed by the correct spelling, OR  Return several suggested alternative queries with the correct spelling  Did you mean … www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.2 Isolated word correction  Fundamental premise – there is a lexicon from which the correct spellings come  Two basic choices for this  A standard lexicon such as  Webster’s English Dictionary  An “industryspecific” lexicon – handmaintained  The lexicon of the indexed corpus  E.g., all words on the web  All names, acronyms etc.  (Including the misspellings) www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.2 Isolated word correction  Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q  What’s “closest”  We’ll study several alternatives  Edit distance (Levenshtein distance)  Weighted edit distance  ngram overlap www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.3 Edit distance  Given two strings S and S , the minimum number of 1 2 operations to convert one to the other  Operations are typically characterlevel  Insert, Delete, Replace, (Transposition)  E.g., the edit distance from dof to dog is 1  From cat to act is 2 (Just 1 with transpose.)  from cat to dog is 3.  Generally found by dynamic programming.  See http://www.merriampark.com/ld.htm for a nice example plus an applet. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.3 Weighted edit distance  As above, but the weight of an operation depends on the character(s) involved  Meant to capture OCR or keyboard errors Example: m more likely to be mistyped as n than as q  Therefore, replacing m by n is a smaller edit distance than by q  This may be formulated as a probability model  Requires weight matrix as input  Modify dynamic programming to handle weights www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 Using edit distances  Given query, first enumerate all character sequences within a preset (weighted) edit distance (e.g., 2)  Intersect this set with list of “correct” words  Show terms you found to user as suggestions  Alternatively,  We can look up all possible corrections in our inverted index and return all docs … slow  We can run with a single most likely correction  The alternatives disempower the user, but save a round of interaction with the user www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 Edit distance to all dictionary terms  Given a (misspelled) query – do we compute its edit distance to every dictionary term  Expensive and slow  Alternative  How do we cut the set of candidate dictionary terms  One possibility is to use ngram overlap for this  This can also be used by itself for spelling correction. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 ngram overlap  Enumerate all the ngrams in the query string as well as in the lexicon  Use the ngram index (recall wildcard search) to retrieve all lexicon terms matching any of the query ngrams  Threshold by number of matching ngrams  Variants – weight by keyboard layout, etc. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 Example with trigrams  Suppose the text is november  Trigrams are nov, ove, vem, emb, mbe, ber.  The query is december  Trigrams are dec, ece, cem, emb, mbe, ber.  So 3 trigrams overlap (of 6 in each term)  How can we turn this into a normalized measure of overlap www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 One option – Jaccard coefficient  A commonlyused measure of overlap  Let X and Y be two sets; then the J.C. is XY /XY  Equals 1 when X and Y have the same elements and zero when they are disjoint  X and Y don’t have to be of the same size  Always assigns a number between 0 and 1  Now threshold to decide if you have a match  E.g., if J.C. 0.8, declare a match www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.4 Matching trigrams  Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd) lo alone lore sloth or border lore morbid rd border card ardent Standard postings “merge” will enumerate … Adapt this to using Jaccard (or another) measure. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.5 Contextsensitive spell correction  Text: I flew from Heathrow to Narita.  Consider the phrase query “flew form Heathrow”  We’d like to respond Did you mean “flew from Heathrow” because no docs matched the query phrase. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.5 Contextsensitive correction  Need surrounding context to catch this.  First idea: retrieve dictionary terms close (in weighted edit distance) to each query term  Now try all possible resulting phrases with one word “fixed” at a time  flew from heathrow  fled form heathrow  flea form heathrow  Hitbased spelling correction: Suggest the alternative that has lots of hits. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.5 Exercise  Suppose that for “flew form Heathrow” we have 7 alternatives for flew, 19 for form and 3 for heathrow. How many “corrected” phrases will we enumerate in this scheme www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.5 Another approach  Break phrase query into a conjunction of biwords (Lecture 2).  Look for biwords that need only one term corrected.  Enumerate only phrases containing “common” biwords. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.3.5 General issues in spell correction  We enumerate multiple alternatives for “Did you mean”  Need to figure out which to present to the user  The alternative hitting most docs  Query log analysis  More generally, rank alternatives probabilistically argmax P(corr query) corr  From Bayes rule, this is equivalent to argmax P(query corr) P(corr) corr Noisy channel Language model www.ThesisScientist.comIntroduction to Information Retrieval SOUNDEX www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.4 Soundex  Class of heuristics to expand a query into phonetic equivalents  Language specific – mainly for names  E.g., chebyshev tchebycheff  Invented for the U.S. census … in 1918 www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.4 Soundex – typical algorithm  Turn every token to be indexed into a 4character reduced form  Do the same with query terms  Build and search an index on the reduced forms  (when the query calls for a soundex match)  http://www.creativyst.com/Doc/Articles/SoundEx1/SoundEx1.htmTop www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.4 Soundex – typical algorithm 1. Retain the first letter of the word. 2. Change all occurrences of the following letters to '0' (zero): 'A', E', 'I', 'O', 'U', 'H', 'W', 'Y'. 3. Change letters to digits as follows:  B, F, P, V  1  C, G, J, K, Q, S, X, Z  2  D,T  3  L  4  M, N  5  R  6 www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.4 Soundex continued 4. Remove all pairs of consecutive digits. 5. Remove all zeros from the resulting string. 6. Pad the resulting string with trailing zeros and return the first four positions, which will be of the form uppercase letter digit digit digit. E.g., Herman becomes H655. Will hermann generate the same code www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.4 Soundex  Soundex is the classic algorithm, provided by most databases (Oracle, Microsoft, …)  How useful is soundex  Not very – for information retrieval  Okay for “high recall” tasks (e.g., Interpol), though biased to names of certain nationalities  Zobel and Dart (1996) show that other algorithms for phonetic matching perform much better in the context of IR www.ThesisScientist.comIntroduction to Information Retrieval What queries can we process  We have  Positional inverted index with skip pointers  Wildcard index  Spellcorrection  Soundex  Queries such as (SPELL(moriset) /3 toronto) OR SOUNDEX(chaikofski) www.ThesisScientist.comIntroduction to Information Retrieval Exercise  Draw yourself a diagram showing the various indexes in a search engine incorporating all the functionality we have talked about  Identify some of the key design choices in the index pipeline:  Does stemming happen before the Soundex index  What about ngrams  Given a query, how would you parse and dispatch subqueries to the various indexes www.ThesisScientist.comIntroduction to Information Retrieval Sec. 3.5 Resources  IIR 3, MG 4.2  Efficient spell retrieval:  K. Kukich. Techniques for automatically correcting words in text. ACM Computing Surveys 24(4), Dec 1992.  J. Zobel and P. Dart. Finding approximate matches in large lexicons. Software practice and experience 25(3), March 1995. http://citeseer.ist.psu.edu/zobel95finding.html  Mikael Tillenius: Efficient Generation and Ranking of Spelling Error Corrections. Master’s thesis at Sweden’s Royal Institute of Technology. http://citeseer.ist.psu.edu/179155.html  Nice, easy reading on spell correction:  Peter Norvig: How to write a spelling corrector http://norvig.com/spellcorrect.html www.ThesisScientist.com