PrasadL05TolerantIR1 Tolerant IR Adapted from Lectures by Prabhakar Raghavan (Google) and Christopher Manning (Stanford)

2 This lecture: “Tolerant” retrieval Wild-card queries For expressiveness to accommodate variants (e.g., automat*) To deal with incomplete information about spelling or multiple spellings (E.g., S*dney) Spelling correction Soundex

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? Sec. 3.1 3

A naïve dictionary An array of struct: char[20] 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? Sec. 3.1 4

Dictionary data structures Two main choices: Hashtables Trees Some IR systems use hashtables, some trees Sec. 3.1 5

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 rehashing Sec. 3.1 6

Root a-m n-z a-huhy-mn-shsi-z aardvark huygens sickle zygot Tree: binary tree Sec. 3.1 7

Tree: B-tree 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]. a-hu hy-m n-z Sec. 3.1 8

Trees Simplest: binary search tree More usual: AVL-trees (main memory), B-trees (disk) Trees require a standard ordering of characters and hence strings. 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 AVL trees and B-trees mitigate the rebalancing problem Sec. 3.1 9

10 Wild-card queries

11 Wild-card queries: * mon*: find all docs containing any word beginning with “mon”. Hashing unsuitable because order not preserved Easy with binary tree (or B-tree) lexicon: retrieve all words in range: mon ≤ w < moo *mon: find words ending in “mon”: harder Maintain an additional B-tree for terms backwards. Can retrieve all words in range: nom ≤ w < non. Exercise: from this, how can we enumerate all terms meeting the wild-card query pro*cent ?

12 Query processing At this point, we have an enumeration of all terms in the dictionary that match the wild-card query. We still have to look up the postings for each enumerated term. E.g., consider the query: se*ate AND fil*er This may result in the execution of many Boolean AND queries.

13 Flexible Handling of *’s B-trees handle *’s at the beginning and at the end of a query term How can we handle *’s in the middle of a query term? Consider co*tion We could look up co* AND *tion in a B-tree and intersect the two term sets Expensive

14 Flexible Handling of *’s The solution: Use Permuterm Index. Transform every wild-card query so that the *’s occur at the end Store each rotation of a word in the dictionary, say, in a B-tree

Permuterm index For term hello, index it under: hello$, ello$h, llo$he, lo$hel, o$hell where $ is a special symbol. 15

16 Permuterm index Queries: For X, lookup on X$ For X*, look up $X* For *X, lookup on X$* For *X*, lookup on X* For X*Y, lookup on Y$X* Query = hel*o X=hel, Y=o Lookup o$hel* m*n  n$m* ~> man moron moon mean …

17 Permuterm query processing Rotate query wild-card to the right Now use B-tree lookup as before.  Problem: Permuterm more than quadruples the size of the dictionary compared to a regular B- tree. (empirical number for English)

18 Bigram indexes Enumerate all k-grams (sequence of k chars) occurring in any term e.g., from text “April is the cruelest month” we get the 2-grams (bigrams) $ is a special word boundary symbol Maintain a second “inverted” index from bigrams to dictionary terms that match each bigram. $a,ap,pr,ri,il,l$,$i,is,s$,$t,th,he,e$,$c,cr,ru, ue,el,le,es,st,t$, $m,mo,on,nt,h$

Bigram index example 19 mo on among $mmace among amortize madden around The k-gram index finds terms based on a query consisting of k-grams (here k=2).

20 Postings list in a 3-gram inverted index 20 k-gram (bigram, trigram,... ) indexes  Note that we now have two different types of inverted indexes  The term-document inverted index for finding documents based on a query consisting of terms  The k-gram index for finding terms based on a query consisting of k-grams

21 Processing n-gram wild-cards 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 incorrectly enumerate moon as well. Must post-filter these terms against query. Surviving enumerated terms are then looked up in the original term-document inverted index. Fast, space efficient (compared to permuterm).

Introduction to Information Retrieval 22 Exercise  Google has very limited support for wildcard queries.  For example, this query doesn’t work very well on Google: [gen* universit*]  Intention: you are looking for the University of Geneva, but don’t know which accents to use for the French words for university and Geneva.  According to Google search basics, 2010-04-29: “Note that the * operator works only on whole words, not parts of words.”  But this is not entirely true. Try [pythag*] and [m*nchen]  Exercise: Why doesn’t Google fully support wildcard queries? 22

Introduction to Information Retrieval 23 Processing wildcard queries in the term- document index  Problem 1: we must potentially execute a large number of Boolean queries.  Most straightforward semantics: Conjunction of disjunctions  For [gen* universit*]: geneva university OR geneva université OR genève university OR genève université OR general universities OR...  Very expensive  Problem 2: Users hate to type.  If abbreviated queries like [pyth* theo*] for [pythagoras’ theorem] are allowed, users will use them a lot.  This would significantly increase the cost of answering queries.  Somewhat alleviated by Google Suggest 23

24 Processing wild-card queries As before, we must execute a Boolean query for each enumerated, filtered term. Wild-cards can result in expensive query execution (very large disjunctions…) Avoid encouraging “laziness” in the UI: Search Type your search terms, use ‘*’ if you need to. E.g., Alex* will match Alexander.

25 Advanced features Avoiding UI clutter is one reason to hide advanced features behind an “Advanced Search” button It also deters most users from unnecessarily hitting the engine with fancy queries

26 Spelling correction

27 Spell correction Two principal uses Correcting document(s) being indexed Retrieving matching documents when query contains a spelling error 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 Context-sensitive Look at surrounding words, e.g., I flew form Heathrow to Narita.

28 Document correction Especially needed for OCR’ed documents Correction algorithms tuned for this: rn vs m Can use domain-specific knowledge E.g., OCR can confuse O and D more often than it would confuse O and I. (However, O and I adjacent on the QWERTY keyboard, so more likely interchanged in typed documents). 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 query-document mapping

29 Query mis-spellings 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 … ?

30 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 “industry-specific” lexicon – hand-maintained The lexicon of the indexed corpus E.g., all words on the web All names, acronyms etc. (Including the mis-spellings)

31 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 Weighted edit distance n-gram overlap Jaccard Coefficient Dice Coefficient Jaro-Winkler Similarity

32 Edit distance Given two strings S 1 and S 2, the minimum number of operations to convert one to the other Basic operations are typically character-level 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.

Transform "SPARTAN" into "PART" StepComparisonEdit necessaryTotal Editing 1."S" to ""delete: +1 edit"S" to "" in 1 edit 2."P" to "P"no edits necessary!"SP" to "P" in 1 edit 3."A" to "A"no edits necessary!"SPA" to "PA" in 1 edit 4."R" to "R"no edits necessary! "SPAR" to "PAR" in 1 edit 5."T" to "T"no edits necessary! "SPART" to "PART" in 1 edit 6."A" to "T"delete: +1 edit "SPARTA" to "PART" in 2 edits 7."N" to "T"delete: +1 edit "SPARTAN" to "PART" in 3 edits

Transform "SEA" into "ATE" 34 StepComparison Edit necessary Total Editing 1."S" to "" delete: +1 edit "S" to "" in 1 edit 2."E" to "" delete: +1 edit "SE" to "" in 2 edits 3."A" to "A" no edits necessary! "SEA" to "A" in 2 edits 4."A" to "T" insert: +1 edit "SEA" to "AT" in 3 edits 5."A" to "E" insert: +1 edit "SEA" to "ATE" in 4 edits

Transform "SEA" into "ATE" 35 StepComparison Edit necessary Total Editing 1."" to "" no edit necessary! "" to "" in 0 edits 2."S" to "A" replace: +1 edit "S" to "A" in 1 edit 3."S" to "T" insert: +1 edit "S" to "AT" in 2 edits 4."E" to "E" no edits necessary! "SE" to "ATE" in 2 edits 5."A" to "E" delete: +1 edit "SEA" to "ATE" in 3 edits

36 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

Edit distance to all dictionary terms? Given a (mis-spelled) 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 n-gram overlap for this This can also be used by itself for spelling correction. Sec. 3.3.4 37

Introduction to Information Retrieval 38 Distance between misspelled word and “correct” word  We will study several alternatives.  Edit distance and Levenshtein distance  Weighted edit distance  k-gram overlap 38

Introduction to Information Retrieval 39 Edit distance  The edit distance between string s 1 and string s 2 is the minimum number of basic operations that convert s 1 to s 2.  Levenshtein distance: The admissible basic operations are insert, delete, and replace  Levenshtein distance dog-do: 1  Levenshtein distance cat-cart: 1  Levenshtein distance cat-cut: 1  Levenshtein distance cat-act: 2  Damerau-Levenshtein distance cat-act: 1  Damerau-Levenshtein includes transposition as a fourth possible operation. 39

Introduction to Information Retrieval 40 Levenshtein distance: Computation 40

Introduction to Information Retrieval 41 Levenshtein distance: Algorithm 41

Introduction to Information Retrieval 46 Levenshtein distance: Example 46

Introduction to Information Retrieval 47 Each cell of Levenshtein matrix 47 cost of getting here from my upper left neighbor (copy or replace) cost of getting here from my upper neighbor (delete) cost of getting here from my left neighbor (insert) the minimum of the three possible “movements”; the cheapest way of getting here

Introduction to Information Retrieval 48 Levenshtein distance: Example 48

Introduction to Information Retrieval 49 Dynamic programming (Cormen et al.)  Optimal substructure: The optimal solution to the problem contains within it subsolutions, i.e., optimal solutions to subproblems.  Overlapping subsolutions: The subsolutions overlap. These subsolutions are computed over and over again when computing the global optimal solution in a brute-force algorithm.  Subproblem in the case of edit distance: what is the edit distance of two prefixes  Overlapping subsolutions: We need most distances of prefixes 3 times – this corresponds to moving right, diagonally, down. 49

Introduction to Information Retrieval 50 Weighted edit distance  As above, but weight of an operation depends on the characters involved.  Meant to capture keyboard errors, e.g., m more likely to be mistyped as n than as q.  Therefore, replacing m by n is a smaller edit distance than by q.  We now require a weight matrix as input.  Modify dynamic programming to handle weights 50

Introduction to Information Retrieval 51 Exercise ❶ Compute Levenshtein distance matrix for OSLO – SNOW ❷ What are the Levenshtein editing operations that transform cat into catcat? 51

Introduction to Information Retrieval 52

Introduction to Information Retrieval 85 How do I read out the editing operations that transform OSLO into SNOW ? 85

96 n-gram overlap : using n-gram indexes for spelling correction Enumerate all the n-grams in the query string as well as in the lexicon  Example: bigram index, misspelled word bordroom  Bigrams: bo, or, rd, dr, ro, oo, om Use the n-gram index (recall wild-card search) to retrieve all lexicon terms matching any of the query n-grams Threshold by number of matching n-grams Variants – weight by keyboard layout, etc. Other uses of string similarity measures Ontology alignment

97 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?

98 One option – Jaccard coefficient A commonly-used measure of overlap Let X and Y be two sets; then the J.C. is 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

99 Matching bigrams Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd) lo or rd alonelordsloth lordmorbid bordercard border ardent Standard postings “merge” will enumerate …

Introduction to Information Retrieval 100 2-gram indexes for spelling correction: bordroom 100

lore Matching trigrams Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd) lo or rd alonesloth morbid bordercard border ardent Standard postings “merge” will enumerate … Adapt this to using Jaccard (or another) measure. Sec. 3.3.4 101

102 Context-sensitive 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.

103 Context-sensitive correction Need surrounding context to catch this. NLP too heavyweight for 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 Hit-based spelling correction: Suggest the alternative that has lots of hits.

Introduction to Information Retrieval 104 Context-sensitive spelling correction  Our example was: an asteroid that fell form the sky  How can we correct form here?  One idea: hit-based spelling correction  Retrieve “correct” terms close to each query term  for flew form munich: flea for flew, from for form, munch for  munich  Now try all possible resulting phrases as queries with one word “fixed” at a time  Try query “flea form munich”  Try query “flew from munich”  Try query “flew form munch”  The correct query “flew from munich” has the most hits.  Suppose we have 7 alternatives for flew, 20 for form and 3 for munich, how many “corrected” phrases will we enumerate? 104

General issues in spell correction We enumerate multiple alternatives for “Did you mean?” to the user The most frequent combination in the corpus The alternative hitting most docs Query log analysis More generally, rank alternatives probabilistically argmax corr P(corr | query) From Bayes rule, this is equivalent to argmax corr P(query | corr) * P(corr) Sec. 3.3.5 105 Noisy channel Language model

Introduction to Information Retrieval 106 Exercise: Understand Peter Norvig’s spelling corrector 106

Microsoft Web N-gram service Provides probability of occurrence of 1-, 2-, 3-, 4- and 5-grams in the Web Corpus (crawled for Bing) Specifically, it provides three different probabilities, corresponding to three different sorts of occurrence Title Anchor Body 107

Using context via Web N-gram service : Tokenization 108

Using context via Web N-gram service : Phrase extraction Tag cloud in Twitris E.g., foreign relations E.g., Tahrir Square E.g., tax returns E.g., college acceptance letter E.g., olympic gold medalist 109

Probabilistic Basis for Phrase Extraction Two successive words A and B should be treated as a phrase AB rather than as a sequence of two words if: Probability (AB) > Probability(A) * Probability(B) In other words, if the probability of their joint occurrence is more than the probability of their coincidental joint occurrence (i.e., obtained through independence assumption as the product of the individual probabilities). This approach can be extended to delimit longer phrases in a sentence. 110

111 Computational cost Spell-correction is computationally expensive Avoid running routinely on every query? Run only on queries that matched few docs

112 Thesauri Thesaurus: language-specific list of synonyms for terms likely to be queried car  automobile, etc. Machine learning methods can assist Can be viewed as hand-made alternative to edit- distance, etc.

113 Query expansion Usually do query expansion rather than index expansion No index blowup Query processing slowed down Docs frequently contain equivalences May retrieve more junk puma  jaguar retrieves documents on cars instead of on sneakers.

114 Soundex

115 Soundex Class of heuristics to expand a query into phonetic equivalents Language specific – mainly for names E.g., chebyshev  tchebycheff

116 Soundex – typical algorithm Turn every token to be indexed into a 4-character 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.htm#Top

117 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

118 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. E.g., Herman becomes H655. Will hermann generate the same code?

Introduction to Information Retrieval 119 Example: Soundex of HERMAN  Retain H  ERMAN → 0RM0N  0RM0N → 06505  06505 → 06505  06505 → 655  Return H655  Note: HERMANN will generate the same code 119

120 Exercise Using the algorithm described above, find the soundex code for your name Do you know someone who spells their name differently from you, but their name yields the same soundex code?

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 Sec. 3.4 121

122 Language detection Many of the components described above require language detection For docs/paragraphs at indexing time For query terms at query time – much harder For docs/paragraphs, generally have enough text to apply machine learning methods For queries, lack sufficient text Augment with other cues, such as client properties/specification from application Domain of query origination, etc.

123 What queries can we process? We have Basic inverted index with skip pointers Wild-card index Spell-correction Soundex Queries such as (SPELL(moriset) /3 toron*to) OR SOUNDEX(chaikofski)

124 Aside – results caching If 25% of your users are searching for britney AND spears then you probably do need spelling correction, but you don’t need to keep on intersecting those two postings lists Web query distribution is extremely skewed, and you can usefully cache results for common queries. Query log analysis

PrasadL05TolerantIR1 Tolerant IR Adapted from Lectures by Prabhakar Raghavan (Google) and Christopher Manning (Stanford)

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PrasadL05TolerantIR1 Tolerant IR Adapted from Lectures by Prabhakar Raghavan (Google) and Christopher Manning (Stanford)

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