Tolerant Retrieval. Searching the Dictionary Tolerant Retrieval. Information Retrieval & Extraction Misbhauddin 1

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1 Tolerant Retrieval Searching the Dictionary Tolerant Retrieval Information Retrieval & Extraction Misbhauddin 1

2 Query Retrieval Dictionary data structures Tolerant retrieval Wild-card queries Soundex Spelling correction Information Retrieval & Extraction Misbhauddin 2

3 Dictionary Data Structure The dictionary data structure stores the term vocabulary, document frequency, pointers to each postings list... in what data structure? Information Retrieval & Extraction Misbhauddin 3

4 Dictionary Data Structure Two main choices: Hash table Tree Some IR systems use hashes, some trees Information Retrieval & Extraction Misbhauddin 4

5 Hash Tables 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 do the expensive operation of rehashing everything Information Retrieval & Extraction Misbhauddin 5

6 Trees Simplest: binary tree More usual: B-trees Trees require a standard ordering of characters and hence strings but we standardly 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 B-trees mitigate the rebalancing problem Information Retrieval & Extraction Misbhauddin 6

7 Binary Trees a-m Root n-z a-hu hy-m n-sh si-z 7 Information Retrieval & Extraction Misbhauddin 7

8 B-Trees Definition: Every internal node 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 Information Retrieval & Extraction Misbhauddin 8

9 Wildcard Queries (*) Information Retrieval & Extraction Misbhauddin 9

10 Wildcard Queries mon*: find all docs containing any word beginning with mon (trailing wild-card queries) Easy with binary tree (or B-tree): retrieve all words in range: mon w < moo *mon: find words ending in mon : harder (leading wild-card queries) Maintain an additional B-tree for terms backwards (reverse B-tree). 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? Information Retrieval & Extraction Misbhauddin 10

11 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 ANDfil*er This may result in the execution of many Boolean AND queries. Information Retrieval & Extraction Misbhauddin 11

12 Index Variations for Wildcard Queries Two strategies: Permuterm indexes k-gram indexes Information Retrieval & Extraction Misbhauddin 12

13 Permuterm How can we handle * s in the middle of query term? co*tion We could look up co* AND *tion in a B-tree and intersect the two term sets Expensive The solution: transform wild-card queries so that the * s occur at the end This gives rise to the Permuterm Index. Information Retrieval & Extraction Misbhauddin 13

14 Permuterm For term hello, index under: hello$, ello$h, llo$he, lo$hel, o$hell where $ is a special symbol Queries: X lookup on X$ {Standard Query no wildcard} X* lookup on $X* {Trailing wildcard query} *X lookup on X$* {Leading wildcard query} X*Y lookup on Y$X* {Wildcard-in-the-middle query} *X* lookup on X* {Leading & Trailing wildcard query} Exercise: X*Y*Z Query = hel*o X=hel, Y=o Lookup o$hel* Information Retrieval & Extraction Misbhauddin 14

15 Permuterm Query Processing Rotate query wild-card to the right Now use B-tree lookup as before Permuterm problem: quadruples lexicon size (Empirical Observation) Information Retrieval & Extraction Misbhauddin 15

16 Bigram (k-gram) 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) $a, ap, pr, ri, il, l$, $i, is, s$, $t, th, he, e$, $c, cr, ru, ue, el, le, es, st, t$, $m, mo, on, nt, h$ $ is a special word boundary symbol Maintain a second inverted index from bigrams to dictionary terms that match each bigram Information Retrieval & Extraction Misbhauddin 16

17 Bigram Index Example The k-gram index finds terms based on a query consisting of k-grams (here k=2) $m mace madden mo on among among amortize around Information Retrieval & Extraction Misbhauddin 17

18 Processing Wildcards Query mon* can now be run as $m AND mo AND on Which is All terms starting with m, containing mo and containing on Gets terms that match AND version of our wildcard query But we d enumerate moon/mormon False Positives Must post-filter these terms against query Surviving enumerated terms are then looked up in the termdocument inverted index Fast, space efficient (compared to permuterm) Information Retrieval & Extraction Misbhauddin 18

19 Processing Wildcard 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 ) pyth* AND prog* If you encourage laziness people will respond! Type your search terms, use * if you need to. E.g., Alex* will match Alexander. Search Information Retrieval & Extraction Misbhauddin 19

20 Soundex Algorithm Information Retrieval & Extraction Misbhauddin 20

21 Soundex Class of heuristics to expand a query into phonetic equivalents Language-specific: Mainly for names Example: Chebyshev -> Tchebysheff Invented for the US Censes in 1918 Information Retrieval & Extraction Misbhauddin 21

22 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 needs a Soundex match Information Retrieval & Extraction Misbhauddin 22

23 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 Information Retrieval & Extraction Misbhauddin 23

24 Soundex Typical Algorithm 4. Remove all pairs of consecutive digits 5. Remove all zeroes from the resulting string 6. Pad the resulting string with trailing zeroes and return the first four positions, which will be of the form <Upper-case Letter> <digit> <digit> <digit> Example: Herman => H655 Will Hermann generate the same code? Information Retrieval & Extraction Misbhauddin 24

25 Soundex Soundex is the classic algorithm, provided by most databases (Oracle, Microsoft) Select * from hr.employee Where SOUNDEX(lastname) = SOUNDEX( Smith ) How useful is soundex? Not very for Information retrieval Lowers the precision Okay for High Recall tasks (E.g Interpol) Information Retrieval & Extraction Misbhauddin 25

26 Spelling Correction Information Retrieval & Extraction Misbhauddin 26

27 Spell Correction Correcting user queries to retrieve right answers Two Approaches Isolated Word Check each word on its own for misspelling Will not catch typos in correctly spelled words Example: Form -> From Context-Sensitive Look at surroinding words Example: I flew form hofuf to riyadh Information Retrieval & Extraction Misbhauddin 27

28 Query Misspellings We can either Retrieve documents indexed by the correct spelling Retrieve several suggested alternative queries with the correct spelling Example: Did you mean? Information Retrieval & Extraction Misbhauddin 28

29 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 misspellings) Information Retrieval & Extraction Misbhauddin 29

30 Isolated word correction Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q What s closest? Several alternatives Edit distance (Levenshtein distance) Weighted edit distance n-gram overlap Information Retrieval & Extraction Misbhauddin 30

31 Intro. Dynamic Programming Fibonacci Series 0, 1, 1, 2, 3, 5, 8, N t = N t-1 + N t-2 Solutions Divide and Conquer Recursion Solve the sub-problems recursively Issue - solving many sub-problems again and again Dynamic Programming Memoization Store the solution of these sub-problems so that we do not have to solve them again Information Retrieval & Extraction Misbhauddin 31

32 Edit Distance (Levenshtein) Given two strings S 1 and S 2, the minimum number of operations to convert one to the other 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 from cat to dog is 3 (Just 1 with transpose.) Generally found by dynamic programming Information Retrieval & Extraction Misbhauddin 32

33 Edit Distance (Levenshtein) S1 Gold Operation: Deletion S1 Gold Operation: Insertion S2 Old Edit Distance: 1 S2 Goaled Edit Distance: 2 S1 S2 Gold Sold Operation: Replace Edit Distance: 1 Information Retrieval & Extraction Misbhauddin 33

34 Edit Distance (Levenshtein): Terminology A string S = S 1, S 2, S 3, S 4, S n Caterpillar (n=11) A substring S = S 1, S 2, S 3, S 4, S k S n Caterpillar (k=3) To find the edit distance between strings S and T, we need to examine their substrings S n -> S 1 j for all j from n-1 to 1 T m -> S 1 k for all j from m-1 to 1 Information Retrieval & Extraction Misbhauddin 34

35 Edit Distance (Levenshtein): Function E(j, k) = D(S 1.j, T 1..k ) E(j, 0) = D(S 1.j, ) => J deletions to get an empty string => j E(0, k) = D(, T 1..k ) => K insertions => k Information Retrieval & Extraction Misbhauddin 35

36 Edit Distance (Levenshtein): Formula E(j, 0) = j E(0, k) = k E(j, k) = min E j 1, k + 1 deletion E j, k insertion E j 1, k 1, Sj = TK Nothing to do E j 1, k 1 + 1, Sj T K Replace Information Retrieval & Extraction Misbhauddin 36

37 E(j, k) = min k E j 1, k + 1 deletion E j, k insertion E j 1, k 1, Sj = TK Nothing to do E j 1, k 1 + 1, Sj T K Replace gold 4 gol 3 go 2 g g go goo good j Information Retrieval & Extraction Misbhauddin 37

38 Weighted Edit Distance As Edit Distance, 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 mis-typed 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 Information Retrieval & Extraction Misbhauddin 38

39 Weighted Edit Distance Modified Formula E(j, k) = min E j 1, k + X deletion E j, k 1 + Y insertion E j 1, k 1, Sj = TK Nothing to do E j 1, k 1 + Z, Sj T K Replace X = Cost of Deletion Y = Cost of Insertion Z = Lookup in the Weight Matrix for Cost(S j, T k ) Information Retrieval & Extraction Misbhauddin 39

40 Using Edit Distance 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 Information Retrieval & Extraction Misbhauddin 40

41 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 n-gram overlap for this This can also be used by itself for spelling correction Information Retrieval & Extraction Misbhauddin 41

42 n-gram overlap Enumerate all the n-grams in the query string as well as in the lexicon 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. Information Retrieval & Extraction Misbhauddin 42

43 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? Information Retrieval & Extraction Misbhauddin 43

44 One option Jaccard coefficient A commonly-used measure of overlap Let X and Y be two sets; then the J.C. is X Ç Y / X ÈY 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 Information Retrieval & Extraction Misbhauddin 44

45 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. Information Retrieval & Extraction Misbhauddin 45

46 Context-sensitive spell 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 Hit-based spelling correction: Suggest the alternative that has lots of hits. Information Retrieval & Extraction Misbhauddin 46

3-1. Dictionaries and Tolerant Retrieval. Most slides were adapted from Stanford CS 276 course and University of Munich IR course.

3-1. Dictionaries and Tolerant Retrieval Most slides were adapted from Stanford CS 276 course and University of Munich IR course. 1 Dictionary data structures for inverted indexes Sec. 3.1 The dictionary