Information Retrieval Tolerant Retrieval

Wild-card queries

Wild Card Queries 1. Trailing wild card queries fan* (e.g. fanatic, fancy, fantasy, etc.) - Use B-tree data structure on the dictionary - Walk down the tree following f, a, n - Retrieve all words w such that: fan ≤ w<fao (i.e. all the words having prefix “fan”) Let set of these terms be W. - Use inverted index to retrieve documents containing terms in W

Wild-card queries: * *tic: find words ending in “tic”: harder Maintain an additional B-tree for terms backwards. Can retrieve all words in range: cit ≤ w < ciu. Once we have all terms in the dictionary that match the wild-card query. We have to look up the postings for each enumerated term to perform retrieval.

General cases (Single *) consider the query: se*tic (e.g. semantic, semiotic, semitic, etc.) Use B-tree to get set of terms (W) having a prefix “se” Use reverse B-tree to get set of terms (R) with suffix “tic” Compute S = W ∩ R (words with prefix se and suffix tic) Use inverted index to retrieve documents containing terms in S B-trees handle *’s at the end of a query term

General wild card queries How can we handle *’s in the middle of query term? (Especially multiple *’s) Two techniques: Both make use of a specially constructed index Solution 1: transform every wild-card query so that the *’s occur at the end -This gives rise to the Permuterm Index. Solution 2: K-gram indexes

Wild card query w is expressed as a Boolean query on the specially constructed index and a superset of the set of dictionary terms matching w is obtained. A post filtering step is used to discard dictionary terms that do not match w Standard Inverted index is then used to retrieve documents

Permuterm index In a permuterm index, dictionary consists of all rotations (with $ marking the end) of each term and Postings of each rotation consists of all dictionary terms containing that rotation. For term hello index under: hello$, ello$h, llo$he, lo$hel, o$hell In the B-tree all rotations of a term will point to the original lexicon term

Permuterm query processing Rotate query wild-card to the right Now use B-tree lookup as before. Permuterm problem: ≈ quadruples lexicon size Query = hel*o  hel*o$ After rotation: o$hel* Now traverse the B-tree seeking o$hel

Query se*m*tic - First find candidate terms in the permuterm index of tic$se - Next, filter out those terms from the candidate set that do not contain m using exhaustive enumeration.

Bigram indexes Enumerate all k-grams (sequence of k chars) occurring in any term e.g., from text “bigram index” we get the 2-grams (bigrams) $ is a special word boundary symbol Maintain an “inverted” index from bigrams to dictionary terms that match each bigram. $b, bi, ig, gr,ra,am, m$, $i, in, nd,de,ex, x$

Bigram index example $b bag big bigram gr grass group bigram A k-gram index is an index in which the dictionary consists of all k-grams that occur in any word in the lexicon Each postings list point from the k-gram to all lexicon words containing that k-gram.

Processing n-gram wild-cards Query pri* can be run as $p AND pr AND ri Fast, space efficient. Gets terms that match AND version of our wildcard query. Matches with words prince, pride, prior, price, priest Also matches with proprietary as it contains 3-gram $p, pr, ri. Must post-filter these terms against query. Surviving enumerated terms are then looked up in the term-document inverted index.

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 that’s why usually SE hide these features behind “Advanced search” button.

Spelling correction

Spell correction Two principal uses Two main flavors: Correcting document(s) being indexed Retrieve 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 …

Document correction Primarily for OCR’ed documents Correction algorithms tuned for this Goal: the index (dictionary) contains fewer OCR-induced misspellings Can use domain-specific 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), e and c, r and n, etc.

Query mis-spellings We can either Retrieve documents indexed by the correct spelling, OR Return several suggested alternative queries with the correct spelling Did you mean … ?

Isolated word correction Makes use of 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)

Isolated word correction Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q What’s “closest”? Edit distance Weighted edit distance n-gram overlap

Edit distance Given two strings S1 and S2, the minimum number of basic operations to transform one to the other Basic operations are typically character-level Insert Delete Replace E.g., the edit distance from cat to dog is 3. Generally found by dynamic programming.

Edit distance t u t o - r Also called “Levenshtein distance” The following alignment between tutor and tumour has a edit distance of 2. t u t o - r t u m o u r Another possible alignment with edit distance 3. t u t - o - r t u - m o u r The best possible alignment corresponds to minimum edit distance.

Weighted edit distance As above, but the weight of an operation depends on the character(s) involved Meant to capture keyboard errors, e.g. 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 (Same ideas usable for OCR, but with different weights) Require weight matrix as input

Minimum edit distance Dynamic programming algorithms can be quite useful for finding minimum edit distance between two sequences. implemented by creating an edit distance matrix. This matrix has one row for each symbol in the source string and one column for each matrix in the target string

Minimum edit distance matrix The (i,j)th cell in this matrix represents the distance between first i character of the source and first j character of the target string. The value in each cell is computed in terms of three possible paths following which we can reach there: The substitution will be 0 if the ith character in the source matches with jth character in the target.

Input: Two strings, X and Y Output: The minimum edit distance between X and Y m  length(X) n  length(Y) for i = 0 to m do dist[i,0]  i for j = 0 to n do dist[0,j]  j for i = 1 to m do for j = 1 to n do dist[i,j] = min { dist[i-1,j] + insert_cost, dist[i-1,j-1] + subst_cost(Xi,Yj), dist[i,j-1] + delet_cost } end

# t u m o u r # 0 1 2 3 4 5 6 t 1 0 1 2 3 4 5 u 2 1 0 1 2 3 4 t 3 2 1 1 2 3 4 o 4 3 2 2 1 2 3 r 5 4 3 3 2 2 2

Using edit distances Given query, first enumerate all dictionary terms within a preset (weighted) edit distance - To reduce search complexity heuristics are used. * consider dictionary terms beginning with the same letter * use permutation index leaving end of string symbol * omit suffix of length l before performing rotation Then look up enumerated dictionary terms in the term-document inverted index

Edit distance to all dictionary terms? Given a (mis-spelled) query – do we compute its edit distance to every dictionary term? Expensive and slow How do we cut the set of candidate dictionary terms? We can use n-gram overlap for this

n-gram overlap Enumerate all the n-grams in the query string as well as in the lexicon Use the n-gram index to retrieve all lexicon terms matching any of the query n-grams Threshold by number of matching n-grams

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?

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

Standard postings “merge” will enumerate … Matching trigrams Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd) lo alone lord sloth or border lord morbid rd ardent border card Standard postings “merge” will enumerate …

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.

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 etc. Suggest the alternative that has lots of hits?

Exercise Suppose that for “flew form Heathrow” we have 7 alternatives for flew, 19 for form and 3 for heathrow.

Another approach Break phrase query into a conjunction of biwords Look for biwords that need only one term corrected. Enumerate phrase matches and … rank them!

General issue in spell correction Will enumerate multiple alternatives for “Did you mean” Need to figure out which one (or small number) to present to the user

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

Soundex

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

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)

Soundex Letters Code 1 2 d t 3 l 4 m n 5 r 6 Keep the first letter Code the rests into digits as shown in table Ignore letters with same Soundex digit Eliminate all zeros Truncate or pad with zeros to one initial letter and three digits Letters Code a e h i o u w y b f p v 1 c g j k q s x z 2 d t 3 l 4 m n 5 r 6 Soundex Phonetic code

Soundex The coding scheme is based on observations like: - vowels are interchangeable - consonants with similar sounds are put in equivalence class Example: Dickson, Dikson, Dixon Developed by Odell and Russell in 1918 and used in US census to match American English names Soundex fails on two names with different initials (e.g.: Karlson, Carlson) Also in other cases (e.g. Rodgers, Rogers)