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Spelling correction

Two di erent methods for spelling correctionff Isolated word spelling correction

Check each word on its own for misspelling Will not catch typos resulting in correctly spelled words, e.

g., an asteroid that fell form the sky Context-sensitive spelling correction

Look at surrounding words Can correct form/from error above

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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 … ?

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Correcting queries

First: isolated word spelling correction Fundamental premise 1: There is a list of “correct w

ords” from which the correct spellings come. Fundamental premise 2: We have a way of computi

ng the distance between a misspelled word and a correct word.

Simple spelling correction algorithm: return the “correct” word that has the smallest distance to the misspelled word.

Example: informaton → information We can use the term vocabulary of the inverted i

ndex as the list of correct words.

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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

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Edit distance

Given two strings S1 and S2, the minimum number of basic operations to covert 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.

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Edit distance

Also called “Levenshtein distance”See http://www.merriampark.com/ld.htm

for a nice example plus an applet to try on your own

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Edit distance

The edit distance between string s1 and string s2 is the minimum number of basic operations to convert s1 to s2.

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

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Levenshtein distance: Computation

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Levenshtein distance: algorithm

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Dynamic programming (Cormen et al.) Optimal substructure: The optimal solution to the proble

m contains within it optimal solutions to subproblems. Overlapping subproblems: The optimal solutions to subpr

oblems (“subsolutions”) overlap. These subsolutions are computed over and over again when computing the global optimal solution.

Optimal substructure: We compute minimum distance of substrings in order to compute the minimum distance of the entire string.

Overlapping subproblems: Need most distances of substrings 3 times (moving right, diagonally, down)

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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

Require weight matrix as inputModify dynamic programming to handle

weights

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Using edit distances

Given query, first enumerate all dictionary terms within a preset (weighted) edit distance

Then look up enumerated dictionary terms in the term-document inverted index Slow but no real fix

How do we cut the set of candidate dictionary terms? Here we use n-gram overlap for this

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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

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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?

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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

YXYX /

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Problem

Can we compute Jaccard coefficient efficiently? Hints

What about the k-grams of a given term with length l? Set operation

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Context-sensitive spelling correction

Our example was: an asteroid that fell form the sky How can we correct form here? Ideas? 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, 19 for form and 3 for munich, how many “corrected” phrases will we enumerate?

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Context-sensitive spelling correction

The “hit-based” algorithm we just outlined is not very e cient.ffi

More e cient alternative: look at “collectioffin” of queries, not documents

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General issues in spelling correction

User interface automatic vs. suggested correction Did you mean only works for one suggestion. What about multiple possible corrections? Tradeo : simple vs. powerful UIff

Cost Spelling correction is potentially expensive. Avoid running on every query? Maybe just on queries that match few documents. Guess: Spelling correction of major search engines is e

cient enough to be run on every query.ffi

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Soundex

Soundex is the basis for finding phonetic (as opposed to orthographic) alternatives.

Example: chebyshev / tchebyscheffAlgorithm:

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

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Soundex algorithm

1 Retain the first letter of the term. 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 to 1 C, G, J, K, Q, S, X, Z to 2 D,T to 3 L to 4 M, N to 5 R to 6

4 Repeatedly remove one out of each pair of consecutive identical digits

5 Remove all zeros from the resulting string; pad the resulting string with trailing zeros and return the first four positions, which will consist of a letter followed by three digits

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Example: Soundex of HERMAN

Retain HERMAN → 0RM0N0RM0N → 0650506505 → 0650506505 → 655Return H655Will HERMANN generate the same code?

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Compute soundex code of your first name.

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How useful is Soundex?

Not very – for information retrievalOk for “high recall” tasks in other applicatio

ns (e.g., Interpol)Zobel and Dart (1996) suggest better alter

natives for phonetic matching in IR.

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The complete search system