tolerant ir

Prasad L05TolerantIR 1

Tolerant IR

Adapted from Lectures by

Prabhakar Raghavan (Google) and

Christopher Manning (Stanford)

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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

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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

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Dictionary data structures

Two main choices: Hashtables Trees

Some IR systems use hashtables, some trees

Sec. 3.1

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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

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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-huhy-m

n-z

Sec. 3.1

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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

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Wild-card queries

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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 termsmeeting the wild-card query pro*cent ?

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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.

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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

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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.

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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*oX=hel, Y=o

Lookup o$hel*

m*nn$m*~> man moron moon mean …

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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)

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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

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mo

on

among

$m mace

among

amortize

madden

around

The k-gram index finds terms based on a query consisting of k-grams (here k=2).

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Postings list in a 3-gram inverted index

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k-gram (bigram, trigram, . . . ) indexesNote that we now have two different types of inverted indexes

The term-document inverted index for finding documents based on a query consisting of termsThe k-gram index for finding terms based on a query consisting of k-grams

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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).

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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.

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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

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Spelling correction

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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.

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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

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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 … ?

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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)

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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

Jaccard Coefficient Dice Coefficient Jaro-Winkler Similarity

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Edit distance

Given two strings S1 and S2, 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"

Step Comparison Edit necessary Total 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"

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Step ComparisonEdit 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"

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Step ComparisonEdit 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

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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

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Introduction to Information RetrievalIntroduction to Information Retrieval

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Distance between misspelled word and “correct” word

We will study several alternatives. Edit distance and Levenshtein distance Weighted edit distance k-gram overlap

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Edit distance The edit distance between string s1 and string s2 is the

minimum number of basic operations that 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 Damerau-Levenshtein distance cat-act: 1

Damerau-Levenshtein includes transposition as a fourth possible operation.

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Levenshtein distance: Computation

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Levenshtein distance: Algorithm

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Levenshtein distance: Example

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Each cell of Levenshtein matrix

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cost of getting here frommy upper left neighbor(copy or replace)

cost of getting herefrom my upper neighbor(delete)

cost of getting here frommy left neighbor (insert)

the minimum of the three possible “movements”;the cheapest way of getting here


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Levenshtein distance: Example

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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.

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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

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Exercise

❶Compute Levenshtein distance matrix for OSLO – SNOW❷What are the Levenshtein editing operations that transform

cat into catcat?

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5252


5353


5454


5555


5656


5757


5858


5959


6060


6161


6262


6363


6464


6565


6666


6767


6868


6969


7070


7171


7272


7373


7474


7575


7676


7777


7878


7979


8080


8181


8282


8383


8484


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How do

I read out the editing operations that transform OSLO into SNOW?

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8686


8787


8888


8989


9090


9191


9292


9393


9494


9595

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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

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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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2-gram indexes for spelling correction: bordroom

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lore

lore

Matching trigrams

Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd)

lo

or

rd

alone sloth

morbid

border card

border

ardent

Standard postings “merge” will enumerate …

Adapt this to using Jaccard (or another) measure.

Sec. 3.3.4

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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.

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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.

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 probabilisticallyargmaxcorr P(corr | query)

From Bayes rule, this is equivalent toargmaxcorr P(query | corr) * P(corr)

Sec. 3.3.5

105Noisy channel Language model

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

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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

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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.

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Computational cost

Spell-correction is computationally expensive

Avoid running routinely on every query?

Run only on queries that matched few docs

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Soundex

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Soundex

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

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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

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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

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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?


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Example: Soundex of HERMAN

Retain H ERMAN → 0RM0N 0RM0N → 06505 06505 → 06505 06505 → 655 Return H655 Note: HERMANN will generate the same code

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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

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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)

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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

tolerant ir

Documents

wildcard query pro

query time

query processingat

query termhow

btrees disktrees

btree lexicon

additional btree

term vocabulary