Prasad L05TolerantIR 1
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
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
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
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 termsmeeting 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$X*
Query = hel*oX=hel, Y=o
Lookup o$hel*
m*nn$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
$m mace
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, . . . ) 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
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).
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
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 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"
34
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"
35
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
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 RetrievalIntroduction 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 RetrievalIntroduction to Information Retrieval
39
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.
39
Introduction to Information RetrievalIntroduction to Information Retrieval
40
Levenshtein distance: Computation
40
Introduction to Information RetrievalIntroduction to Information Retrieval
41
Levenshtein distance: Algorithm
41
Introduction to Information RetrievalIntroduction to Information Retrieval
42
Levenshtein distance: Algorithm
42
Introduction to Information RetrievalIntroduction to Information Retrieval
43
Levenshtein distance: Algorithm
43
Introduction to Information RetrievalIntroduction to Information Retrieval
44
Levenshtein distance: Algorithm
44
Introduction to Information RetrievalIntroduction to Information Retrieval
45
Levenshtein distance: Algorithm
45
Introduction to Information RetrievalIntroduction to Information Retrieval
46
Levenshtein distance: Example
46
Introduction to Information RetrievalIntroduction to Information Retrieval
47
Each cell of Levenshtein matrix
47
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
Introduction to Information RetrievalIntroduction to Information Retrieval
48
Levenshtein distance: Example
48
Introduction to Information RetrievalIntroduction 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 RetrievalIntroduction 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 RetrievalIntroduction to Information Retrieval
51
Exercise
❶Compute Levenshtein distance matrix for OSLO – SNOW❷What are the Levenshtein editing operations that transform
cat into catcat?
51
Introduction to Information RetrievalIntroduction 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
YXYX /
Introduction to Information RetrievalIntroduction to Information Retrieval
100
2-gram indexes for spelling correction: bordroom
100
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
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.
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 : 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
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 <uppercase letter> <digit> <digit> <digit>.
E.g., Herman becomes H655.
Will hermann generate the same code?
Introduction to Information RetrievalIntroduction 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
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