1. Tolerant IR Adapted from Lectures by Prabhakar Raghavan (Google) and
Christopher Manning (Stanford)
A pattern is a set of syntactic features that must occur in a text segment.
Text segments satisfying the pattern spec is said to MATCH the pattern.
Typically dictionaries are implemented either using Hashing or using Search Trees.
Depending on the distribution of keys and the choice of the hash function,
Hashing can be very efficient for searching (even in the presence of updates).
On the other hand, search trees have significant advantage if we consider memory
hierachies (disk) and searching terms that are variants of each other
(e.g., common prefix, range queries).
Prasad
L05TolerantIR

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
We develop techniques that provide more flexible expression of search query,
are robust wrt typographical errors in the query, as well as alternative spellings.
New patterns in query and corresponding modifications to index structure for execution.
The basic idea is to add an additional “indexing” module that takes
an encoding of wildcard query and returns collection of terms,
which is looked up in standard index to obtain documents.
(1) Permuterm approach adds an additional “index” layer containing all rotations and
their mapping back to their originals
(The new module is significantly larger because it stores permutations)
(2) n-gram approach adds another “index” layer containing n-grams and their
mapping back to terms that contain it.
(for answering query we first get several lists of docs based on n-grams,
intersect them, and then clean up false positives.)
Approaches to correct spelling errors.
(1) Doc vs Query (2) Context Free vs Context Sensitive
(3) Query: Edit Distance vs n-gram based
Soundex : because people may not know the correct spelling and may “guess” spell
based on sound (recall “Information need” focus)

3. Dictionary data structures for inverted indexes
Sec. 3.1
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?

4. A naïve dictionary An array of struct: char[20] int Postings *
Sec. 3.1
A naïve dictionary
An array of struct:
char[20] int Postings *
20 bytes 4/8 bytes /8 bytes
How do we store a dictionary in memory efficiently?
How do we quickly look up elements at query time?

5. Dictionary data structures
Sec. 3.1
Dictionary data structures
Two main choices:
Hashtables
Trees
Some IR systems use hashtables, some trees

6. Hashtables Each vocabulary term is hashed to an integer Pros: Cons:
Sec. 3.1
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

7. Trees Simplest: binary search tree
Sec. 3.1
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

8. Sec. 3.1
Tree: B-tree
a-hu
n-z
hy-m
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].

9. Wild-card queries
Expressive search requires more sophisticated data structures

10. 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 terms meeting the wild-card query pro*cent ?
pro* intersection *cent
The result is a collection of words that have pro as prefix and cent as suffix.
(We reserve the query AND for “intersecting” sets of document ids.)
“Approximate” query mapped to a set of words
Succinct
If the same query were applied to the whole document, you may get hits
on document such as “accent has to be professional” causing false
positives and requiring filtering.
Exercise: from this, how can we enumerate all terms
meeting the wild-card query pro*cent ?

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 AND fil*er
This may result in the execution of many Boolean AND queries.
The semantics of se*ate (or fil*er) is a set of document ids containing a word from the specified word collection.
Wildcard query => set of terms = std index =>union result set
Intersect results of se* and *ate to obtain larger list of index terms
Collect postings list of these index terms as p1
Similarly collect p2 for fil*er
Then intersect

12. 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
Whereas the permuterm index is simple, it can lead to a considerable blowup
from the number of rotations per term; for a dictionary of English terms, this
can represent an almost ten-fold space increase.
QUERY with * at the end : Dictionary remains the same
QUERY with * at the beginning: Dictionary + Reverse Dictionary
QUERY with * at the middle : place all rotated versions in the dictionary
potentially an order blow-up in size

13. 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
Mapping arbitrarily positioned wildcard to terminal wildcard query
 Permuterm index
Whereas the permuterm index is simple, it can lead to a considerable blowup
from the number of rotations per term; for a dictionary of English terms, this
can represent an almost ten-fold space increase.
QUERY with * at the end : Dictionary remains the same
QUERY with * at the beginning: Dictionary + Reverse Dictionary
QUERY with * at the middle : place all rotated versions in the dictionary
potentially an order blow-up in size

14. Permuterm index For term hello, index it under:
hello$, ello$h, llo$he, lo$hel, o$hell
where $ is a special symbol.
Permuterm index (which can be a B-Tree) eventually yields terms
which are then converted into postings list (2-level index)
X* lookup on X*$
X*Y*Z lookup on X*Z intersect *Y*
X*$ intersect Y* intersect Z$X*
Prefix – Substring – Suffix criteria
(However, for X*Y1*Y2*Z the order of Y1 and Y2 cannot be maintained,
Similarly issues of overlap.)
We can view Permuterm index as a separate preprocessing index to
get normal terms before search or integrate it as one inverted index
m*n => n$m* ~> man, moron, moon, mean, etc

15. Permuterm index Queries: For X, lookup on X$ For X*, look up $X*
For X*Y, lookup on Y$X*
m*n
n$m*
~> man
moron
moon
mean …
Generic wildcard queries => prefix queries on permuterm index
X* lookup on X*$
X*Y*Z lookup on Z$X* to obtain terms matching X*Z
Subsequently intersect these terms with terms obtained using Y*
(‘$’ will appear within * -> substring begin and end YE$B)
Prefix – Substring – Suffix criteria
(However, for X*Y1*Y2*Z the order of Y1 and Y2 cannot be maintained,
Similarly issues of overlap.)
We can view Permuterm index as a separate preprocessing index to
get normal terms before search or integrate it as one inverted index
m*n => n$m* ~> man, moron, moon, mean, etc
Query = hel*o
X=hel, Y=o
Lookup o$hel*

16. 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)
But what about a query such as fi*mo*er? In this case we first enumerate
the terms in the dictionary that are in the permuterm index of er$fi*.
Not all such dictionary terms will have the string “mo” in the middle –
we filter these out by exhaustive enumeration, checking each candidate to see
if it contains “mo”. In this example, the term “fishmonger” would survive this
Filtering but “filibuster” would not. We then run the surviving terms through
the standard inverted index for document retrieval.

17. 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.
$a,ap,pr,ri,il,l$,$i,is,s$,$t,th,he,e$,$c,cr,ru,
ue,el,le,es,st,t$, $m,mo,on,nt,h$
Another approach to deal with query ending in *. Without blowing up the dictionary with all rotated forms.
*ab*cd* => {ab, cd}
Use an additional module that maps n-grams of a
QUERY that ends in * to (original) dictionary words (alternative to permuterm) (using term list intersections)
HUGE-DICT->Postings (with redundancy) Vs N-GRAMS -> (ORIGINAL-)DICT -> POSTINGS
Bigram = 2 consequetive letters
(in document context : bigram is 2 consequetive words : e.g., Microsoft’s Web N-gram Service)

18. Bigram index example
The k-gram index finds terms based on a query consisting of k-grams (here k=2). $m
mace
madden mo
among
amortize on
among
around

19. Postings list in a 3-gram inverted index
k-gram (bigram, trigram, ) indexes
Note that we now have two different types of inverted indexes
The term-document inverted index for finding documents based on a query consisting of terms
The k-gram index for finding terms based on a query consisting of k-grams 20

20. 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).
In n-gram based approaches, there is possibility of a false positive,
So it requires a confirmatory test at the end.
In 2-gram approach, query “red*” with 2-grams $r, re, ed, d$ matches “$retired$”

21. 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.

22. 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
Make expensive queries more effort to use to make sure they do not get misused.

23. Spelling correction Efficient spell retrieval:
K. Kukich. Techniques for automatically correcting words in text. ACM Computing Surveys 24(4), Dec 1992.
J. Zobel and P. Dart.  Finding approximate matches in large lexicons.  Software - practice and experience 25(3), March
Nice, easy reading on spell correction:
Mikael Tillenius: Efficient Generation and Ranking of Spelling Error Corrections. Master’s thesis at Sweden’s Royal Institute of Technology.

24. Spell correction Two principal uses Two main flavors:
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.

25. 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
Heuristics based on document source

26. Query mis-spellings Our principal focus here We can either
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 … ?
Nldb vs vldb
Use ‘”incorrect” form because it has local significance – common mis-spelling turned into Proper-noun
Find words in the neighborhood more likely to be sought after

27. 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)
Cohesia domain lib for materials and process specs
Also use clickstream to deal with popular variants
Detection of curse words – “Cursing in English on Twitter”

28. 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
In addition, we may use corpus-based statistics
such as relative frequency of occurrence of various alternatives
and user query-based statistics
such as relative frequency of occurrence in various local/global queries

29. 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.
Cf. correcting parsing errors in good old days (Refernce: Backhouse’s book on Parsing)
Also called “Levenshtein distance”
See for a nice example plus an applet. [not working now]

30. 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"
"SPA" to "PA" in 1 edit 4.
"R" to "R"
"SPAR" to "PAR" in 1 edit 5.
"T" to "T"
"SPART" to "PART" in 1 edit 6.
"A" to "T"
delete: +1 edit
"SPARTA" to "PART" in 2 edits 7.
"N" to "T"
"SPARTAN" to "PART" in 3 edits

31. Transform "SEA" into "ATE" Step Comparison Edit necessary
Total Editing 1.
"S" to ""
delete: +1 edit
"S" to ""  in 1 edit 2.
"E" to ""
"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"
"SEA" to "ATE" in 4 edits

32. Transform "SEA" into "ATE" Step Comparison Edit 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

33. 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
(Some literature formulates weighted edit distance as a probability of the error)
Use n-gram technique to reduce the number of terms to be considered for
computing edit distance from the query before final alternative spellings for retrieval
are determined

34. Edit distance to all dictionary terms?
Sec
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.
Alternative is to generate everything up to edit distance k and then intersect. Fine for distance 1; okay for distance 2. This is generally enough (Norvig).

35. Distance between misspelled word and “correct” word
We will study several alternatives.
Edit distance and Levenshtein distance
Weighted edit distance
k-gram overlap 38

36. 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

37. Levenshtein distance: Computation40

38. Levenshtein distance: Algorithm41

39. Levenshtein distance: Algorithm42

40. Levenshtein distance: Algorithm43

41. Levenshtein distance: Algorithm44

42. Levenshtein distance: Algorithm45

43. Levenshtein distance: Example46

44. Each cell of Levenshtein matrix
cost of getting here from
my upper left neighbor
(copy or replace)
cost of getting here
from my upper neighbor
(delete)
my left neighbor (insert)
the minimum of the three possible “movements”;
the cheapest way of getting here 47

45. Levenshtein distance: Example48

46. 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

47. 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

48. Exercise Compute Levenshtein distance matrix for OSLO – SNOW
What are the Levenshtein editing operations that transform cat into catcat? 51

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82. I read out the editing operations that transform OSLO into SNOW?
How do
I read out the editing operations that transform OSLO into SNOW? 85

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93. 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

94. 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?

95. 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
Limited ordering involved
Other alternatives Dice coefficient, Jaro-Winkler distance

96. 2-gram indexes for spelling correction: bordroom
100

97. 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.

98. 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.
Suppose that for “flew form Heathrow” we have 7 alternatives for flew, 19 for form and 3 for heathrow.
How many “corrected” phrases will we enumerate in this scheme?
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!

99. General issues in spell correction
Sec
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 probabilistically
argmaxcorr P(corr | query)
From Bayes rule, this is equivalent to argmaxcorr P(query | corr) * P(corr)
P(corr) => apriori probability based on query log analysis?
In our example, the biword ‘fled fore’ is likely to be rare compared to the biword ‘flew from’.
Noisy channel
Language model

100. 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

101. Using context via Web N-gram service : Tokenization

102. 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

103. 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.

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

105. Soundex

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

107. 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)

108. Soundex – typical algorithm
Retain the first letter of the word.
Change all occurrences of the following letters to '0' (zero):   'A', E', 'I', 'O', 'U', 'H', 'W', 'Y'.
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
Letters that sound similar have same code – vowels ignored
Biplav vs Viplav different; Dime vs Time mapped to different codes
though sound the same …
Prasad (=> P623), Prathima and Pramod are mapped to different codes.
Public and Pivelog are mapped to the same code.

109. Will hermann generate the same code?
Soundex continued
Remove all pairs of consecutive digits.
Remove all zeros from the resulting string.
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.
Hermann => H655
Will hermann generate the same code?

110. Example: Soundex of HERMAN
Retain H
ERMAN → 0RM0N
0RM0N → 06505
06505 → 06505
06505 → 655
Return H655
Note: HERMANN will generate the same code
119

111. 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?

112. Sec. 3.4
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

113. 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)

114. 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
Nice, easy reading on spell correction:
Peter Norvig: How to write a spelling corrector