Introduction to Information Retrieval
CS276: Information Retrieval and Web Search
Pandu Nayak and Prabhakar Raghavan
Lecture 3: Dictionaries and tolerant retrieval
Recap of the previous lecture
The type/token distinction
Terms are normalized types put in the dictionary
Hyphens, apostrophes, compounds, CJK
Term equivalence classing:
Numbers, case folding, stemming, lemmatization
Encoding a tree-like structure in a postings list
Biword indexes for phrases
Positional indexes for phrases/proximity queries
Dictionary data structures
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?
A naïve dictionary
An array of struct:
char 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?
Dictionary data structures
Two main choices:
Some IR systems use hashtables, some trees
Each vocabulary term is hashed to an integer
(We assume you’ve seen hashtables before)
Lookup is faster than for a tree: O(1)
No easy way to find minor variants:
No prefix search [tolerant retrieval]
If vocabulary keeps growing, need to occasionally do the expensive operation of rehashing everything
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].
Simplest: binary tree
More usual: B-trees
Trees require a standard ordering of characters and hence strings … but we typically have one
Solves the prefix problem (terms starting with hyp)
Slower: O(log M) [and this requires balanced tree]
Rebalancing binary trees is expensive
But B-trees mitigate the rebalancing problem
Wild-card queries: *
mon*: find all docs containing any word beginning with “mon”.
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 ?
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.
B-trees handle *’s at the end of a query term
How can we handle *’s in the middle of query term?
We could look up co* AND *tion in a B-tree and intersect the two term sets
The solution: transform wild-card queries so that the *’s occur at the end
This gives rise to the Permuterm Index.
For term hello, index under:
hello$, ello$h, llo$he, lo$hel, o$hell
where $ is a special symbol.
X lookup on X$ X* lookup on $X*
*X lookup on X$* *X* lookup on X*
X*Y lookup on Y$X* X*Y*Z ??? Exercise!
Query = hel*o
Permuterm query processing
Rotate query wild-card to the right
Now use B-tree lookup as before.
Permuterm problem: ≈ quadruples lexicon size
Empirical observation for English.
Bigram (k-gram) 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.
Bigram index example
The k-gram index finds terms based on a query consisting of k-grams (here k=2).
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 enumerate moon.
Must post-filter these terms against query.
Surviving enumerated terms are then looked up in the term-document inverted index.
Fast, space efficient (compared to permuterm).
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…)
pyth* AND prog*
If you encourage “laziness” people will respond!
Two principal uses
Correcting document(s) being indexed
Correcting user queries to retrieve “right” answers
Two main flavors:
Check each word on its own for misspelling
Will not catch typos resulting in correctly spelled words
e.g., from →form
Look at surrounding words,
e.g., I flew form Heathrow to Narita.
Especially needed for OCR’ed documents
Correction algorithms are tuned for this: rn/m
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).
But also: 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
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 …
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)
Isolated word correction
Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q
We’ll study several alternatives
Edit distance (Levenshtein distance)
Weighted edit distance
Given two strings S1 and S2, the minimum number of operations to convert one to the other
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.
See http://www.merriampark.com/ld.htm for a nice example plus an applet.
Weighted edit distance
As above, but the weight of an operation depends on the character(s) involved
Meant to capture OCR or keyboard errors
Example: 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
This may be formulated as a probability model
Requires weight matrix as input
Modify dynamic programming to handle weights
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
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
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.
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
Variants – weight by keyboard layout, etc.
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
Consider the query lord – we wish to identify words matching 2 of its 3 bigrams (lo, or, rd)
lo ⇒ alone → lore → sloth
or ⇒ border → lore → morbid
rd ⇒ ardent → border → card
Standard postings “merge” will enumerate …
Adapt this to using Jaccard (or another) measure.
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.
Need surrounding context to catch 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?
Break phrase query into a conjunction of biwords (Lecture 2).
Look for biwords that need only one term corrected.
Enumerate only phrases containing “common” biwords.
General issues in spell correction
We enumerate multiple alternatives for “Did you mean?”
Need to figure out which to present to the user
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)
Noisy channel Language model
Class of heuristics to expand a query into phonetic equivalents
Language specific – mainly for names
E.g., chebyshev → tchebycheff
Invented for the U.S. census … in 1918
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 – 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
M, N →5
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
E.g., Herman becomes H655.
Will hermann generate the same code?
What queries can we process?
Positional inverted index with skip pointers
Queries such as
(SPELL(moriset) /3 toron*to) OR SOUNDEX(chaikofski)
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
Draw yourself a diagram showing the various indexes in a search engine incorporating all the functionality we have talked about
Identify some of the key design choices in the index pipeline:
Does stemming happen before the Soundex index?
What about n-grams?
Given a query, how would you parse and dispatch sub-queries to the various indexes?
IIR 3, MG 4.2
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 1995. http://citeseer.ist.psu.edu/zobel95finding.html
Mikael Tillenius: Efficient Generation and Ranking of Spelling Error Corrections. Master’s thesis at Sweden’s Royal Institute of Technology. http://citeseer.ist.psu.edu/179155.html
Nice, easy reading on spell correction:
Peter Norvig: How to write a spelling corrector