1. CS 430 / INFO 430 Information Retrieval
Lecture 6
Boolean Methods

2. Course Administration
Assignments
You are encouraged to use existing Java or C++ classes, e.g., to manage data structures.
If you do, you must acknowledge them in your report. In addition, for a data structure, you should explain why this structure is appropriate for the use you make of it.

3. Porter Stemmer A multi-step, longest-match stemmer.
M. F. Porter, An algorithm for suffix stripping. (Originally published in Program, 14 no. 3, pp , July 1980.)
Notation
v vowel(s)
c constant(s)
(vc)m vowel(s) followed by constant(s), repeated m times
Any word can be written: [c](vc)m[v]
m is called the measure of the word

4. Porter's Stemmer Multi-Step Stemming Algorithm Complex suffixes
Complex suffixes are removed bit by bit in the different steps. Thus:
GENERALIZATIONS
becomes GENERALIZATION (Step 1)
becomes GENERALIZE (Step 2)
becomes GENERAL (Step 3)
becomes GENER (Step 4)
[In this example, note that Steps 3 and 4 appear to be unhelpful for information retrieval.]

5. Porter Stemmer: Step 1a Suffix Replacement Examples
sses ss caresses -> caress
ies i ponies -> poni
ties > ti
ss ss caress -> caress
s cats > cat
At each step, carry out the longest match only.

6. Porter Stemmer: Step 1b Conditions Suffix Replacement Examples
(m > 0) eed ee feed -> feed
agreed -> agree
(*v*) ed null plastered -> plaster
bled -> bled
(*v*) ing null motoring -> motor
sing -> sing
*v* - the stem contains a vowel

7. Porter Stemmer: Step 5a (m>1) e -> probate -> probat
rate -> rate
(m=1 and not *o) e -> cease -> ceas
*o - the stem ends cvc, where the second c is not w, x or y (e.g. -wil, -hop).

8. Porter Stemmer: Results
Suffix stripping of a vocabulary of 10,000 words
Number of words reduced in step 1:
step 2:
step 3:
step 4:
step 5:
Number of words not reduced:
The resulting vocabulary of stems contained 6370 distinct entries. Thus the suffix stripping process reduced the size of the vocabulary by about one third.

9. Exact Matching (Boolean Model)
Documents
Query
Index database
Mechanism for determining whether a document matches a query.
Set of hits

10. Boolean Queries Boolean query: two or more search terms, related by
logical operators, e.g.,
and or not
Examples:
abacus and actor
abacus or actor
(abacus and actor) or (abacus and atoll)
not actor

11. Boolean Diagram
not (A or B)
A and B A B
A or B

12. Adjacent and Near Operators
abacus adj actor
Terms abacus and actor are adjacent to each other as in the string
"abacus actor"
abacus near 4 actor
Terms abacus and actor are near to each other as in the string
"the actor has an abacus"
Some systems support other operators, such as with (two terms in the same sentence) or same (two terms in the same paragraph).

13. Evaluation of Boolean Operators
Precedence of operators must be defined:
adj, near high
and, not
or low
Example
A and B or C and B
is evaluated as
(A and B) or (C and B)

14. Evaluating a Boolean Query
Examples: abacus and actor
Postings for abacus
Postings for actor
Document 19 is the only document that contains both terms, "abacus" and "actor". 3 19 22
To evaluate the and operator, merge the two inverted lists with a logical AND operation. 2 19 29

15. Evaluating an Adjacency Operation
Examples: abacus adj actor
Postings for abacus
Postings for actor
Document 19, locations 212 and 213, is the only occurrence of the terms "abacus" and "actor" adjacent.

16. Query Matching: Boolean Methods
Query: (abacus or asp*) and actor
1. From the index file (word list), find the postings file for:
"abacus"
every word that begins "asp"
"actor"
Merge these posting lists. For each document that occurs in any of the postings lists, evaluate the Boolean expression to see if it is true or false.
Step 2 should be carried out in a single pass.

17. Use of Postings File for Query Matching
1 abacus
2 actor 66
3 aspen
4 atoll 3 70

18. Query Matching: Vector Ranking Methods
Query: abacus asp*
1. From the index file (word list), find the postings file for:
"abacus"
every word that begins "asp"
Merge these posting lists. Calculate the similarity to the query for each document that occurs in any of the postings lists.
Sort the similarities to obtain the results in ranked order.
Steps 2 and 3 should be carried out in a single pass.

19. Contrast of Ranking with Matching
With matching, a document either matches a query exactly or not at all
• Encourages short queries
• Requires precise choice of index terms
• Requires precise formulation of queries (professional training)
With retrieval using similarity measures, similarities range from 0 to 1 for all documents
• Encourages long queries, to have as many dimensions as possible
• Benefits from large numbers of index terms
• Benefits from queries with many terms, not all of which need
match the document

20. Problems with the Boolean model
Counter-intuitive results:
Query q = a and b and c and d and e
Document d has terms a, b, c and d, but not e
Intuitively, d is quite a good match for q, but it is rejected by the Boolean model.
Query q = a or b or c or d or e
Document d1 has terms a, b, c, d, and e
Document d2 has term a, but not b, c, d or e
Intuitively, d1 is a much better match than d2, but the Boolean model ranks them as equal.

21. Problems with the Boolean model (continued)
Boolean is all or nothing
• Boolean model has no way to rank documents.
• Boolean model allows for no uncertainty in assigning index terms to documents.
• The Boolean model has no provision for adjusting the importance of query terms.

22. Extending the Boolean model
Term weighting
• Give weights to terms in documents and/or queries.
• Combine standard Boolean retrieval with vector ranking of results
Fuzzy sets
• Relax the boundaries of the sets used in Boolean retrieval

23. Ranking methods in Boolean systems
SIRE (Syracuse Information Retrieval Experiment)
Term weights
• Add term weights to documents
Weights calculated by the standard method of
term frequency * inverse document frequency.
Ranking
• Calculate results set by standard Boolean methods
• Rank results by vector distances

24. Relevance feedback in SIRE
SIRE (Syracuse Information Retrieval Experiment)
Relevance feedback is particularly important with Boolean
retrieval because it allow the results set to be expanded
• Results set is created by standard Boolean retrieval
• User selects one document from results set
• Other documents in collection are ranked by vector
distance from this document
[Relevance feedback will be covered in a later lecture.]

25. Boolean model as sets
d is either in the set A or not in A. d A

26. Boolean model as fuzzy sets
d is more or less in A. d A

27. Fuzzy Sets: Basic concept
• A document has a term weight associated with each index term. The term weight measures the degree to which that term characterizes the document.
• Term weights are in the range [0, 1]. (In the standard Boolean model all weights are either 0 or 1.)
• For a given query, calculate the similarity between the query and each document in the collection.
• This calculation is needed for every document that has a non-zero weight for any of the terms in the query.

28. Fuzzy Sets Fuzzy set theory
dA is the degree of membership of an element to set A
intersection (and)
dAB = min(dA, dB)
union (or)
dAB = max(dA, dB)

29. Fuzzy Sets Fuzzy set theory example standard fuzzy
set theory set theory dA dB
and dAB
or dAB

30. MMM: Mixed Min and Max model
Terms: a1, a2, , an
Document: d, with index-term weights: d1, d2, , dn
qor = (a1 or a2 or or an)
Query-document similarity:
S(qor, d) = or * max(d1, d2,.. , dn) + (1 - or) * min(d1, d2,.. , dn)
With regular Boolean logic, all di = 1 or 0, or = 1

31. MMM: Mixed Min and Max model
Terms: a1, a2, , an
Document: d, with index-term weights: d1, d2, , dn
qand = (a1 and a2 and and an)
Query-document similarity:
S(qand, d) = and * min(d1,.. , dn) + (1 - and)* max(d1,.. , dn)
With regular Boolean logic, all di = 1 or 0, and = 1

32. MMM: Mixed Min and Max model
Experimental values:
all di = 1 or 0
and in range [0.5, 0.8]
or > 0.2
Computational cost is low. Retrieval performance much improved.

33. Other Models Paice model
The MMM model considers only the maximum and minimum document weights. The Paice model takes into account all of the document weights. Computational cost is higher than MMM.
P-norm model
Document d, with term weights: dA1, dA2, , dAn
Query terms are given weights, a1, a2, ,an
Operators have coefficients that indicate degree of strictness
Query-document similarity is calculated by considering each document and query as a point in n space.

34. Test data CISI CACM INSPEC P-norm 79 106 210 Paice 77 104 206
MMM
Percentage improvement over standard Boolean model (average best precision)
Lee and Fox, 1988

35. Reading
E. Fox, S. Betrabet, M. Koushik, W. Lee, Extended Boolean Models, Frake, Chapter 15
Methods based on fuzzy set concepts