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A Formal Study of Information Retrieval Heuristics

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A Formal Study of Information Retrieval Heuristics

Hui Fang, Tao Tao and ChengXiang Zhai

Department of Computer Science

University of Illinois, Urbana-Champaign

USA

- Retrieval heuristics are necessary for good retrieval performance.
- E.g. TF-IDF weighting, document length normalization

- Similar formulas may have different performances.
- Performance is sensitive to parameter setting.

Inversed Document Frequency

- Pivoted Normalization Method
- Dirichlet Prior Method
- Okapi Method

1+ln(c(w,d))

Parameter sensitivity

Document Length Normalization

Alternative TF transformation

Term Frequency

Empirical Observations in IR (Cont.)

- How can we formally characterize these necessary retrieval heuristics?
- Can we predict the empirical behavior of a method without experimentation?

Outline

- Formalized heuristic retrieval constraints
- Analytical evaluation of the current retrieval formulas
- Benefits of constraint analysis
- Better understanding of parameter optimization
- Explanation of performance difference
- Improvement of existing retrieval formulas

Let q be a query with only one term w.

w

q :

If

d1:

and

d2:

then

TF weighting heuristic I: Give a higher score to a document with more occurrences of a query term.

- TFC1

Let q be a query and w1, w2be two query terms.

w1

w2

q:

Assume

and

d1:

If

and

d2:

then

TF weighting heuristic II: Favor a document with more distinct query terms.

- TFC2

Doc 1

Doc 2

...

…

SVM

SVM

Tutorial

Tutorial

…

…

…

SVM

SVM

Tutorial

Tutorial

…

IDF weighting heuristic:Penalize the words popular in the collection; Give higher weights to discriminative terms.

Query: SVM TutorialAssume IDF(SVM)>IDF(Tutorial)

SVMTutorial

w1

w2

q:

Let q be a query and w1, w2be two query terms.

d1:

Assume

d2:

and

and

for all other words w.

If

and

then

- TDC

- LNC1

q:

Let q be a query.

d1:

If for some word

d2:

but for other words

then

- LNC2

q:

Let q be a query.

If

and

d1:

d2:

then

Document length normalization heuristic:Penalize long documents(LNC1); Avoid over-penalizing long documents (LNC2) .

Let q be a query with only one term w.

w

q:

If

d1:

d2:

and

then

TF-LN heuristic:Regularize the interaction of TF and document length.

- TF-LNC

Query: SVM TutorialAssume IDF(SVM)>IDF(Tutorial)

Doc 1

...

…

SVM

SVM

SVM

Tutorial

Tutorial

…

IDF weighting heuristic:Penalize the words popular in the collection; Give higher weights to discriminative terms.

Doc 2

…

…

Tutorial

SVM

SVM

Tutorial

Tutorial

…

- Provide an approximate bound for the parameters
- A constraint may be satisfied only if the parameter is within a particular interval.

- Compare different formulas analytically without experimentations
- When a formula does not satisfy the constraint, it often indicates non-optimality of the formula.

- Suggest how to improve the current retrieval models
- Violation of constraints may pinpoint where a formula needs to be improved.

Optimal s (for average precision)

Parameter sensitivity of s

Avg. Prec.

0.4

s

LNC2 s<0.4

- Pivoted Normalization Method

Negative when df(w) is large Violate many constraints

keyword query

verbose query

Avg. Prec

Avg. Prec

Okapi

Pivoted

s or b

s or b

- Okapi Method

Modified Okapi

verbose query

keyword query

Avg. Prec.

Avg. Prec.

Okapi

Pivoted

s or b

s or b

- Modified Okapi Method

Make Okapi satisfy more constraints; expected to help verbose queries

- Conclusions
- Retrieval heuristics can be captured through formally defined constraints.
- It is possible to evaluate a retrieval formula analytically through constraint analysis.

- Future Work
- Explore additional necessary heuristics
- Apply these constraints to many other retrieval methods
- Develop new retrieval formulas through constraint analysis

The End

Thank you!