- •List of Tables
- •List of Figures
- •Table of Notation
- •Preface
- •Boolean retrieval
- •An example information retrieval problem
- •Processing Boolean queries
- •The extended Boolean model versus ranked retrieval
- •References and further reading
- •The term vocabulary and postings lists
- •Document delineation and character sequence decoding
- •Obtaining the character sequence in a document
- •Choosing a document unit
- •Determining the vocabulary of terms
- •Tokenization
- •Dropping common terms: stop words
- •Normalization (equivalence classing of terms)
- •Stemming and lemmatization
- •Faster postings list intersection via skip pointers
- •Positional postings and phrase queries
- •Biword indexes
- •Positional indexes
- •Combination schemes
- •References and further reading
- •Dictionaries and tolerant retrieval
- •Search structures for dictionaries
- •Wildcard queries
- •General wildcard queries
- •Spelling correction
- •Implementing spelling correction
- •Forms of spelling correction
- •Edit distance
- •Context sensitive spelling correction
- •Phonetic correction
- •References and further reading
- •Index construction
- •Hardware basics
- •Blocked sort-based indexing
- •Single-pass in-memory indexing
- •Distributed indexing
- •Dynamic indexing
- •Other types of indexes
- •References and further reading
- •Index compression
- •Statistical properties of terms in information retrieval
- •Dictionary compression
- •Dictionary as a string
- •Blocked storage
- •Variable byte codes
- •References and further reading
- •Scoring, term weighting and the vector space model
- •Parametric and zone indexes
- •Weighted zone scoring
- •Learning weights
- •The optimal weight g
- •Term frequency and weighting
- •Inverse document frequency
- •The vector space model for scoring
- •Dot products
- •Queries as vectors
- •Computing vector scores
- •Sublinear tf scaling
- •Maximum tf normalization
- •Document and query weighting schemes
- •Pivoted normalized document length
- •References and further reading
- •Computing scores in a complete search system
- •Index elimination
- •Champion lists
- •Static quality scores and ordering
- •Impact ordering
- •Cluster pruning
- •Components of an information retrieval system
- •Tiered indexes
- •Designing parsing and scoring functions
- •Putting it all together
- •Vector space scoring and query operator interaction
- •References and further reading
- •Evaluation in information retrieval
- •Information retrieval system evaluation
- •Standard test collections
- •Evaluation of unranked retrieval sets
- •Evaluation of ranked retrieval results
- •Assessing relevance
- •A broader perspective: System quality and user utility
- •System issues
- •User utility
- •Results snippets
- •References and further reading
- •Relevance feedback and query expansion
- •Relevance feedback and pseudo relevance feedback
- •The Rocchio algorithm for relevance feedback
- •Probabilistic relevance feedback
- •When does relevance feedback work?
- •Relevance feedback on the web
- •Evaluation of relevance feedback strategies
- •Pseudo relevance feedback
- •Indirect relevance feedback
- •Summary
- •Global methods for query reformulation
- •Vocabulary tools for query reformulation
- •Query expansion
- •Automatic thesaurus generation
- •References and further reading
- •XML retrieval
- •Basic XML concepts
- •Challenges in XML retrieval
- •A vector space model for XML retrieval
- •Evaluation of XML retrieval
- •References and further reading
- •Exercises
- •Probabilistic information retrieval
- •Review of basic probability theory
- •The Probability Ranking Principle
- •The 1/0 loss case
- •The PRP with retrieval costs
- •The Binary Independence Model
- •Deriving a ranking function for query terms
- •Probability estimates in theory
- •Probability estimates in practice
- •Probabilistic approaches to relevance feedback
- •An appraisal and some extensions
- •An appraisal of probabilistic models
- •Bayesian network approaches to IR
- •References and further reading
- •Language models for information retrieval
- •Language models
- •Finite automata and language models
- •Types of language models
- •Multinomial distributions over words
- •The query likelihood model
- •Using query likelihood language models in IR
- •Estimating the query generation probability
- •Language modeling versus other approaches in IR
- •Extended language modeling approaches
- •References and further reading
- •Relation to multinomial unigram language model
- •The Bernoulli model
- •Properties of Naive Bayes
- •A variant of the multinomial model
- •Feature selection
- •Mutual information
- •Comparison of feature selection methods
- •References and further reading
- •Document representations and measures of relatedness in vector spaces
- •k nearest neighbor
- •Time complexity and optimality of kNN
- •The bias-variance tradeoff
- •References and further reading
- •Exercises
- •Support vector machines and machine learning on documents
- •Support vector machines: The linearly separable case
- •Extensions to the SVM model
- •Multiclass SVMs
- •Nonlinear SVMs
- •Experimental results
- •Machine learning methods in ad hoc information retrieval
- •Result ranking by machine learning
- •References and further reading
- •Flat clustering
- •Clustering in information retrieval
- •Problem statement
- •Evaluation of clustering
- •Cluster cardinality in K-means
- •Model-based clustering
- •References and further reading
- •Exercises
- •Hierarchical clustering
- •Hierarchical agglomerative clustering
- •Time complexity of HAC
- •Group-average agglomerative clustering
- •Centroid clustering
- •Optimality of HAC
- •Divisive clustering
- •Cluster labeling
- •Implementation notes
- •References and further reading
- •Exercises
- •Matrix decompositions and latent semantic indexing
- •Linear algebra review
- •Matrix decompositions
- •Term-document matrices and singular value decompositions
- •Low-rank approximations
- •Latent semantic indexing
- •References and further reading
- •Web search basics
- •Background and history
- •Web characteristics
- •The web graph
- •Spam
- •Advertising as the economic model
- •The search user experience
- •User query needs
- •Index size and estimation
- •Near-duplicates and shingling
- •References and further reading
- •Web crawling and indexes
- •Overview
- •Crawling
- •Crawler architecture
- •DNS resolution
- •The URL frontier
- •Distributing indexes
- •Connectivity servers
- •References and further reading
- •Link analysis
- •The Web as a graph
- •Anchor text and the web graph
- •PageRank
- •Markov chains
- •The PageRank computation
- •Hubs and Authorities
- •Choosing the subset of the Web
- •References and further reading
- •Bibliography
- •Author Index
6.1 Parametric and zone indexes |
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Example |
DocID |
Query |
sT |
sB |
Judgment |
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Φ1 |
37 |
linux |
1 |
1 |
Relevant |
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Φ2 |
37 |
penguin |
0 |
1 |
Non-relevant |
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Φ3 |
238 |
system |
0 |
1 |
Relevant |
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Φ4 |
238 |
penguin |
0 |
0 |
Non-relevant |
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Φ5 |
1741 |
kernel |
1 |
1 |
Relevant |
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Φ6 |
2094 |
driver |
0 |
1 |
Relevant |
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Φ7 |
3191 |
driver |
1 |
0 |
Non-relevant |
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Figure 6.5 An illustration of training examples.
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sT |
sB |
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Score |
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0 |
0 |
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0 |
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0 |
1 |
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1 − g |
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1 |
0 |
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g |
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1 |
1 |
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1 |
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Figure 6.6 The four possible combinations of sT and sB. |
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where we have quantized the editorial relevance judgment r(dj, qj) to 0 or 1. |
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Then, the total error of a set of training examples is given by |
(6.4) |
∑ ε(g, Φj). |
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j |
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The problem of learning the constant g from the given training examples |
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then reduces to picking the value of g that minimizes the total error in (6.4). |
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Picking the best value of g in (6.4) in the formulation of Section 6.1.3 re- |
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duces to the problem of minimizing a quadratic function of g over the inter- |
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val [0, 1]. This reduction is detailed in Section 6.1.3. |
6.1.3 |
The optimal weight g |
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We begin by noting that for any training example Φj for which sT (dj, qj) = 0 |
and sB(dj, qj) = 1, the score computed by Equation (6.2) is 1 − g. In similar fashion, we may write down the score computed by Equation (6.2) for the three other possible combinations of sT (dj, qj) and sB(dj, qj); this is summarized in Figure 6.6.
Let n01r (respectively, n01n) denote the number of training examples for which sT (dj, qj) = 0 and sB(dj, qj) = 1 and the editorial judgment is Relevant (respectively, Non-relevant). Then the contribution to the total error in Equation (6.4) from training examples for which sT(dj, qj) = 0 and sB(dj, qj) = 1
Online edition (c) 2009 Cambridge UP
116 |
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6 Scoring, term weighting and the vector space model |
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is |
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[1 − (1 − g)]2n01r + [0 − (1 − g)]2n01n. |
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By writing in similar fashion the error contributions from training examples |
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of the other three combinations of values for sT (dj, qj) and sB(dj, qj) (and |
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extending the notation in the obvious manner), the total error corresponding |
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to Equation (6.4) is |
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(6.5) |
(n01r + n10n)g2 + (n10r + n01n)(1 − g)2 + n00r + n11n. |
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By differentiating Equation (6.5) with respect to g and setting the result to |
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zero, it follows that the optimal value of g is |
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(6.6) |
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n10r + n01n |
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n10r + n10n + n01r + n01n |
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?Exercise 6.1
When using weighted zone scoring, is it necessary for all zones to use the same Boolean match function?
Exercise 6.2
In Example 6.1 above with weights g1 = 0.2, g2 = 0.31 and g3 = 0.49, what are all the distinct score values a document may get?
Exercise 6.3
Rewrite the algorithm in Figure 6.4 to the case of more than two query terms.
Exercise 6.4
Write pseudocode for the function WeightedZone for the case of two postings lists in Figure 6.4.
Exercise 6.5
Apply Equation 6.6 to the sample training set in Figure 6.5 to estimate the best value of g for this sample.
Exercise 6.6
For the value of g estimated in Exercise 6.5, compute the weighted zone score for each (query, document) example. How do these scores relate to the relevance judgments in Figure 6.5 (quantized to 0/1)?
Exercise 6.7
Why does the expression for g in (6.6) not involve training examples in which sT(dt, qt) and sB(dt, qt) have the same value?
Online edition (c) 2009 Cambridge UP