- •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
2.4 Positional postings and phrase queries |
43 |
will discuss in Section 5.3 (page 95). Indeed, moving to a positional index also changes the asymptotic complexity of a postings intersection operation, because the number of items to check is now bounded not by the number of documents but by the total number of tokens in the document collection T. That is, the complexity of a Boolean query is Θ(T) rather than Θ(N). However, most applications have little choice but to accept this, since most users now expect to have the functionality of phrase and proximity searches.
Let’s examine the space implications of having a positional index. A posting now needs an entry for each occurrence of a term. The index size thus depends on the average document size. The average web page has less than 1000 terms, but documents like SEC stock filings, books, and even some epic poems easily reach 100,000 terms. Consider a term with frequency 1 in 1000 terms on average. The result is that large documents cause an increase of two orders of magnitude in the space required to store the postings list:
|
Expected |
Expected entries |
Document size |
postings |
in positional posting |
1000 |
1 |
1 |
100,000 |
1 |
100 |
While the exact numbers depend on the type of documents and the language being indexed, some rough rules of thumb are to expect a positional index to be 2 to 4 times as large as a non-positional index, and to expect a compressed positional index to be about one third to one half the size of the raw text (after removal of markup, etc.) of the original uncompressed documents. Specific numbers for an example collection are given in Table 5.1 (page 87) and Table 5.6 (page 103).
2.4.3Combination schemes
The strategies of biword indexes and positional indexes can be fruitfully combined. If users commonly query on particular phrases, such as Michael Jackson, it is quite inefficient to keep merging positional postings lists. A combination strategy uses a phrase index, or just a biword index, for certain queries and uses a positional index for other phrase queries. Good queries to include in the phrase index are ones known to be common based on recent querying behavior. But this is not the only criterion: the most expensive phrase queries to evaluate are ones where the individual words are common but the desired phrase is comparatively rare. Adding Britney Spears as a phrase index entry may only give a speedup factor to that query of about 3, since most documents that mention either word are valid results, whereas adding The Who as a phrase index entry may speed up that query by a factor of 1000. Hence, having the latter is more desirable, even if it is a relatively less common query.
Online edition (c) 2009 Cambridge UP
44
NEXT WORD INDEX
?
2 The term vocabulary and postings lists
Williams et al. (2004) evaluate an even more sophisticated scheme which employs indexes of both these sorts and additionally a partial next word index as a halfway house between the first two strategies. For each term, a next word index records terms that follow it in a document. They conclude that such a strategy allows a typical mixture of web phrase queries to be completed in one quarter of the time taken by use of a positional index alone, while taking up 26% more space than use of a positional index alone.
Exercise 2.8 |
[ ] |
Assume a biword index. Give an example of a document which will be returned for a query of New York University but is actually a false positive which should not be returned.
Exercise 2.9 |
[ ] |
Shown below is a portion of a positional index in the format: term: doc1: hposition1, position2, . . . i; doc2: hposition1, position2, . . . i; etc.
angels: 2: h36,174,252,651i; 4: h12,22,102,432i; 7: h17i; fools: 2: h1,17,74,222i; 4: h8,78,108,458i; 7: h3,13,23,193i; fear: 2: h87,704,722,901i; 4: h13,43,113,433i; 7: h18,328,528i;
in: 2: h3,37,76,444,851i; 4: h10,20,110,470,500i; 7: h5,15,25,195i; rush: 2: h2,66,194,321,702i; 4: h9,69,149,429,569i; 7: h4,14,404i; to: 2: h47,86,234,999i; 4: h14,24,774,944i; 7: h199,319,599,709i; tread: 2: h57,94,333i; 4: h15,35,155i; 7: h20,320i;
where: 2: h67,124,393,1001i; 4: h11,41,101,421,431i; 7: h16,36,736i;
Which document(s) if any match each of the following queries, where each expression within quotes is a phrase query?
a. “fools rush in”
b. “fools rush in” AND “angels fear to tread”
Exercise 2.10 |
[ ] |
Consider the following fragment of a positional index with the format: |
|
word: document: hposition, position, . . .i; document: hposition, . . .i |
|
. . . |
|
Gates: 1: h3i; 2: h6i; 3: h2,17i; 4: h1i; |
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IBM: 4: h3i; 7: h14i; |
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Microsoft: 1: h1i; 2: h1,21i; 3: h3i; 5: h16,22,51i; |
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The /k operator, word1 /k word2 finds occurrences of word1 within k words of word2 (on either side), where k is a positive integer argument. Thus k = 1 demands that word1 be adjacent to word2.
a.Describe the set of documents that satisfy the query Gates /2 Microsoft.
b.Describe each set of values for k for which the query Gates /k Microsoft returns a different set of documents as the answer.
Online edition (c) 2009 Cambridge UP