Document representations and measures of relatedness in vec-
14.1 Document representations and measures of relatedness in vec-
tor spaces As in Chapter 6 , we represent documents as vectors in R |V| in this chapter. To illustrate properties of document vectors in vector classification, we will render these vectors as points in a plane as in the example in Figure 14.1 . In reality, document vectors are length-normalized unit vectors that point to the surface of a hypersphere. We can view the 2D planes in our figures as projections onto a plane of the surface of a hyper-sphere as shown in Figure 14.2 . Distances on the surface of the sphere and on the projection plane are approximately the same as long as we restrict ourselves to small areas of the surface and choose an appropriate projection Exercise 14.1 . Preliminary draft c 2008 Cambridge UP 292 14 Vector space classification Decisions of many vector space classifiers are based on a notion of dis- tance, e.g., when computing the nearest neighbors in kNN classification. We will use Euclidean distance in this chapter as the underlying distance measure. We observed earlier Exercise 6.18 , page 131 that there is a direct correspondence between cosine similarity and Euclidean distance for length- normalized vectors. In vector space classification, it rarely matters whether the relatedness of two documents is expressed in terms of similarity or dis- tance. However, in addition to documents, centroids or averages of vectors also play an important role in vector space classification. Centroids are not length- normalized. For unnormalized vectors, dot product, cosine similarity and Euclidean distance all have different behavior in general Exercise 14.6 . We will be mostly concerned with small local regions when computing the sim- ilarity between a document and a centroid, and the smaller the region the more similar the behavior of the three measures is. ? Exercise 14.1 For small areas, distances on the surface of the hypersphere are approximated well by distances on its projection Figure 14.2 because α ≈ sin α for small angles. For what size angle is the distortion α sin α i 1.01, ii 1.05 and iii 1.1?14.2 Rocchio classification
Parts
» cambridge introductiontoinformationretrieval2008 readingversion
» An example information retrieval problem
» A first take at building an inverted index
» Processing Boolean queries cambridge introductiontoinformationretrieval2008 readingversion
» The extended Boolean model versus ranked retrieval
» References and further reading
» Obtaining the character sequence in a document
» Tokenization Determining the vocabulary of terms
» Dropping common terms: stop words
» Normalization equivalence classing of terms
» Stemming and lemmatization Determining the vocabulary of terms
» Faster postings list intersection via skip pointers
» Biword indexes Positional postings and phrase queries
» Positional indexes Positional postings and phrase queries
» Combination schemes Positional postings and phrase queries
» Search structures for dictionaries
» General wildcard queries Wildcard queries
» k-gram indexes for wildcard queries
» Implementing spelling correction Spelling correction
» Forms of spelling correction Edit distance
» k-gram indexes for spelling correction
» Context sensitive spelling correction
» Phonetic correction cambridge introductiontoinformationretrieval2008 readingversion
» Hardware basics Blocked sort-based indexing
» Single-pass in-memory indexing cambridge introductiontoinformationretrieval2008 readingversion
» Distributed indexing cambridge introductiontoinformationretrieval2008 readingversion
» Dynamic indexing cambridge introductiontoinformationretrieval2008 readingversion
» References and further reading Exercises
» Heaps’ law: Estimating the number of terms Zipf’s law: Modeling the distribution of terms
» Blocked storage Dictionary compression
» Variable byte codes γ Postings file compression
» Exercises cambridge introductiontoinformationretrieval2008 readingversion
» Weighted zone scoring Parametric and zone indexes
» Learning weights Parametric and zone indexes
» The optimal weight Parametric and zone indexes
» Inverse document frequency Term frequency and weighting
» Tf-idf weighting Term frequency and weighting
» Dot products The vector space model for scoring
» Queries as vectors Computing vector scores
» Sublinear tf scaling Maximum tf normalization
» Document and query weighting schemes Pivoted normalized document length
» Inexact top Efficient scoring and ranking
» Index elimination Champion lists
» Static quality scores and ordering
» Impact ordering Efficient scoring and ranking
» Cluster pruning Efficient scoring and ranking
» Tiered indexes Query-term proximity
» Designing parsing and scoring functions
» Vector space scoring and query operator interaction
» Information retrieval system evaluation
» Standard test collections cambridge introductiontoinformationretrieval2008 readingversion
» Evaluation of unranked retrieval sets
» Evaluation of ranked retrieval results
» Critiques and justifications of the concept of relevance
» Results snippets cambridge introductiontoinformationretrieval2008 readingversion
» 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
» Vocabulary tools for query reformulation Query expansion
» Basic XML concepts cambridge introductiontoinformationretrieval2008 readingversion
» A vector space model for XML retrieval
» Text-centric vs. data-centric XML retrieval
» Review of basic probability theory
» The 10 loss case The Probability Ranking Principle
» Deriving a ranking function for query terms
» Probability estimates in theory
» Probability estimates in practice
» Probabilistic approaches to relevance feedback
» An appraisal of probabilistic models
» Tree-structured dependencies between terms Okapi BM25: a non-binary model
» Finite automata and language models
» Multinomial distributions over words
» Using query likelihood language models in IR
» Estimating the query generation probability
» Ponte and Croft’s Experiments
» Language modeling versus other approaches in IR
» Extended language modeling approaches
» The text classification problem
» The Bernoulli model cambridge introductiontoinformationretrieval2008 readingversion
» Mutual information Feature selection
» Frequency-based feature selection Feature selection for multiple classifiers
» Evaluation of text classification
» Document representations and measures of relatedness in vec-
» Rocchio classification cambridge introductiontoinformationretrieval2008 readingversion
» Time complexity and optimality of kNN
» Linear versus nonlinear classifiers
» Classification with more than two classes
» The bias-variance tradeoff cambridge introductiontoinformationretrieval2008 readingversion
» Support vector machines: The linearly separable case
» Soft margin classification Extensions to the SVM model
» Multiclass SVMs Nonlinear SVMs
» Experimental results Extensions to the SVM model
» Choosing what kind of classifier to use
» Improving classifier performance Issues in the classification of text documents
» A simple example of machine-learned scoring
» Result ranking by machine learning
» Clustering in information retrieval
» Evaluation of clustering cambridge introductiontoinformationretrieval2008 readingversion
» Cluster cardinality in K-means
» Model-based clustering cambridge introductiontoinformationretrieval2008 readingversion
» Centroid clustering cambridge introductiontoinformationretrieval2008 readingversion
» Optimality of HAC cambridge introductiontoinformationretrieval2008 readingversion
» Divisive clustering cambridge introductiontoinformationretrieval2008 readingversion
» Cluster labeling cambridge introductiontoinformationretrieval2008 readingversion
» Implementation notes cambridge introductiontoinformationretrieval2008 readingversion
» Term-document matrices and singular value decompositions
» Low-rank approximations cambridge introductiontoinformationretrieval2008 readingversion
» Latent semantic indexing cambridge introductiontoinformationretrieval2008 readingversion
» Background and history cambridge introductiontoinformationretrieval2008 readingversion
» The web graph Web characteristics
» Advertising as the economic model
» Near-duplicates and shingling cambridge introductiontoinformationretrieval2008 readingversion
» Features a crawler Features a crawler
» Distributing indexes cambridge introductiontoinformationretrieval2008 readingversion
» Connectivity servers cambridge introductiontoinformationretrieval2008 readingversion
» Anchor text and the web graph
» The PageRank computation PageRank
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