Debapriyo Majumdar

TopX: efficient and versatile top-k query processing for semistructured data

Recent IR extensions to XML query languages such as Xpath 1.0 Full-Text or the NEXI query language of the INEX benchmark series reflect the emerging interest in IR-style ranked retrieval over semistructured data. TopX is a top-k retrieval engine for text and semistructured data. It terminates query execution as soon as it can safely determine the k top-ranked result elements according to a monotonic score aggregation function with respect to a multidimensional query. It efficiently supports vague search on both content- and structure-oriented query conditions for dynamic query relaxation with controllable influence on the result ranking. The main contributions of this paper unfold into four main points: (1) fully implemented models and algorithms for ranked XML retrieval with XPath Full-Text functionality, (2) efficient and effective top-k query processing for semistructured data, (3) support for integrating thesauri and ontologies with statistically quantified relationships among concepts, leveraged for word-sense disambiguation and query expansion, and (4) a comprehensive description of the TopX system, with performance experiments on large-scale corpora like TREC Terabyte and INEX Wikipedia.

Why spectral retrieval works

We argue that the ability to identify pairs of related terms is at the heart of what makes spectral retrieval work in practice. Schemes such as latent semantic indexing (LSI) and its descendants have this ability in the sense that they can be viewed as computing a matrix of term-term relatedness scores which is then used to expand the given documents (not the queries). For almost all existing spectral retrieval schemes, this matrix of relatedness scores depends on a fixed low-dimensional subspace of the original term space. We instead vary the dimension and study for each term pair the resultin curve of relatedness scores. We find that it is actually the shape of this curve which is indicative for the term-pair relatedness, and not any of the individual relatedness scores on the curve. We derive two simple, parameterless algorithms that detect this shape and that consistently outperform previous methods on a number of test collections. Our curves also shed light on the effectiveness of three fundamental types of variations of the basic LSI scheme.

Discovering a term taxonomy from term similarities using principal component analysis

We show that eigenvector decomposition can be used to extract a term taxonomy from a given collection of text documents. So far, methods based on eigenvector decomposition, such as latent semantic indexing (LSI) or principal component analysis (PCA), were only known to be useful for extracting symmetric relations between terms. We give a precise mathematical criterion for distinguishing between four kinds of relations of a given pair of terms of a given collection: unrelated (car – fruit), symmetrically related (car – automobile), asymmetrically related with the first term being more specific than the second (banana – fruit), and asymmetrically related in the other direction (fruit – banana). We give theoretical evidence for the soundness of our criterion, by showing that in a simplified mathematical model the criterion does the apparently right thing. We applied our scheme to the reconstruction of a selected part of the open directory project (ODP) hierarchy, with promising results.

Sequences characterizing k -trees

A non-decreasing sequence of n integers is the degree sequence of a 1-tree (i.e., an ordinary tree) on n vertices if and only if there are least two 1’s in the sequence, and the sum of the elements is 2(n–1). We generalize this result in the following ways. First, a natural generalization of this statement is a necessary condition for k-trees, and we show that it is not sufficient for any k > 1. Second, we identify non-trivial sufficient conditions for the degree sequences of 2-trees. We also show that these sufficient conditions are almost necessary using bounds on the partition function p(n) and probabilistic methods. Third, we generalize the characterization of degrees of 1-trees in an elegant and counter-intuitive way to yield integer sequences that characterize k-trees, for all k.