Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

Chemoinformatics Research at the University of Sheffield: A History and Citation Analysis

This paper reviews the work of the Chemoinformatics Research Group in the Department of Information Studies at the University of Sheffield, focusing particularly on the work carried out in the period 1985-2002. Four major research areas are discussed, these involving the development of methods for: substructure searching in databases of three-dimensional structures, including both rigid and flexible molecules; the representation and searching of the Markush structures that occur in chemical patents; similarity searching in databases of both two-dimensional and three-dimensional structures; and compound selection and the design of combinatorial libraries. An analysis of citations to 321 publications from the Group shows that it attracted a total of 3725 residual citations during the period 1980-2002. These citations appeared in 411 different journals, and involved 910 different citing organizations from 54 different countries, thus demonstrating the widespread impact of the Group's work

Rapid Quantification of Molecular Diversity for Selective Database Acquisition

There is an increasing need to expand the structural diversity of the molecules investigated in lead-discovery programs. One way in which this can be achieved is by acquiring external datasets that will enhance an existing database. This paper describes a rapid procedure for the selection of external datasets using a measure of structural diversity that is calculated from sums of pairwise intermolecular structural similarities

Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio

Information based clustering

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial assumptions about the structure of data. Here we reformulate the clustering problem from an information theoretic perspective which avoids many of these assumptions. In particular, our formulation obviates the need for defining a cluster "prototype", does not require an a priori similarity metric, is invariant to changes in the representation of the data, and naturally captures non-linear relations. We apply this approach to different domains and find that it consistently produces clusters that are more coherent than those extracted by existing algorithms. Finally, our approach provides a way of clustering based on collective notions of similarity rather than the traditional pairwise measures.Comment: To appear in Proceedings of the National Academy of Sciences USA, 11 pages, 9 figure