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

Fast Approximate KK-Means via Cluster Closures

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate $k$-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, image data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate $k$-means algorithms in terms of clustering quality and efficiency

A link density clustering algorithm based on automatically selecting density peaks for overlapping community detection

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