Entropy-scaling search of massive biological data

Many data sets exhibit 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 data set'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 data set 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 (3700x 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. Source code: http://gems.csail.mit.edu.