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Calculation of near-neighbor interactions among high dimensional, irregularlydistributed data points is a fundamental task to many graph-based orkernel-based machine learning algorithms and applications. Such calculations,involving large, sparse interaction matrices, expose the limitation ofconventional data-and-computation reordering techniques for improving space andtime locality on modern computer memory hierarchies. We introduce a novelmethod for obtaining a matrix permutation that renders a desirable sparsityprofile. The method is distinguished by the guiding principle to obtain aprofile that is block-sparse with dense blocks. Our profile model and measurecapture the essential properties affecting space and time locality, and permitvariation in sparsity profile without imposing a restriction to a fixedpattern. The second distinction lies in an efficient algorithm for obtaining adesirable profile, via exploring and exploiting multi-scale cluster structurehidden in but intrinsic to the data. The algorithm accomplishes its task withkey components for lower-dimensional embedding with data-specific principalfeature axes, hierarchical data clustering, multi-level matrix compressionstorage, and multi-level interaction computations. We provide experimentalresults from case studies with two important data analysis algorithms. Theresulting performance is remarkably comparable to the BLAS performance for thebest-case interaction governed by a regularly banded matrix with the samesparsity.

Rapid Near-Neighbor Interaction of High-dimensional Data via Hierarchical Clustering