Efficient methods for grouping vectors into low-rank clusters

Authors:
Aaditya V. Rangan
Affiliations:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
Venue:
Journal of Computational Physics
Year:
2011

Citing 7
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Abstract

We present a few practical algorithms for sorting vectors into low-rank clusters. These algorithms rely on a subdivision scheme applied to the space of projections from d-dimensions to 1-dimension. This subdivision scheme can be thought of as a higher-dimensional generalization of quicksort. Given the ability to quickly sort vectors into low-rank clusters, one can efficiently search a matrix for low-rank sub-blocks of large diameter. The ability to detect large-diameter low-rank sub-blocks has many applications, ranging from data-analysis to matrix-compression.