SC16 Salt Lake City, UT

36. Minimizing Communication for Tensor Decompositions

Authors: Travis Bartley (University of California, Irvine)Mona Elkoussy (University of California, Irvine)Anima Anandkumar (University of California, Irvine)Aparna Chandramowlishwaran (University of California, Irvine)

Abstract: Previous research in numerical linear algebra has proven that the same communication lower bound is attained by variety of algorithms, including matrix multiplication, LU factorization, Cholesky factorization, and algorithms for eigenvalues and singular values. This article extends this result to three tensor decomposition methods. For computing the CP decomposition, the alternating least squares method (CP-ALS) is studied. For the Tucker decomposition, the higher-order singular value decomposition (HOSVD) and higher-order orthogonal iteration (HOOI) methods are studied. For each method, this article contributes an algorithm that attains the previously mentioned communication lower bound.

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