Tensor decompositions have become a central tool in machine learning to extract interpretable patterns from multiway arrays of data. However, computing the approximate Canonical Polyadic Decomposition (aCPD), one of the most important tensor decomposition model, remains a challenge. In this work, we propose several algorithms based on extrapolation that improve over existing alternating methods for aCPD. We show on several simulated and real data sets that carefully designed extrapolation can significantly improve the convergence speed hence reduce the computational time, especially in difficult scenarios.
We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.
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