More Efficient Sampling for Tensor Decomposition

• URL: http://arxiv.org/abs/2110.07631v1
• Date: Thu, 14 Oct 2021 18:00:31 GMT
• Title: More Efficient Sampling for Tensor Decomposition
• Authors: Osman Asif Malik
• Abstract summary: We propose sampling-based ALS methods for the CP and tensor ring decompositions. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.
• Score: 2.28438857884398
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.

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