Riemannian preconditioned coordinate descent for low multi-linear rank approximation

Mohammad Hamed; Reshad Hosseini

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arXiv · 2109.01632

Riemannian preconditioned coordinate descent for low multi-linear rank approximation

Mohammad Hamed·Reshad Hosseini

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Abstract

This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold. We use a Riemmanian coordinate descent method for solving the problem, and also provide a global convergence analysis matching that of the coordinate descent method in the Euclidean setting. We also show that each step of our method with the unit step-size is actually a step of the orthogonal iteration algorithm. Experimental results show the computational advantage of our method for high-dimensional tensors.

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BibTeX RIS

Mohammad Hamed, Reshad Hosseini. 2021-09-03. Riemannian preconditioned coordinate descent for low multi-linear rank approximation. https://arxiv.org/abs/2109.01632

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