# A spectral PALM algorithm for matrix and tensor-train based Dictionary Learning

Source: [A spectral PALM algorithm for matrix and tensor-train based Dictionary Learning](<https://www.sota2.com/research/paper/68fa59151e209131ce9b3c40>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:41:26.149Z

Authors: Domitilla Brandoni, Margherita Porcelli, Valeria Simoncini

Published: 2021-07-24T16:27:57.000Z

## Abstract

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image dataset. The resulting constrained optimization problem is nonconvex and non-smooth, providing several computational challenges for its solution. To preserve multidimensional data features, various tensor DL formulations have been introduced, adding to the problem complexity. We develop a new alternating algorithm for the solution of the DL problem both in the matrix and tensor frameworks; in the latter case a new formulation based on Tensor-Train decompositions is also proposed. The new method belongs to the Proximal Alternating Linearized Minimization (PALM) algorithmic family, with the inclusion of second order information to enhance efficiency. We discuss a rigorous convergence analysis, and report on the new method performance on the image classification of several benchmark datasets.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2107.11644>)

[PDF](<https://arxiv.org/pdf/2107.11644.pdf>)