Online multidimensional dictionary learning

• URL: http://arxiv.org/abs/2503.09337v1
• Date: Wed, 12 Mar 2025 12:31:29 GMT
• Title: Online multidimensional dictionary learning
• Authors: Ferdaous Ait Addi, Abdeslem Hafid Bentbib, Khalide Jbilou,
• Abstract summary: We propose a generalization of the dictionary learning technique using the t-product framework.<n>We address the dictionary learning problem through online methods suitable for tensor structures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the dictionary learning technique using the t-product framework, enabling efficient handling of multidimensional tensor data. We address the dictionary learning problem through online methods suitable for tensor structures. To effectively address the sparsity problem, we utilize an accelerated Iterative Shrinkage-Thresholding Algorithm (ISTA) enhanced with an extrapolation technique known as Anderson acceleration. This approach significantly improves signal reconstruction results. Extensive experiments prove that our proposed method outperforms existing acceleration techniques, particularly in applications such as data completion. These results suggest that our approach can be highly beneficial for large-scale tensor data analysis in various domains.

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