Efficient algorithms for the Hadamard decomposition
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908331211227136 |
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| author | Wertz, Samuel Vandaele, Arnaud Gillis, Nicolas |
| author_facet | Wertz, Samuel Vandaele, Arnaud Gillis, Nicolas |
| contents | The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to solve this problem, leveraging an alternating optimization approach that decomposes the global non-convex problem into a series of convex sub-problems. To improve performance, we explore advanced initialization strategies inspired by the singular value decomposition (SVD) and incorporate acceleration techniques by introducing momentum-based updates. Beyond optimizing the two-matrix case, we also extend the Hadamard decomposition framework to support more than two low-rank matrices, enabling approximations with higher effective ranks while preserving computational efficiency. Finally, we conduct extensive experiments to compare our method with the existing gradient descent-based approaches for the Hadamard decomposition and with traditional low-rank approximation techniques. The results highlight the effectiveness of our proposed method across diverse datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient algorithms for the Hadamard decomposition Wertz, Samuel Vandaele, Arnaud Gillis, Nicolas Machine Learning Signal Processing Optimization and Control The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to solve this problem, leveraging an alternating optimization approach that decomposes the global non-convex problem into a series of convex sub-problems. To improve performance, we explore advanced initialization strategies inspired by the singular value decomposition (SVD) and incorporate acceleration techniques by introducing momentum-based updates. Beyond optimizing the two-matrix case, we also extend the Hadamard decomposition framework to support more than two low-rank matrices, enabling approximations with higher effective ranks while preserving computational efficiency. Finally, we conduct extensive experiments to compare our method with the existing gradient descent-based approaches for the Hadamard decomposition and with traditional low-rank approximation techniques. The results highlight the effectiveness of our proposed method across diverse datasets. |
| title | Efficient algorithms for the Hadamard decomposition |
| topic | Machine Learning Signal Processing Optimization and Control |
| url | https://arxiv.org/abs/2504.13633 |