Higher order multi-dimension reduction methods via Einstein product
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915635118735360 |
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| author | Zahir, Alaeddine Jbilou, Khalide Ratnani, Ahmed |
| author_facet | Zahir, Alaeddine Jbilou, Khalide Ratnani, Ahmed |
| contents | This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both supervised and unsupervised learning paradigms. Additionally, we investigate variants such as repulsion graphs and kernel methods for linear approaches. Furthermore, we present two generalizations for each method, based on single or multiple weights. We demonstrate the straightforward nature of these generalizations and provide theoretical insights. Numerical experiments are conducted, and results are compared with original methods, highlighting the efficiency of our proposed methods, particularly in handling high-dimensional data such as color images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18171 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order multi-dimension reduction methods via Einstein product Zahir, Alaeddine Jbilou, Khalide Ratnani, Ahmed Numerical Analysis This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both supervised and unsupervised learning paradigms. Additionally, we investigate variants such as repulsion graphs and kernel methods for linear approaches. Furthermore, we present two generalizations for each method, based on single or multiple weights. We demonstrate the straightforward nature of these generalizations and provide theoretical insights. Numerical experiments are conducted, and results are compared with original methods, highlighting the efficiency of our proposed methods, particularly in handling high-dimensional data such as color images. |
| title | Higher order multi-dimension reduction methods via Einstein product |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.18171 |