Tensor PCA from basis in tensor space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909363298369536 |
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| author | Turchetti, Claudio Falaschetti, Laura |
| author_facet | Turchetti, Claudio Falaschetti, Laura |
| contents | The aim of this paper is to present a mathematical framework for tensor PCA. The proposed approach is able to overcome the limitations of previous methods that extract a low dimensional subspace by iteratively solving an optimization problem. The core of the proposed approach is the derivation of a basis in tensor space from a real self-adjoint tensor operator, thus reducing the problem of deriving a basis to an eigenvalue problem. Three different cases have been studied to derive: i) a basis from a self-adjoint tensor operator; ii) a rank-1 basis; iii) a basis in a subspace. In particular, the equivalence between eigenvalue equation for a real self-adjoint tensor operator and standard matrix eigenvalue equation has been proven. For all the three cases considered, a subspace approach has been adopted to derive a tensor PCA. Experiments on image datasets validate the proposed mathematical framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02803 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tensor PCA from basis in tensor space Turchetti, Claudio Falaschetti, Laura Numerical Analysis Computer Vision and Pattern Recognition Machine Learning The aim of this paper is to present a mathematical framework for tensor PCA. The proposed approach is able to overcome the limitations of previous methods that extract a low dimensional subspace by iteratively solving an optimization problem. The core of the proposed approach is the derivation of a basis in tensor space from a real self-adjoint tensor operator, thus reducing the problem of deriving a basis to an eigenvalue problem. Three different cases have been studied to derive: i) a basis from a self-adjoint tensor operator; ii) a rank-1 basis; iii) a basis in a subspace. In particular, the equivalence between eigenvalue equation for a real self-adjoint tensor operator and standard matrix eigenvalue equation has been proven. For all the three cases considered, a subspace approach has been adopted to derive a tensor PCA. Experiments on image datasets validate the proposed mathematical framework. |
| title | Tensor PCA from basis in tensor space |
| topic | Numerical Analysis Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2305.02803 |