Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911983869100032 |
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| author | Larsen, Brett W. Kolda, Tamara G. Zhang, Anru R. Williams, Alex H. |
| author_facet | Larsen, Brett W. Kolda, Tamara G. Zhang, Anru R. Williams, Alex H. |
| contents | The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness in the infinite dimensional modes. Further, CP-HiFi does not require the observed data to lie on a regular and finite rectangular grid and naturally incorporates misaligned data. We detail the methodology and illustrate it on a synthetic example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data Larsen, Brett W. Kolda, Tamara G. Zhang, Anru R. Williams, Alex H. Numerical Analysis Machine Learning The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness in the infinite dimensional modes. Further, CP-HiFi does not require the observed data to lie on a regular and finite rectangular grid and naturally incorporates misaligned data. We detail the methodology and illustrate it on a synthetic example. |
| title | Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2408.05677 |