A note on generalized tensor CUR approximation for tensor pairs and tensor triplets based on the tubal product
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909984580698112 |
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| author | Ahmadi-Asl, Salman Rezaeian, Naeim Ramazani, Keivan |
| author_facet | Ahmadi-Asl, Salman Rezaeian, Naeim Ramazani, Keivan |
| contents | In this note, we briefly present a generalized tensor CUR (GTCUR) approximation for tensor pairs (X,Y) and tensor triplets (X,Y,Z) based on the tubal product (t-product). We use the tensor Discrete Empirical Interpolation Method (TDEIM) to do these extensions. We show how the TDEIM can be utilized to generalize the classical tensor CUR (TCUR) approximation, which acts only on a single tensor, to jointly compute the TCUR of two and three tensors. This approach can be used to sample relevant lateral/horizontal slices of one data tensor relative to one or two other data tensors. For some special cases, the Generalized TCUR (GTCUR) approximation is reduced to the classical TCUR for both tensor pairs and tensor triplets in a similar fashion as shown for the matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on generalized tensor CUR approximation for tensor pairs and tensor triplets based on the tubal product Ahmadi-Asl, Salman Rezaeian, Naeim Ramazani, Keivan Numerical Analysis In this note, we briefly present a generalized tensor CUR (GTCUR) approximation for tensor pairs (X,Y) and tensor triplets (X,Y,Z) based on the tubal product (t-product). We use the tensor Discrete Empirical Interpolation Method (TDEIM) to do these extensions. We show how the TDEIM can be utilized to generalize the classical tensor CUR (TCUR) approximation, which acts only on a single tensor, to jointly compute the TCUR of two and three tensors. This approach can be used to sample relevant lateral/horizontal slices of one data tensor relative to one or two other data tensors. For some special cases, the Generalized TCUR (GTCUR) approximation is reduced to the classical TCUR for both tensor pairs and tensor triplets in a similar fashion as shown for the matrices. |
| title | A note on generalized tensor CUR approximation for tensor pairs and tensor triplets based on the tubal product |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2305.00754 |