Tensor Decomposition with Unaligned Observations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916888797249536 |
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| author | Tang, Runshi Kolda, Tamara Zhang, Anru R. |
| author_facet | Tang, Runshi Kolda, Tamara Zhang, Anru R. |
| contents | This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a versatile loss function that effectively accounts for various types of data, including binary, integer-valued, and positive-valued types. Additionally, we propose an optimization algorithm for computing tensor decompositions with unaligned observations, along with a stochastic gradient method to enhance computational efficiency. A sketching algorithm is also introduced to further improve efficiency when using the $\ell_2$ loss function. To demonstrate the efficacy of our methods, we provide illustrative examples using both synthetic data and an early childhood human microbiome dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor Decomposition with Unaligned Observations Tang, Runshi Kolda, Tamara Zhang, Anru R. Machine Learning Numerical Analysis Computation Methodology This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a versatile loss function that effectively accounts for various types of data, including binary, integer-valued, and positive-valued types. Additionally, we propose an optimization algorithm for computing tensor decompositions with unaligned observations, along with a stochastic gradient method to enhance computational efficiency. A sketching algorithm is also introduced to further improve efficiency when using the $\ell_2$ loss function. To demonstrate the efficacy of our methods, we provide illustrative examples using both synthetic data and an early childhood human microbiome dataset. |
| title | Tensor Decomposition with Unaligned Observations |
| topic | Machine Learning Numerical Analysis Computation Methodology |
| url | https://arxiv.org/abs/2410.14046 |