Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908447591628800 |
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| author | Azmoodeh, Shayan K. Subramani, Krishna Smaragdis, Paris |
| author_facet | Azmoodeh, Shayan K. Subramani, Krishna Smaragdis, Paris |
| contents | We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to learn numerical approximations to solve the problem. Modeling signals as continuous-time stochastic processes, we unify the approaches to both the PCA and ICA problems in the continuous setting through a contrast function term in the network loss, enforcing the desired statistical properties of the source signals (decorrelation, independence) learned in the decomposition. This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals where standard techniques are not applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA Azmoodeh, Shayan K. Subramani, Krishna Smaragdis, Paris Machine Learning Signal Processing We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to learn numerical approximations to solve the problem. Modeling signals as continuous-time stochastic processes, we unify the approaches to both the PCA and ICA problems in the continuous setting through a contrast function term in the network loss, enforcing the desired statistical properties of the source signals (decorrelation, independence) learned in the decomposition. This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals where standard techniques are not applicable. |
| title | Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2507.09091 |