Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA

• URL: http://arxiv.org/abs/2507.09091v1
• Date: Sat, 12 Jul 2025 00:20:16 GMT
• Title: Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA
• Authors: Shayan K. Azmoodeh, Krishna Subramani, Paris Smaragdis,
• Abstract summary: We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA)<n>We provide a model-agnostic framework to learn implicit neural approximations to solve the problem.<n>This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals.
• Score: 11.995977581000503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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