{"ID":2895333,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09091","arxiv_id":"2507.09091","title":"Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA","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.","short_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-...","url_abs":"https://arxiv.org/abs/2507.09091","url_pdf":"https://arxiv.org/pdf/2507.09091v1","authors":"[\"Shayan K. Azmoodeh\",\"Krishna Subramani\",\"Paris Smaragdis\"]","published":"2025-07-12T00:20:16Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"eess.SP\",\"stat.ML\"]","methods":"[]","has_code":false}