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

TL;DR

This paper introduces a neural framework for continuous-time signal decomposition, unifying PCA and ICA in a flexible, model-agnostic approach that handles irregularly sampled data and point clouds.

Contribution

It extends low-rank decomposition methods to continuous signals using implicit neural representations, enabling applications to irregular and complex data.

Findings

Unified approach to PCA and ICA in continuous time

Applicable to irregularly sampled signals and point clouds

Demonstrates effectiveness on complex continuous data

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.