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

2025-07-11

AI Summary

This work addresses low-rank decomposition of continuous-time vector-valued signals. We propose the first model-agnostic implicit neural signal representation framework, unifying continuous-domain generalizations of principal component analysis (PCA) and independent component analysis (ICA). The method models signals as differentiable implicit neural stochastic processes; statistical constraints—namely decorrelation and independence—are implicitly enforced via a contrastive-function-based loss, eliminating reliance on discrete or regular sampling. Enabled by end-to-end gradient-based optimization, the framework achieves robust component separation on irregularly sampled signals and point cloud data. It significantly improves generalization under missing-data and non-uniform sampling regimes, demonstrating superior performance in challenging real-world acquisition scenarios where conventional discrete-domain methods fail.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Generalize PCA and ICA for continuous-time signals
• Develop neural framework for signal decomposition
• Enable decomposition for irregularly sampled data

Innovation

• Implicit neural representation for signal decomposition
• Unified PCA and ICA via contrast function
• Continuous domain enables irregular signal processing