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

Traditional Low Rank Decompositions Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are foundational techniques in statistical signal processing and dimensionality reduction [1, 2, 3]. Both methods aim to recover latent source signals from observed mixtures by identifying a (linear) transformation that reveals underlying structure in the data. PCA achieves this by finding statistically decorrelated source components, whereas ICA seeks maximally statistically independent components through higher-order statistics [4]. These methods have widespread application in dataset feature generation and blind signal separation. Traditional formulations of PCA and ICA operate on finite-dimensional vectors (discretely indexed), and there exist established algorithms to compute the source signal vectors from given datasets [1, 3].