$\sigma$-PCA: a unified neural model for linear and nonlinear principal component analysis

arXiv:2311.13580v3 Announce Type: replace
Abstract: Linear principal component analysis (PCA), nonlinear PCA, and linear independent component analysis (ICA) -- those are three methods with single-layer autoencoder formulations for learning special linear transformations from data. Linear PCA learns orthogonal transformations that orient axes to maximise variance, but it suffers from a subspace rotational indeterminacy: it fails to find a unique rotation for axes that share the same variance. Both nonlinear PCA and linear ICA reduce the subspace indeterminacy from rotational to …

abstract analysis arxiv autoencoder cs.ai cs.lg data independent layer linear pca stat.ml type variance