Nonlinear Dimensionality Reduction Via Polynomial Principal Component Analysis

In this paper, we introduce Poly-PCA, a nonlinear dimensionality reduction technique which can capture arbitrary nonlinearities in high-dimensional and dynamic data. Instead of optimizing over the space of nonlinear functions of high-dimensional data Poly-PCA models the data as nonlinear functions in the latent variables, leading to relatively fast optimization. Poly-PCA can handle nonlinearities which do not preserve the topology and geometry of the latents. Applying Poly-PCA to a nonlinear dynamical system successfully recovered the phase-space of the latent variables.