Chaotic attractor learning and how to deal with nonlinear singularities

In linear regression it is common practice to use principal component analysis (PCA) to find and remove directions in the input space that are not covered by the observed data. PCA fails to identify these `singular directions´ if the data lie on a lower dimensional nonlinear subspace. Typically, this is the case for data observed from deterministic chaotic systems. In this paper we present a viable nonlinear counterpart for principal component regression, and show why this algorithm can learn stable models for chaotic dynamics where other approaches often fail. The algorithm is applied to an experimental chaotic bubble column, with data highly contaminated with system noise and measurement errors