Dimensionality reduction for nonlinear time series
David DeMers · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
A technique for recoding multidimensional data in a representation of reduced dimensionality is presented. A non-linear encoder-decoder for multidimensional data with compact representations is developed. The technique of training a neural network to learn the identity map through a `bottleneck' is extended to networks with non-linear representations, and an objective function which penalizes entropy of the hidden unit activations is shown to result in low dimensional encodings. For scalar time series data, a common technique is phase-space reconstruction by embedding the time-lagged scalar signal in a higher dimensional space. Choosing the proper embedding dimension is difficult. By using non-linear dimensionality reduction, the intrinsic dimensionality of the underlying system may be estimated.