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.
"Dimensionality reduction for nonlinear time series", Proc. SPIE 1766, Neural and Stochastic Methods in Image and Signal Processing, (16 December 1992); doi: 10.1117/12.130829; https://doi.org/10.1117/12.130829