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Disembedology and chaotic noise reduction

There have been many new methods for analyzing chaotic data proposed in the past few years. Not only can one do passive measurement of the dimensions and characteristic exponents of a chaotic data set, one can now also improve the data set by reducing the noise level. In addition, one can also predict its future for short times. These techniques for chaotic data analysis often start with a procedure of `embedding', or reconstruction of the attractors in some Euclidean space Rd. However, the inverse problem of the embedding, namely, to recover a best scalar time series from a given array of points in Rd, is often ignored. In this paper, we describe optimization criteria for disembedding.