Embedded Chaotic Time Series: Applications in Prediction and Spatio-temporal Classification

The Deterministic Versus Stochastic algorithm developed by Martin Casdagli is modified to produce two new, methodologies, each of which selectively uses embedding space nearest neighbors. Neighbors which are considered prediction relevant are retained for local linear prediction, while those which are considered likely to represent noise are ignored. For many time series, it is shown possible to improve on local linear prediction with both of the new algorithms. Furthermore, the theory of embedology is applied to determine a length of test sequence sufficient for accurate classification of moving objects. Sequentially recorded feature vectors of a moving object form a training trajectory in feature space. Each of the sequences of feature vector components is a time series, and under certain conditions, each of these time series has approximately the same fractal dimension. The embedding theorem is applied to this fractal dimension to establish a number of observations sufficient to determine the feature space trajectory of the object. It is argued that this number is a reasonable test sequence length for use in object classification. Experiments with data corresponding to five military vehicles observed following a projected Lorenz trajectory on a viewing sphere show that this number is indeed adequate