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The theory of embedded time series is shown applicable for determining a reasonable lower bound on the length of test sequence required 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 may be applied to this fractal dimension to establish a sufficient number of observations to determine the feature space trajectory of the object. It is argued that this number is a reasonable lower bound on 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 bound is indeed adequate.

Time series prediction has widespread application, ranging from predicting the stock market to trying to predict future locations of scud missiles. The embedology theorem sets forth the procedures for state space manipulation and reconstruction for time series prediction. This includes embedding the time series into a higher dimensional space in order to form an attractor, a structure defined by the embedded vectors. In this paper, embedology is combined with neural technologies in an effort to create a more accurate prediction algorithm. The algorithms tested are embedology, neural networks, and Euclidean space nearest neighbors. Local linear training methods are compared to the use of the nearest neighbors as the training set for a neural network. The results of these experiments determine that the neural algorithms have the best prediction accuracies. The performance of the nearest neighbor trained neural network validates the applicability of the local linear training set.

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