An application of embedology to spatio-temporal pattern recognition

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.