Using the Karhunen-Loeve expansion for feature extraction on small sample sets

A general task in the field of signal processing and control consists in representing signals by a small number of features, i.e. the mapping of an n-dimensional signal onto an m-dimensional feature vector. Examples for widely used features are the position of maxima, minima, gradients or certain integral values of the signal curve, although it is obvious that the original curves can hardly be reconstructed from these features. The Karhunen-Loeve (K-L) expansion on the other hand provides the means to approximate the n-dimensional sample vectors of a random distribution by m features such that the mean-square error is minimized. However, these m basis vectors of the K-L-expansion may not be appropriate for representing signals which are not distributed according to the covariance matrix of the given sample set. In this paper, a method is presented which improves the representation of signals with a distribution deviating from the given distribution by reducing the dependence of the feature vectors on the sample set. Feature vectors spanning a subspace of slowly varying functions are combined with basis vectors of the K-L-expansion in order to increase the robustness of the features