Reduced polynomial classifier using within-class standardizing transform

In this paper we introduce a novel, reduced dimension, Polynomial Regression based Classifier (PRC). The classical PRC expands the observed feature data set by considering higher order data statistics. The herein presented novel PRC preliminary performs projections of the data on suitable subspaces associated with the different classes. The projection operation is followed by discarding the contributions due to the higher order mixed sample moments evaluated on the data. Thereby, the overall polynomial approximation order is maintained while the dimensionality of the expanded feature space exploited by the reduced dimension classifier is drastically reduced. We assess the performance of both the full and the reduced PRC by numerical simulations on different scenarios. The reduced dimension PRC performs at least as well as the classical PRC with a significantly lower number of involved terms. This paves the way for extensively exploiting the PRC flexibility and applicability to complex classification problem although in resource limited system environments, such as, for instance, real-time applications on FPGAs.