Risk upper bound for a NM-type multiresolution classification scheme of random signals by Daubechies wavelets

We propose an adaptive multistage classification scheme, based on the principle of multiresolution, using a naturally hierarchical wavelet representation of signals. The use of this principle in the context of a multi-class recognition task leads to the multistage binary classification tree, where recognition at different stages is performed with varying degrees of precision. In the paper, multistage minimum-distance NM-type binary classifier with reject option is introduced and examined. We analyze the upper bound of risk of the developed multistage classifier, especially paying attention to the impact of free (design) parameters on the efficiency of the classifier. The theoretical considerations are illustrated by simulation experiment and practical examples based on some benchmarks.