43. Wavelet Algorithm for Hierarchical Pattern Recognition

The idea, presented in this article, is based on a combination of hierarchical classifier with multiresolution representation of signals in the Daubechies wavelet bases. The paper concerns a multi-class recognition of random signals. It presents a multistage classifier with a hierarchical tree structure, based on a multiscale representation of signals in wavelet bases. Classes are hierarchically grouped in macro-classes and the established aggregation defines a decision tree. In each macro-class, the existence of deterministic pattern of signals is assumed. A global loss function with reject option is proposed for the multistage classifier and two strategies for the choice of loss function parameters are discussed. An analysis of risk is performed for a local (binary) attraction-limited minimum distance classifier for wavelet approximation of signals. This leads to proposals, relating to the upper estimate of the risk, called the guaranteed risk. Its value depends on the several parameters as the wavelet scale of signal representation, the support length of wavelet function, or the variance of the random noise in the macro-class. Finally, the guaranteed risk of the multistage classifier is derived.