Unsupervised Learning, Minimum Risk Adaptive Pattern Classification

摘要

A recursive Bayes optimal solution is found for the problem of sequential, multicategory pattern recognition, when unsupervised learning is required. The parametric model used for this investigation allows for (i) both constant and time-varying unknown parameter vectors, (ii) partially unknown probability laws of the hypotheses and time-varying parameters, (iii) dependence of observations of finite past as well as present hypotheses and parameters, and, most significantly, (iv) parameter-conditional dependence of both observations and the information source up to any finite Markov orders. For finite or quantized parameter spaces the optimal (minimum risk) learning system is found and shown to be realizable in recursive form with finite memory requirements. By a matrix formulation, the system is represented as a combination of delay-feedback dynamic systems. The asymptotic properties of the optimal solution are studied, and it is shown that as a result of the martingale nature of the learning sequences, the optimal system is asymptotically stable and convergent. As an illustration of the applicability of the results, the general formulation is shown to be directly applicable to the construction of optimum unsupervised learning m-ary communication receivers in the presence of such problems as lack of symbol synchronization, intersymbol interference, correlated noise, random channel parameters, unknown signal waveforms and statistically dependent symbols. (Author)