Convergence of Vector Quantization–Based Classifiers to the Bayes Optimal Classifier with Applications to Hybrid System Identification

Vector quantization techniques have been extensively explored as interpretable, data-driven ap- proaches within machine learning, demonstrating significant utility in hybrid system identification. In this study, we establish convergence guarantees for a general framework of quantization-based classifiers, encompassing histogram-based methods, variants of the generalized Lloyd’s algorithm, learning vector quantization, and online deterministic annealing techniques. Utilizing principles from histogram estimation, we analyze the conditions under which these algorithms converge to the Bayes optimal error. These findings provide a rigorous theoretical foundation for the appli- cation of quantization-based algorithms in machine learning tasks associated with cyber-physical systems. An illustrative application in hybrid system identification is also presented.