Analysis of learning vector quantization algorithms for pattern classification

Although the family of LVQ algorithms have been widely used for pattern classification and have achieved a great success, the rigorous theoretical studies on the classification performance of LVQ algorithms have seldom been made. In this paper, the asymptotical performance of LVQ1, LVQ2 and LVQ2.1 algorithms have been studied thoroughly, and three significant conclusions have been achieved respectively. Furthermore, a simple modification scheme to LVQ2 algorithm has been developed and analyzed on the asymptotical performance, which can produce the optimal or nearly-optimal classifier in the stable equilibrium state for the classification problems with classes overlapping