Unifying cost and information in information-theoretic competitive learning

In this paper, we introduce costs into the framework of information maximization and try to maximize the ratio of information to its associated cost. We have shown that competitive learning is realized by maximizing mutual information between input patterns and competitive units. One shortcoming of the method is that maximizing information does not necessarily produce representations faithful to input patterns. Information maximizing primarily focuses on some parts of input patterns that are used to distinguish between patterns. Therefore, we introduce the cost, which represents average distance between input patterns and connection weights. By minimizing the cost, final connection weights reflect input patterns well. We applied the method to a political data analysis, a voting attitude problem and a Wisconsin cancer problem. Experimental results confirmed that, when the cost was introduced, representations faithful to input patterns were obtained. In addition, improved generalization performance was obtained within a relatively short learning time.