Robust Boundary Learning for Multi-class Classification Problems

The objective of pattern classification is minimizing generalization errors for innumerable unknown samples. In the structural risk minimization (SRM) principle, both empirical errors and complexities of classifiers are minimized instead of minimizing generalization errors. We define a criterion about both of empirical errors and complexities for multiclass classifiers directly, and propose a perceptron-based linear classifier obtained as the minimum solution of the criterion. Due to this direct measurement, our classifier is robust against outliers and mislabeled training samples. We discuss the advantages of our classifier by comparing with conventional classifiers such as support vector machines and neural networks. We verify classification ability of our classifier by experiments on benchmark datasets.