Super-class Discriminant Analysis: A novel solution for heteroscedasticity

The heteroscedasticity problem is a great challenge in pattern recognition, particularly in statistics-based methods. The traditional method that is mainly used to solve this problem is heteroscedastic Discriminant Analysis. In this study, we propose a novel solution to the problem, called Super-class Discriminant Analysis (SCDA). Our method uses the “divide and conquer” methodology to partition the heteroscedastic dataset into super-classes with reduced heteroscedasticity and models them separately. Theoretically, a super-class should contain a set of classes having the same within-class variation. In practice, a heteroscedastic dataset can be coarsely divided into several super-classes based on certain semantic criteria such as gender or race. We evaluate our method with toy data and three real-world datasets, which can be divided into super-classes according to gender and race. Experimental results indicate that the proposed method can effectively resolve the problem of heteroscedasticity.