Feature extraction based on a linear separability criterion

Though Fisher discriminant analysis (FDA) can perform feature extraction very well on data with simple distributions, it still has a number of shortcomings. For one, it usually fails to extract genuine optimal features from real-world data when such data exhibits an other-than-normal distribution. This is especially so when data exhibits a complex distribution, in which cases FDA is not able to obtain representative features at all. A second shortcoming is that FDA may not produce a sufficient number of transforming axes for the purpose of capturing representative features. This is because the maximum possible rank of the between-class scatter matrix does not exceed L-1, meaning that there are at most L-1 effective transforming axes, where L is the number of sample classes. In this paper, we develop a novel FDA method that deals with both of these problems. The novel FDA method is developed on the basis of the maximization of the distance between two arbitrary samples from two different classes and the minimization of the distance between samples in the same class. Besides this novel FDA method makes available a greater number of effective transforming axes than sample classes; it can extract representative features from data with a normal or complex distribution. We also propose three alternative forms of this novel FDA method. Experiments show that the novel FDA method outperforms a standard FDA. ICIC International