Regularized Scatter Measure for Linear Feature Extraction

There exist two classical linear methods for feature extraction, i.e. principal component analysis (PCA) and Fisher discriminant analysis (FDA). PCA best represents the data while FDA best separates the data in the least squares sense with different scatter measures from samples. This paper discusses a regularized scatter measure (RSM) as a linear combination of within-class and between-class scatters for feature extraction. The tradeoff between for representation and for discrimination is controlled via some suitable regularization parameters and the corresponding eigenvalue problem is resolved without singularity. Experiments on two different size data sets demonstrate the effectiveness of the method. In addition, we can see that the counterpart of PCA, i.e. minor component analysis (MCA), is to optimize one special case of RSM. And this provides another easy way for understanding why MCA outperforms PCA for feature extraction in one-class classification problem.