Feature selection by analyzing class regions approximated by ellipsoids

In our previous work, we have developed a method for selecting features based on the analysis of class regions approximated by hyperboxes. In this paper, we select features analyzing class regions approximated by ellipsoids. First, for a given set of features, each class region is approximated by an ellipsoid with the center and the covariance matrix calculated by the data belonging to the class. Then, similar to our previous work, the exception ratio is defined to represent the degree of overlaps in the class regions approximated by ellipsoids. From the given set of features, we temporally delete each feature, one at a time, and calculate the exception ratio. Then, the feature whose associated exception ratio is the minimum is deleted permanently. We iterate this procedure while the exception ratio or its increase is within a specified value by feature deletion. The simulation results show that our current method is better than the principal component analysis (PCA) and performs better than our previous method, especially when the distributions of class data are not parallel to the feature axes.