The goal of statistical pattern classification is, given a training set as finite examples, to develop a classifier which can assign the class label to any forthcoming patterns and minimizes the probability of error. We first review briefly the statistical framework to classify numerical vector patterns through intuitive examples and show what the problem is and what is important. Then, we describe the nonparametric classification approach called the convex subclass method, which is also exploitable for exploratory data analysis. The key idea is a decomposition of the complicated discriminative structure of given data into smaller, easy-to-handle convex pieces. We consider representing the dispersion of each class data against other classes by covering positive samples with some simple convex sets (such as boxes, balls, ellipsoids, half-spaces, convex hulls, or cylinders). According to this approach, we introduce a combinatorial classifier based on a family of balls, each of which is the minimum covering sphere for a subset of positive samples and does not contain any negative samples.