Description of the classifiers

With xij we denote the value of variable j (j = 1, ..., p) for sample i (i = 1, ..., n); xi is the set of variables for sample i and x is the set of variables for all samples. Some of the n samples are known to belong to Class 1 (n1 samples) and the others to Class 2 (n2, n1 +n2 = n); the proportion of samples from Class 1 and 2 is denoted by k1 = n1/n and k2 = n2/n, respectively, and yi = {−1, 1} is the class membership for sample i. Let ŷi = c(xi) be the predicted class for sample i.