Nested Cavity Classifier: performance and remedy

Many articles and books considered the assessment of classifiers using simulated and real-world datasets (e.g., (Raudys and Pikelis, 1980; Efron and Tibshirani, 1997; Hastie et al., 2001)); but none of them considered a systematic assessment of NCC. However, Inselberg and Avidan (2000) compared NCC with other classifiers only on few real high-dimensional datasets; that study mentioned the superiority of NCC over other classifiers. NCC, as described below, builds decision regions geometrically using convex hulls. This partitioning mechanism has a drawback on the performance of the NCC (as explained in Section 3). NCC classifies any testing observation--regardless to its class, whether "class 1" or "class 2"--as class, say, "class 2" as long as it does not lie inside the range of the training data set; i.e., within the minimum and maximum values of each dimension. Since this is not always true, the present article proposes combining NCC with LDA to classify observations outside the range of the training set.