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Unsupervised classification via convex absolute value inequalities

We consider the problem of classifying completely unlabelled data using convex inequalities that contain absolute values of the data. This allows each data point to belong to either one of two classes by entering the inequality with a plus or minus value. Using such absolute value inequalities in support vector machine classifiers, unlabelled data can be successfully partitioned into two classes that capture most of the correct labels dropped from the data. Inclusion of partially labelled data leads to a semisupervised classifier. Computational results include unsupervised and semisupervised classification of the Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set.