Pattern classification by concurrently determined piecewise linear and convex discriminant functions

This paper develops a new methodology for pattern classification by concurrently determined k piecewise linear and convex discriminant functions. Toward the end, we design a new l1-norm distance metric for measuring misclassification errors and use it to develop a mixed 0-1 integer and linear program (MILP) for the k piecewise linear and convex separation of data. The proposed model is meritorious in that it considers the synergy as well as the individual role of the k hyperplanes in constructing a decision surface and exploits the advances in theory and algorithms and the advent of powerful softwares for MILP for its solution. With artificially created data, we illustrate pros and cons of pattern classification by the proposed methodology. With six benchmark classification datasets, we demonstrate that the proposed approach is effective and competitive with well-established learning methods. In summary, the classifiers constructed by the proposed approach obtain the best prediction rates on three of the six datasets and the second best records for two of the remaining three datasets.