Data separation via a finite number of discriminant functions: A global optimization approach

This paper presents a mixed 0-1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.