A Multi-criteria Convex Quadratic Programming model for credit data analysis
Decision Support Systems
Pattern classification by concurrently determined piecewise linear and convex discriminant functions
Computers and Industrial Engineering
On data classification by iterative linear partitioning
Discrete Applied Mathematics
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
Computers and Industrial Engineering
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Let two sets of patterns be represented by two finite point sets in ann-dimensional Euclidean spaceE^{n}. If the convex hulls of the two sets do not intersect, the sets can be strictly separated by a plane. Such a plane can be constructed by the Motzkin-Schoenberg error-correction procedure or by linear programming. More often than not, however, the convex hulls of the two point sets do intersect, in which case strict separation by a plane is not possible any more. One may then resort to separation by more than one plane. In this paper, we show how two sets can be strictly separated by one or more planes or surfaces (nonlinear manifolds) via linear programming. A computer program that implements the present method has been written and successfully tested on a number of real problems.