Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis
William H. Wolberg, Olvi L. Mangasarian, Rudy Setiono · Minds at UW (University of Wisconsin) · 1989
A decision problem associated with a fundamental nonconvex model for linearly inseparable pattern sets is shown to be NP-complete. Another nonconvex model that employs an ??-norm instead of the 2-norm, can be solved in polynomial time by solving 2n linear programs, where n is the (usually small) dimensionality of the pattern space. An effective LP-based finite algorithm is proposed for solving the latter model. The algorithm is employed to obtain a nonconvex piecewise-linear function for separating points representing measurements made on fine needle aspirates taken from benign and malignant human breasts. A computer program trained on 369 samples has correctly diagnosed each of 45 new samples encountered and is currently in use at the University of Wisconsin Hospitals.