## Hybrid Misclassification Minimization (1995)

Venue: | Advances in Computational Mathematics |

Citations: | 15 - 7 self |

### BibTeX

@INPROCEEDINGS{Chen95hybridmisclassification,

author = {Chunhui Chen and O. L. Mangasarian},

title = {Hybrid Misclassification Minimization},

booktitle = {Advances in Computational Mathematics},

year = {1995},

pages = {127--136}

}

### OpenURL

### Abstract

Given two finite point sets A and B in the n-dimensional real space R n , we consider the NP-complete problem of minimizing the number of misclassified points by a plane attempting to divide R n into two halfspaces such that each open halfspace contains points mostly of A or B . This problem is equivalent to determining a plane fx j x T w = flg that maximizes the number of points x 2 A satisfying x T w ? fl, plus the number of points x 2 B satisfying x T w ! fl. A simple but fast algorithm is proposed that alternates between (i) minimizing the number of misclassified points by translation of the separating plane, and (ii) a rotation of the plane so that it minimizes a weighted average sum of the distances of the misclassified points to the separating plane. Existence of a global solution to an underlying hybrid minimization problem is established. Computational comparison with a parametric approach to solve the NP-complete problem indicates that our approach is considerably ...

### Citations

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Citation Context ...MM average of 2.32 PMM average of 22.3 Table 1. Comparison of Hybrid Misclassification Minimization (HMM) with Parametric Misclassification Minimization (PMM) [8, 1] & Robust Linear Programming (RLP) =-=[2]-=- m Training Set Correctness Date Set k Testing Set Correctness n Time Seconds SPARCstation 20 Average LPs Solved HMM PMM RLP 28 89.12 95.92 84.343 WBC Prognosis 119 72.24 71.33 66.048 32 0.71 10.65 0.... |

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Citation Context ...y more difficult and in fact is NP-complete, as shown in Proposition 2 of Section 2 below. This problem was considered in [8], where a parametric minimization approach was proposed and implemented in =-=[1]-=-. Although the parametric procedure is effective, it is costly computationally, which is to be expected since the underlying problem is NP-complete. In the present approach we shall propose a fast alt... |

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Citation Context ...e (WBCD) and other data sets from the Irvine Machine Learning Database Repository [10] as well as the Star/Galaxy database collected by Odewahn [12] and the Wisconsin Breast Cancer Prognosis Database =-=[9, 16]-=-. For each data set, a separating plane was obtained by three methods: the parametric misclassification minimization (PMM) procedure of [8, 1], the HMM Algorithm 5 of Section 2, and the robust linear ... |