Sampling Based on Minimal Consistent Subset for Hyper Surface Classification

For hyper surface classification (HSC), based on the concept of minimal consistent subset for a disjoint cover set (MCSC), a judgmental sampling method is proposed to select a representative subset from the original sample set in this paper. The sampling method depends on sample distribution. HSC can directly solve the nonlinear multi-class classification problems and observe the sample distribution. The sample distribution is obtained by adaptively dividing the sample space, and the classification model of hyper surface is directly used to classify large database based on Jordan curve theorem in topology while sampling for MCSC. The number of MCSC is calculated. MCSC has the same classification model with the entire sample set and can totally reflect its classification ability. For any subset of the sample set that contains MCSC, the classification ability remains the same. Moreover, a formula is put forward that can predict the testing accuracy exactly when some samples are deleted from MCSC. So MCSC is the best way of sampling from the original sample set for Hyper Surface Classification method.