Study on Complexity in Hyper Surface Classification

Hyper Surface Classification (HSC) is a simple covering based classification algorithm.Experiments show that HSC can efficiently and accurately classify large-sized data in two-dimensional space and three-dimensional space.However,little research has been done on theoretical problems in HSC.This paper studies several theoretical problems in HSC.First,the paper shows that given the biggest dividing level l,the VC dimension of the hypothesis space is d2l.Under the PAC theory,it arrives at the conclusion on sample complexity,the algorithm probably learn a hypothesis that is approximately correct.Then,the time complexity and space complexity are analyzed.Finally,sample set without contradiction is defined,and show that if the inputting sample set is a finite sample set without contradiction,the algorithm must be convergent.