The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between t...The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.展开更多
This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,...This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.展开更多
基金Supported by the National Natural Science Foundation of China (No.60277101, No.60301003, No.60431020), Beijing Foundation (No.3052005), and Beijing Munici-pal Commission of Education Project (KM200410005030).
文摘The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.
文摘This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.
