Relationship Between Support Vector Set and Kernel Functions in SVM

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摘要：Based on a constructive learning approach, covering algorithms, we investigatethe relationship between support vector sets and kernel functions in support vector machines(SVM). An interesting result is obtained. That is, in the linearly non-separable case, any sampleof a given sample set K can become a support vector under a certain kernel function. The resultshows that when the sample set K is linearly non-separable, although the chosen kernel functionsatisfies Mercer's condition its corresponding support vector set is not necessarily the subsetof K that plays a crucial role in classifying K. For a given sample set, what is the subsetthat plays the crucial role in classification? In order to explore the problem, a new concept,boundary or boundary points, is defined and its properties are discussed. Given a sample setK, we show that the decision functions for classifying the boundary points of K are the sameas that for classifying the K itself. And the boundary points of K only depend on K and thestructure of the space at which K is located and independent of the chosen approach for findingthe boundary. Therefore, the boundary point set may become the subset of K that plays acrucial role in classification. These results are of importance to understand the principle of thesupport vector machine (SVM) and to develop new learning algorithms.http://www.cqvip.com//QK/85226X/200205/6840007.html

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关键词：relationship relations Functions relation function 机器学习 支持向量机 学习理论