关键词: 不定核, 再生核Kre?n空间（RKKS）, 不定核主成分分析（IKPCA）, 不定核支持向量机（IKSVM）

Abstract:

Recently, indefinite kernel support vector machine (IKSVM) has attracted great attention in the machine learning community as more and more indefinite metric kernel matrices have occurred. However, the existing IKSVM algorithms are usually unable to solve the problems of information redundancy and sample sparsity caused by high-dimensional data. In view of the research status, the existing mainstream IKSVM algorithms are studied.Based on the stabilization problem of IKSVM in the reproducing kernel Kre?n spaces (RKKS), this paper proves theoretically that the essence of the IKSVM is the sequential application of indefinite kernel principal component analysis (IKPCA) and support vector machine (SVM) in reduced spaces, and proposes a novel learning framework for IKSVM: two-phase indefinite kernel support vector machine (TP-IKSVM). The TP-IKSVM solves the IKSVM problem by applying IKPCA and SVM successively, combining the advantages of IKPCA in alleviating redundancy and sample sparsity caused by high-dimensional datasets and the good generalization performance of SVM in reduced spaces. Experimental results on real world datasets show the classification accuracy of TP-IKSVM is better than that of the existing mainstream IKSVM algorithms.

Key words: indefinite kernel, reproducing kernel Kre?n spaces (RKKS), indefinite kernel principal component analysis (IKPCA), indefinite kernel support vector machine (IKSVM)