Extraction of Dimension Reduced Features from Empirical Kernel Vector

This paper proposes a feature extraction method from the given empirical kernel vector. We show the necessary condition for the feature extraction mapping to make the trained classifier by using the linear SVM with the extracted feature vectors equivalent to the one obtained by the standard kernel SVM. The proposed feature extraction mapping is defined by using the eigen values and eigen vectors of the Gram matrix. Since the eigen vector problem of the Gram matrix is closely related with the kernel Principal Component Analysis, we can extract a dimension reduced feature vector. This feature extraction method becomes equivalent to the kernel SVM if the full dimension is used. The proposed feature extraction method was evaluated by the experiments using the standard data sets. The cross-validation values of the proposed method were improved and the recognition rates were comparable with the original kernel SVM. The number of extracted features was very low compared to the number of features of the kernel SVM.