Non-linear feature extraction by linear PCA using local kernel

This paper presents how to extract non-linear features by linear PCA. KPCA is effective but the computational cost is the drawback. To realize both non-linearity and low computational cost simultaneously, the idea of local kernel is used. The mapped features of the polynomial kernel can be described explicitly. When input features are divided into some local features and the polynomial kernel is applied to each local features independently, the dimension of mapped features does not become so high. In addition, the inner product with all local mapped features corresponds to the local summation kernel. Thus, KPCA with the local summation kernel can be solved by linear PCA. The proposed approach is evaluated in object categorization problem which requires high non-linearity and computational cost. The proposed method gives much higher accuracy than linear PCA. The computational cost is lower than KPCA though the accuracy is slightly worse than KPCA.