An Efficient Incremental Kernel Principal Component Analysis for Online Feature Selection

In this paper, a feature extraction method for online classification problems is proposed by extending kernel principal component analysis (KPCA). In our previous work, we proposed an incremental KPCA algorithm which could learn a new input incrementally without keeping all the past training data. In this algorithm, eigenvectors are represented by a linear sum of linearly independent data which are selected from given training data. A serious drawback of the previous IKPCA is that many independent data are prone to be selected during learning and this causes large computation and memory costs. For this problem, we propose a novel approach to the selection of independent data; that is, they are not selected in the high-dimensional feature space but in the low-dimensional eigenspace spanned by the current eigenvectors. Using this method, the number of independent data is restricted to the number of eigenvectors. This restriction makes the learning of the modified IKPCA (M-IKPCA) very fast without loosing the approximation accuracy against true eigenvectors. To verify the effectiveness of M-IKPCA, the learning time and the accuracy of eigenspaces are evaluated using two UCI benchmark datasets. As a result, we confirm that the learning of M-IKPCA is at least 5 times faster than the previous version of IKPCA.