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all the past data, and the eigen-feature space is rotated by solving an eigenvalue problem once for each data chunk. The experiment results show that the learning time of the proposed CIKPCA is greatly reduced as compared with KPCA and IKPCA without sacrificing recognition accuracy.

An incremental learning algorithm of Kernel Prin cipal Component Analysis (KPCA) called Chunk Incremental KPCA (CIKPCA) has been proposed for online feature extrac tion in pattern recognition. CIKPCA can reduce the number of times to solve the eigenvalue problem compared with the conventional incremental KPCA when a small number of data are simultaneously given as a stream of data chunks. However, our previous work suggests that the computational costs of the independent data selection in CIKPCA could dominate over those of the eigenvalue decomposition when a large chunk of data are given. To verify this, we investigate the influence of the chunk size to the learning time in CIKPCA. As a result, CIKPCA requires more learning time than IKPCA unless a large chunk of data are divided into small chunks (e.g., less than 50).

In this paper, a new incremental learning algo rithm of Kernel Principal Component Analysis (KPCA) is proposed for online feature extraction in pattern recognition problems. The proposed algorithm is derived by extending the Takeuchi et al.'s Incremental KPCA (T-IKPCA) that can learn a new data incrementally without keeping past training data.However, even if more than two data are given in a chunk, T-IKPCA should learn them individually; that is, in order to update the eigen-feature space, the eigenvalue decomposition should be performed for every data in the chunk. To alleviate this problem, we extend T-IKPCA such that an eigen-feature space learning is conducted by performing the eigenvalue decomposition only once for a chunk of given data. In the proposed IKPCA, whenever a new chunk of training data are given, linearly independent data are first selected based on the cumulative proportion. Then, the eigenspace augmentation is conducted by calculating the coefficients for the selected linearly independent data, and the eigen-feature space is rotated based on the rotation matrix that can be obtained by solving a kernel eigenvalue problem. To verify the effectiveness of the proposed IKPCA, the learning time and the accuracy of eigenvectors are evaluated using the three VCI benchmark data sets. From the experimental results, we confirm that the proposed IKPCA can learn an eigen-feature space very fast without sacrificing the recognition accuracy.