A fast Incremental Kernel Principal Component Analysis for data streams

Kernel Principal Component Analysis (KPCA) is widely used feature extraction as it have been proven that KPCA is powerful in many areas in pattern recognition. Considering that the conventional KPCA should decompose a kernel matrix of all training data, this would be an unrealistic assumption for data streams in real-world applications. Therefore, in this paper, we propose an online feature extraction called Chunk Incremental Kernel Principal Component Analysis (CIKPCA) that can handle data streams in an incremental mode. In the proposed method, the training data are assumed to be given in a chunk of multiple data at one time. In CIKPCA, an eigen-feature space is updated by solving the eigenvalue decomposition once whenever a chunk of data is given. However, if a chunk size is large, a kernel matrix to be decomposed is also large, resulting in high computational time. Considering that not all the data are useful for the eigen-feature space learning, the data in a chunk are first selected based on the importance. Several benchmark data sets in the UCI Machine Learning Repository are used to evaluate the performance of the proposed method. The experimental results show that our proposed method can accelerate the learning of the eigen-feature space compared to Takeuchi et al.'s IKPCA without reducing the recognition accuracy.