Online multilinear principal component analysis

Recently, the problem of extracting tensor object feature is studied and a very elegant solution, multilinear principal component analysis (MPCA), is proposed, which is motivated as a tool for tensor object dimension reduction and feature extraction by operating directly on the original tensor data. However, the original MPCA is an offline learning method and not suitable for processing online data since it generates the best projection matrices by learning on the whole training data set at once. In this study, we propose an online multilinear principal component analysis (OMPCA) algorithm and prove that the sequence generated by OMPCA converges to a stationary point of the total tensor scatter maximizing problem. Experiment results of an OMPCA-based support higher-order tensor machine for classification, show that OMPCA significantly lowers the time of dimension reduction with little sacrifice of recognition accuracy.