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Volume 2019, Article ID 5937274, 17 pages
Research Article

Two-Phase Incremental Kernel PCA for Learning Massive or Online Datasets

1School of Computer Science and Technology, Shandong Technology and Business University, Yantai, China
2Shandong Co-Innovation Center of Future Intelligent Computing, Yantai, China
3BASIRA Lab, Faculty of Computer and Informatics, Istanbul Technical University, Istanbul, Turkey
4School of Science and Engineering, Computing, University of Dundee, UK
5Department of Brain and Cognitive Engineering, Korea University, Seoul 02841, Republic of Korea
6School of Electronic Engineering, Xian University of Posts and Telecommunications, Xi’an, China
7School of Computer Science and Engineering, Xidian University, Xi’an, China
8Department of Radiology and BRIC, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Correspondence should be addressed to Dinggang Shen; ude.cnu.dem@nehsgd

Received 2 October 2018; Revised 17 December 2018; Accepted 8 January 2019; Published 11 February 2019

Guest Editor: Jose Garcia-Rodriguez

Copyright © 2019 Feng Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As a powerful nonlinear feature extractor, kernel principal component analysis (KPCA) has been widely adopted in many machine learning applications. However, KPCA is usually performed in a batch mode, leading to some potential problems when handling massive or online datasets. To overcome this drawback of KPCA, in this paper, we propose a two-phase incremental KPCA (TP-IKPCA) algorithm which can incorporate data into KPCA in an incremental fashion. In the first phase, an incremental algorithm is developed to explicitly express the data in the kernel space. In the second phase, we extend an incremental principal component analysis (IPCA) to estimate the kernel principal components. Extensive experimental results on both synthesized and real datasets showed that the proposed TP-IKPCA produces similar principal components as conventional batch-based KPCA but is computationally faster than KPCA and its several incremental variants. Therefore, our algorithm can be applied to massive or online datasets where the batch method is not available.