Abstract
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.
Highlights
As a conventional linear subspace analysis method, principal component analysis (PCA) can only produce linear subspace feature extractors [1], which are unsuitable for highly complex and nonlinear data distributions
We proposed a novel incremental feature extraction method termed as TP-IKPCA which endowed kernel principal component analysis (KPCA) with the capability of handling dynamic or large-scale datasets
The proposed TP-IKPCA differs from the existing incremental approaches in providing an explicit form of the mapped data and the updating process of kernel principal component (KPC) is performed in an explicit space
Summary
As a conventional linear subspace analysis method, principal component analysis (PCA) can only produce linear subspace feature extractors [1], which are unsuitable for highly complex and nonlinear data distributions. As a nonlinear extension of PCA, kernel principal component analysis (KPCA) [2] can capture the higher-order statistical information contained in data, producing nonlinear subspaces for better feature extraction performance. This has propelled the use of KPCA in a wide range of applications such as pattern recognition, statistical analysis, image processing, and so on [3,4,5,6,7,8]. KPCA firstly projects all samples from the input space into a kernel space using nonlinear mapping and extracts the principal components (PCs) in the kernel space. The extracted kernel principal component (KPC) of the mapped data is nonlinear with respect to the original input space
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