Abstract
We introduce a technique to improve iterative kernel principal component analysis (KPCA) robust to outliers due to undesirable artifacts such as noises, alignment errors, or occlusion. The proposed iterative robust KPCA (rKPCA) links the iterative updating and robust estimation of principal directions. It inherits good properties from these two ideas for reducing the time complexity, space complexity, and the influence of these outliers on estimating the principal directions. In the asymptotic stability analysis, we also show that our iterative rKPCA converges to the weighted kernel principal kernel components from the batch rKPCA. Experimental results are presented to confirm that our iterative rKPCA achieves the robustness as well as time saving better than batch KPCA.
Highlights
Principal component analysis (PCA) is a classical dimension reduction method which has been applied in many applications, such as data visualization, image reconstruction, biomedical study, etc
Level-1 Haar wavelet kernel and Order-4 Symlet wavelet kernel [16] are applied to the Lena picture and a series of face images respectively in order to show how the iterative robust KPCA (rKPCA) reduces the influence of outliers in image reconstruction
We insert artificial contaminated data into the data as outliers. These results show that our proposed iterative rKPCA can extract the principal components close to those resulted from the data without outliers
Summary
Principal component analysis (PCA) is a classical dimension reduction method which has been applied in many applications, such as data visualization, image reconstruction, biomedical study, etc. Our proposed rKPCA advances iterative updating techniques for robust estimation of principal directions, our work studies the asymptotic stability analysis for the iterative rKPCA and proves the convergence. Using any monotonically increasing weight functions, our method confirms the asymptotic convergence of the iterative rKPCA. This asymptotic stability analysis is a critical issue while an iterative updating scheme is used (like iterative KPCA). Mathematical proofs confirm the sufficient conditions of the asymptotic properties for the mean and kernel principal components obtained by the iterative rKPCA
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