A note on robust kernel principal component analysis

Abstract

Extending the classical principal component analysis (PCA), the kernel PCA (Schölkopf, Smola and Müller, 1998) effectively extracts nonlinear structures of high dimensional data. But similar to PCA, the kernel PCA can be sensitive to outliers. Various approaches have been proposed in the literature to robustify the classical PCA. However, it is not immediately clear how these approaches can be "kernelized" in practice. In this paper, we propose a robust kernel PCA procedure. We show that the proposed method can be easily computed. Simulations and a real example in the financial service also demonstrate the competitive performance of our approach when there are outlying observations.

Robust dimension reduction

“…In Ref a simple graphical procedure was proposed to detect and visualize the influential observations in ordinary Kernel PCA. Other related papers include Wang et al, Deng et al, Pang et al, and Huang and Yeh …”

“…In Ref 35 a simple graphical procedure was proposed to detect and visualize the influential observations in ordinary Kernel PCA. Other related papers include Wang et al, 39 Deng et al, 40 Pang et al, 41 and Huang and Yeh. 42 Another possible way to improve the robustness against outliers is by modifying the loss function.…”

Climate Change Policies and Employment in Eastern Europe and Central Asia

“…This high number skews the PCA analysis as literature suggests. It is widely recognized that the Kernel PCA can be extremely sensitive to outlying observations, and conclusions can be misleading(Deng, Yuan and Sudjianto, 2007) 16 Annex 4 describes the definitions and data sources used to construct the different adaptability indicators included in the analysis. Annex 5 also presents the values of adaptability indicators by country.…”