FR-KECA: Fuzzy robust kernel entropy component analysis

• We propose a fuzzy theory based kernel entropy component analysis (KECA) algorithm.
• We propose three fuzzy robust KECA (FR-KECA) algorithms for data transformation.
• Experimental results show that all FR-KECA algorithms outperform original KECA.
• FR-KECA algorithm has potential for noise corrupted high dimensional data.

Kernel entropy component analysis (KECA) is a newly proposed spectral method for data transformation and dimensionality reduction. Different from other spectral methods, KECA reveals structure related to the Renyi entropy of the input space data set. Therefore, it is not necessary to select the top eigenvalues and eigenvectors of the kernel matrix. Consequently, KECA has been successfully applied in many areas due to its special properties. However, similar to other spectral methods, KECA also suffers from the problem of noise sensitivity, because small entropy values in the input space may be associated with noise. To improve the robustness against noise of spectral methods, fuzzy set theory has been successfully introduced into some spectral methods, which is a simple and effective solution. In this paper, we propose the fuzzy robust KECA (FR-KECA) algorithm based on fuzzy set theory to improve the robustness. The main idea of FR-KECA is to induce the fuzzy item to optimize the kernel entropy components in KECA, which makes the transformed data more robust. Three FR-KECA algorithms are proposed, and then evaluated in three data transformation experiments and two dimensionality reduction experiments with five commonly used datasets. The experimental results indicate that the proposed three FR-KECA algorithms outperform the original KECA in both data transformation and dimensionality reduction at least 0.7% up to 4.3% for different data sets, suggesting that the proposed FR-KECA algorithms have the potential to be applied to noise-corrupted high dimensional data.