A Novel Kernel Correlation Coefficient with Robustness Against Nonlinear Attenuation and Impulsive Noise

In this paper, we propose a new kernel correlation coefficient (KECC), with an emphasis on its robustness against impulsive noise and/or monotonic nonlinear transformations. To gain further insight, we compared KECC with other four correlation coefficients, namely, Pearson's product moment correlation coefficient (PPMCC), Kendall's tau (KT), Spearman's rho (SR) and order statistics correlation coefficient (OSCC). Extensive simulation experiments were conducted under linear, nonlinear, normal and contaminated Gaussian models (CGM) based on seven means of performance evaluation. Theoretical analysis showed that KECC satisfies various desired properties. Numerical results suggest that KECC performs equally well with the optimal PPMCC under the bivariate normal model, and outperforms the others when impulsive noise and/or nonlinearity exist in the data. Moreover, KECC can detect accurately the time delay of signals corrupted by impulsive noise. Last but not least, KECC runs in linearithmic time, only slightly slower than the fastest PPMCC. The advantages of KECC revealed in this work might shed new light on the topic of correlation analysis, which is important in many areas including signal processing.