Nonlinear Component Analysis Based on Correntropy

In this paper, we propose a new nonlinear principal component analysis based on a generalized correlation function which we call correntropy. The data is nonlinearly transformed to a feature space, and the principal directions are found by eigen-decomposition of the correntropy matrix, which has the same dimension as the standard covariance matrix for the original input data. The correntropy matrix characterizes the nonlinear correlations between the data. With the correntropy function, one can efficiently compute the principal components in the feature space by projecting the transformed data onto those principal directions. We give the derivation of the new method and present simulation results.