Indefinite Kernel Entropy Component Analysis

Kernel Entropy Component Analysis (KECA) is a new spectral method which has been proposed recently. Via a kernel-based Renyi entropy estimator which is expressed in terms of projections onto kernel feature space principal axes, it directly related to the Renyi entropy of the input space data set. In the KECA, choice of kernel functions must be obey Mercer´s condition. Means the kernel function used in KECA must be positive semi-definite. However, the theoretically optimal functions in the Parzen windows is in fact indefinite, we address the Indefinite Kernel Entropy Component Analysis (IKECA), as a natural extension of KECA to indefinite kernels.