Kernel Entropy Component Analysis

We introduce kernel entropy component analysis (kernel ECA) as a new method for data transformation and dimensionality reduction. Kernel ECA reveals structure relating to the Renyi entropy of the input space data set, estimated via a kernel matrix using Parzen windowing. This is achieved by projections onto a subset of entropy preserving kernel principal component analysis (kernel PCA) axes. This subset does not need, in general, to correspond to the top eigenvalues of the kernel matrix, in contrast to the dimensionality reduction using kernel PCA. We show that kernel ECA may produce strikingly different transformed data sets compared to kernel PCA, with a distinct angle-based structure. A new spectral clustering algorithm utilizing this structure is developed with positive results. Furthermore, kernel ECA is shown to be an useful alternative for pattern denoising.