In the context of time series data mining, recent studies exploit kernels constructed from elastic distances such as Dynamic Time Warping within kernel based methods. Yet matrix, related to Gram matrices, constructed from these kernels do not always have the required definiteness property which can make them unsuitable for such use. Emerging approaches dedicated to the regularization of time elastic kernels can be used in place of classical ones such as direct spectral approaches. We present in this paper a recent regularization method ($K_ {DTW}$) for the DTW kernel and propose an experimental study exploiting a kernel principal component analysis for evaluating the ability of some kernels (elastic v.s. non elastic, definite v.s. not definite) to provide good classifications of the analyzed data, while providing an important reduction of dimensionality. This study shows the effectiveness of the regularization technique for time elastic kernels that is behind $K_ {DTW}$