  We tackle the change-point problem with data belonging to a general set. We
build a penalty for choosing the number of change-points in the kernel-based
method of Harchaoui and Capp{\'e} (2007). This penalty generalizes the one
proposed by Lebarbier (2005) for one-dimensional signals. We prove a
non-asymptotic oracle inequality for the proposed method, thanks to a new
concentration result for some function of Hilbert-space valued random
variables. Experiments on synthetic data illustrate the accuracy of our method,
showing that it can detect changes in the whole distribution of data, even when
the mean and variance are constant.
