  In this paper we study the kernel change-point algorithm (KCP) proposed by
Arlot, Celisse and Harchaoui (2012), which aims at locating an unknown number
of change-points in the distribution of a sequence of independent data taking
values in an arbitrary set. The change-points are selected by model selection
with a penalized kernel empirical criterion. We provide a non-asymptotic result
showing that, with high probability, the KCP procedure retrieves the correct
number of change-points, provided that the constant in the penalty is
well-chosen; in addition, KCP estimates the change-points location at the
optimal rate. As a consequence, when using a characteristic kernel, KCP detects
all kinds of change in the distribution (not only changes in the mean or the
variance), and it is able to do so for complex structured data (not necessarily
in $\mathbb{R}^d$). Most of the analysis is conducted assuming that the kernel
is bounded; part of the results can be extended when we only assume a finite
second-order moment.
