  Several statistical approaches based on reproducing kernels have been
proposed to detect abrupt changes arising in the full distribution of the
observations and not only in the mean or variance. Some of these approaches
enjoy good statistical properties (oracle inequality, \ldots). Nonetheless,
they have a high computational cost both in terms of time and memory. This
makes their application difficult even for small and medium sample sizes ($n<
10^4$). This computational issue is addressed by first describing a new
efficient and exact algorithm for kernel multiple change-point detection with
an improved worst-case complexity that is quadratic in time and linear in
space. It allows dealing with medium size signals (up to $n \approx 10^5$).
Second, a faster but approximation algorithm is described. It is based on a
low-rank approximation to the Gram matrix. It is linear in time and space. This
approximation algorithm can be applied to large-scale signals ($n \geq 10^6$).
These exact and approximation algorithms have been implemented in \texttt{R}
and \texttt{C} for various kernels. The computational and statistical
performances of these new algorithms have been assessed through empirical
experiments. The runtime of the new algorithms is observed to be faster than
that of other considered procedures. Finally, simulations confirmed the higher
statistical accuracy of kernel-based approaches to detect changes that are not
only in the mean. These simulations also illustrate the flexibility of
kernel-based approaches to analyze complex biological profiles made of DNA copy
number and allele B frequencies. An R package implementing the approach will be
made available on github.
