Kernel change-point analysis
Zaid Harchaoui, Francis Bach and Eric Moulines
In: NIPS 2008, Vancouver, Canada(2009).
We introduce a kernel-based method for change-point analysis within a sequence
of temporal observations. Change-point analysis of an unlabelled sample of observations
consists in, first, testing whether a change in the distribution occurs within
the sample, and second, if a change occurs, estimating the change-point instant
after which the distribution of the observations switches from one distribution to
another different distribution. We propose a test statistic based upon themaximum
kernel Fisher discriminant ratio as a measure of homogeneity between segments.
We derive its limiting distribution under the null hypothesis (no change occurs),
and establish the consistency under the alternative hypothesis (a change occurs).
This allows to build a statistical hypothesis testing procedure for testing the presence
of a change-point, with a prescribed false-alarm probability and detection
probability tending to one in the large-sample setting. If a change actually occurs,
the test statistic also yields an estimator of the change-point location. Promising
experimental results in temporal segmentation of mental tasks from BCI data and
pop song indexation are presented.