Kernel change-point detection

Sylvain Arlot (1) , Alain Celisse (2, 3) , Zaid Harchaoui (4)

1 SIERRA - Statistical Machine Learning and Parsimony
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 MODAL - MOdel for Data Analysis and Learning
4 LEAR - Learning and recognition in vision

We tackle the change-point problem with data belonging to a general set. We propose a penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Cappé (2007). This penalty generalizes the one proposed for one dimensional signals by Lebarbier (2005). We prove it satisfies a non-asymptotic oracle inequality by showing a new concentration result in Hilbert spaces. Experiments on synthetic and real data illustrate the accuracy of our method, showing it can detect changes in the whole distribution of data, even when the mean and variance are constant. Our algorithm can also deal with data of complex nature, such as the GIST descriptors which are commonly used for video temporal segmentation.

Mots clés: model selection; kernel methods; change-point problem; concentration inequality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Sylvain Arlot, Alain Celisse, Zaid Harchaoui. Kernel change-point detection. 2012. ⟨hal-00671174v1⟩