Change Detection Using Directional Statistics

This paper addresses the task of change detection from noisy multivariate time-series data. One major feature of our approach is to leverage directional statistics as the noise-robust signature of time-series data. To capture major patterns, we introduce a regularized maximum likelihood equation for the von Mises-Fisher distribution, which simultaneously learns directional statistics and sample weights to filter out unwanted samples contaminated by the noise. We show that the optimization problem is reduced to the trust region subproblem in a certain limit, where global optimality is guaranteed. To evaluate the amount of changes, we introduce a novel distance measure on the Stiefel manifold. The method is validated with real-world data from an ore mining system.1