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We consider the problem of detecting multiple changes in multiple independenttime series. The search for the best segmentation can be expressed as aminimization problem over a given cost function. We focus on dynamicprogramming algorithms that solve this problem exactly. When the number ofchanges is proportional to data length, an inequality-based pruning ruleencoded in the PELT algorithm leads to a linear time complexity. Another typeof pruning, called functional pruning, gives a close-to-linear time complexitywhatever the number of changes, but only for the analysis of univariate timeseries.  We propose a few extensions of functional pruning for multiple independenttime series based on the use of simple geometric shapes (balls andhyperrectangles). We focus on the Gaussian case, but some of our rules can beeasily extended to the exponential family. In a simulation study we compare thecomputational efficiency of different geometric-based pruning rules. We showthat for small dimensions (2, 3, 4) some of them ran significantly faster thaninequality-based approaches in particular when the underlying number of changesis small compared to the data length.

Geometric-Based Pruning Rules For Change Point Detection in Multiple Independent Time Series