Multiple change point detection in tensors

This paper proposes a criterion for detecting change structures in tensor data. To accommodate tensor structure with structural mode that is not suitable to be equally treated and summarized in a distance to measure the difference between any two adjacent tensors, we define a mode-based signal-screening Frobenius distance for the moving sums of slices of tensor data to handle both dense and sparse model structures of the tensors. As a general distance, it can also deal with the case without structural mode. Based on the distance, we then construct signal statistics using the ratios with adaptive-to-change ridge functions. The number of changes and their locations can then be consistently estimated in certain senses, and the confidence intervals of the locations of change points are constructed. The results hold when the size of the tensor and the number of change points diverge at certain rates, respectively. Numerical studies are conducted to examine the finite sample performances of the proposed method. We also analyze two real data examples for illustration.