  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.
