  Subsequence clustering of time series is an essential task in data mining,
and interpreting the resulting clusters is also crucial since we generally do
not have prior knowledge of the data. Thus, given a large collection of tensor
time series consisting of multiple modes, including timestamps, how can we
achieve subsequence clustering for tensor time series and provide interpretable
insights? In this paper, we propose a new method, Dynamic Multi-network Mining
(DMM), that converts a tensor time series into a set of segment groups of
various lengths (i.e., clusters) characterized by a dependency network
constrained with l1-norm. Our method has the following properties. (a)
Interpretable: it characterizes the cluster with multiple networks, each of
which is a sparse dependency network of a corresponding non-temporal mode, and
thus provides visible and interpretable insights into the key relationships.
(b) Accurate: it discovers the clusters with distinct networks from tensor time
series according to the minimum description length (MDL). (c) Scalable: it
scales linearly in terms of the input data size when solving a non-convex
problem to optimize the number of segments and clusters, and thus it is
applicable to long-range and high-dimensional tensors. Extensive experiments
with synthetic datasets confirm that our method outperforms the
state-of-the-art methods in terms of clustering accuracy. We then use real
datasets to demonstrate that DMM is useful for providing interpretable insights
from tensor time series.
