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.

本文提出了一种名为 Dynamic Multi-network Mining（DMM）的新方法，用于将张量时间序列转化为一组具有多种长度（即聚类）的段群，并结合 l1-norm 的依赖网络对其进行子序列聚类，以实现可解释性、准确性和可扩展性，并通过实验验证了其在聚类准确性方面优于现有方法。

张量时间序列的动态多网络挖掘

Dynamic Multi-Network Mining of Tensor Time Series

This paper introduces an algorithm for the detection of change-points and the
identification of the corresponding subsequences in transient multivariate
time-series data (MTSD). The analysis of such data has become more and more
important due to the increase of availability in many industrial fields.
Labeling, sorting or filtering highly transient measurement data for training
condition based maintenance (CbM) models is cumbersome and error-prone. For
some applications it can be sufficient to filter measurements by simple
thresholds or finding change-points based on changes in mean value and
variation. But a robust diagnosis of a component within a component group for
example, which has a complex non-linear correlation between multiple sensor
values, a simple approach would not be feasible. No meaningful and coherent
measurement data which could be used for training a CbM model would emerge.
Therefore, we introduce an algorithm which uses a recurrent neural network
(RNN) based Autoencoder (AE) which is iteratively trained on incoming data. The
scoring function uses the reconstruction error and latent space information. A
model of the identified subsequence is saved and used for recognition of
repeating subsequences as well as fast offline clustering. For evaluation, we
propose a new similarity measure based on the curvature for a more intuitive
time-series subsequence clustering metric. A comparison with seven other
state-of-the-art algorithms and eight datasets shows the capability and the
increased performance of our algorithm to cluster MTSD online and offline in
conjunction with mechatronic systems.

本文介绍了一种用于检测变点和识别瞬态多变量时间序列数据中相应子序列的算法，该算法使用基于递归神经网络 (RNN) 的自编码器 (AE)，通过重构误差和潜在空间信息来建立子序列模型，提出一种基于曲率的相似性度量进行更直观的时间序列子序列聚类，通过与其他七种算法的对比实验表明，我们的算法可以更好地在线及离线聚类多变量时间序列数据。

基于自编码器的迭代建模与多元时间序列子序列聚类算法

Autoencoder Based Iterative Modeling and Multivariate Time-Series  Subsequence Clustering Algorithm

Subsequence clustering of multivariate time series is a useful tool for
discovering repeated patterns in temporal data. Once these patterns have been
discovered, seemingly complicated datasets can be interpreted as a temporal
sequence of only a small number of states, or clusters. For example, raw sensor
data from a fitness-tracking application can be expressed as a timeline of a
select few actions (i.e., walking, sitting, running). However, discovering
these patterns is challenging because it requires simultaneous segmentation and
clustering of the time series. Furthermore, interpreting the resulting clusters
is difficult, especially when the data is high-dimensional. Here we propose a
new method of model-based clustering, which we call Toeplitz Inverse
Covariance-based Clustering (TICC). Each cluster in the TICC method is defined
by a correlation network, or Markov random field (MRF), characterizing the
interdependencies between different observations in a typical subsequence of
that cluster. Based on this graphical representation, TICC simultaneously
segments and clusters the time series data. We solve the TICC problem through
alternating minimization, using a variation of the expectation maximization
(EM) algorithm. We derive closed-form solutions to efficiently solve the two
resulting subproblems in a scalable way, through dynamic programming and the
alternating direction method of multipliers (ADMM), respectively. We validate
our approach by comparing TICC to several state-of-the-art baselines in a
series of synthetic experiments, and we then demonstrate on an automobile
sensor dataset how TICC can be used to learn interpretable clusters in
real-world scenarios.

本研究提出了一种基于 Toeplitz Inverse Covariance 的模型聚类方法，称为 TICC，通过马尔科夫随机场描述聚类中子序列中不同观测之间的相互依赖性，从而在同时分割和聚类时间序列数据的过程中实现了可扩展性且解释性更强的结果。