Spatial clustering has been widely used for spatial data mining and knowledge
discovery. An ideal multivariate spatial clustering should consider both
spatial contiguity and aspatial attributes. Existing spatial clustering
approaches may face challenges for discovering repeated geographic patterns
with spatial contiguity maintained. In this paper, we propose a Spatial
Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both
attributes and spatial relationships of geographic objects for multivariate
spatial clustering. A subregion is created for each geographic object serving
as the basic unit when performing clustering. A Markov random field is then
constructed to characterize the attribute dependencies of subregions. Using a
spatial consistency strategy, nearby objects are encouraged to belong to the
same cluster. To test the performance of the proposed STICC algorithm, we apply
it in two use cases. The comparison results with several baseline methods show
that the STICC outperforms others significantly in terms of adjusted rand index
and macro-F1 score. Join count statistics is also calculated and shows that the
spatial contiguity is well preserved by STICC. Such a spatial clustering method
may benefit various applications in the fields of geography, remote sensing,
transportation, and urban planning, etc.

本文提出了一种基于 STICC 方法的多元空间聚类方法，该方法通过构建马尔可夫随机场以表征子区域之间的属性依赖关系，利用空间一致性策略鼓励附近的对象归属于同一聚类，应用实验表明 STICC 算法对于保持空间连续性和发现重复地理模式等方面优于其他基线方法。

STICC: 一种考虑空间连续性的多变量空间聚类方法用于重复地理模式发现

STICC: A multivariate spatial clustering method for repeated geographic pattern discovery with consideration of spatial contiguity

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。