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

Unsupervised text encoding models have recently fueled substantial progress
in NLP. The key idea is to use neural networks to convert words in texts to
vector space representations based on word positions in a sentence and their
contexts, which are suitable for end-to-end training of downstream tasks. We
see a strikingly similar situation in spatial analysis, which focuses on
incorporating both absolute positions and spatial contexts of geographic
objects such as POIs into models. A general-purpose representation model for
space is valuable for a multitude of tasks. However, no such general model
exists to date beyond simply applying discretization or feed-forward nets to
coordinates, and little effort has been put into jointly modeling distributions
with vastly different characteristics, which commonly emerges from GIS data.
Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in
mammals provide a multi-scale periodic representation that functions as a
metric for location encoding and is critical for recognizing places and for
path-integration. Therefore, we propose a representation learning model called
Space2Vec to encode the absolute positions and spatial relationships of places.
We conduct experiments on two real-world geographic data for two different
tasks: 1) predicting types of POIs given their positions and context, 2) image
classification leveraging their geo-locations. Results show that because of its
multi-scale representations, Space2Vec outperforms well-established ML
approaches such as RBF kernels, multi-layer feed-forward nets, and tile
embedding approaches for location modeling and image classification tasks.
Detailed analysis shows that all baselines can at most well handle distribution
at one scale but show poor performances in other scales. In contrast,
Space2Vec's multi-scale representation can handle distributions at different
scales.

提出了一个名为 Space2Vec 的表示学习模型，用于将地点的绝对位置和空间关系进行编码，并在地理数据和图像分类两个任务上得到了比径向基函数和多层前馈神经网络等传统机器学习方法更好的效果，其特点是具有多尺度表示能力。