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Spatial ordering and encoding for geographic data mining and visualization

机译：空间排序和编码，用于地理数据挖掘和可视化

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摘要

Geographic information (e.g., locations, networks, and nearest neighbors) are unique and different from other aspatial attributes (e.g., population, sales, or income). It is a challenging problem in spatial data mining and visualization to take into account both the geographic information and multiple aspatial variables in the detection of patterns. To tackle this problem, we present and evaluate a variety of spatial ordering methods that can transform spatial relations into a one-dimensional ordering and encoding which preserves spatial locality as much possible. The ordering can then be used to spatially sort temporal or multivariate data series and thus help reveal patterns across different spaces. The encoding, as a materialization of spatial clusters and neighboring relations, is also amenable for processing together with aspatial variables by any existing (non-spatial) data mining methods. We design a set of measures to evaluate nine different ordering/encoding methods, including two space-filling curves, six hierarchical clustering based methods, and a one-dimensional Sammon mapping (a multidimensional scaling approach). Evaluation results with various data distributions show that the optimal ordering/encoding with the complete-linkage clustering consistently gives the best overall performance, surpassing well-known space-filling curves in preserving spatial locality. Moreover, clustering-based methods can encode not only simple geographic locations, e.g., x and y coordinates, but also a wide range of other spatial relations, e.g., network distances or arbitrarily weighted graphs.
机译：地理信息（例如位置，网络和最近的邻居）是唯一的，并且与其他空间属性（例如人口，销售或收入）不同。在空间数据挖掘和可视化中，在模式检测中同时考虑地理信息和多个空间变量是一个具有挑战性的问题。为了解决这个问题，我们提出并评估了各种空间排序方法，这些方法可以将空间关系转换为一维排序和编码，从而尽可能保留空间局部性。然后，可以使用该排序对时间或多元数据序列进行空间排序，从而帮助揭示不同空间上的模式。作为空间聚类和相邻关系的实现的编码，也适合通过任何现有（非空间）数据挖掘方法与空间变量一起处理。我们设计了一套方法来评估九种不同的排序/编码方法，包括两条空间填充曲线，六种基于层次聚类的方法以及一维Sammon映射（多维缩放方法）。具有各种数据分布的评估结果表明，具有完整链接聚类的最佳排序/编码始终提供最佳的整体性能，在保留空间局部性方面超过了众所周知的空间填充曲线。而且，基于聚类的方法不仅可以对简单的地理位置（例如，x和y坐标）进行编码，而且还可以对各种其他空间关系（例如，网络距离或任意加权的图）进行编码。

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