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收稿：2018-09-06，
修回：2018-11-18，
纸质出版：2019-06-16
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目的
2
平行坐标是经典的多维数据可视化方法，但在用于地理空间多维数据分析时，往往存在空间位置信息缺失和空间关联分析不确定等问题。对此，本文设计了一种有效关联平行坐标和地图的地理空间多维数据可视分析方法。
方法
2
根据多维属性信息对地理空间位置进行聚类分析，引入Voronoi图和颜色明暗映射对地理空间各类区域进行显著标识，利用平行坐标呈现地理空间多维属性信息，引入互信息度量地理空间聚类与属性类别的相关性，动态地确定平行坐标轴排列顺序，进一步计算属性轴与地图之间数据线的绑定位置，对数据线的布局进行优化处理，降低地图与平行坐标系间数据线分布的紊乱程度。
结果
2
有效集成上述可视化设计及数据分析方法，设计与实现一种基于平行坐标轴动态排列的地理空间多维数据可视化分析系统，提供便捷的用户交互模式，通过2组具有明显地理空间多维属性特征的数据进行测试，验证了本文可视分析方法的有效性和实用性。
结论
2
本文提出的可视分析方法和工具可以帮助用户快速分析地理空间多维属性存在的空间分布特征及其关联模式，为地理空间多维数据的探索提供了有效手段。
Objective
2
Geospatial multi-dimensional data are mainly composed of spatial location and attribute information
which can effectively record and describe events and phenomena
such as social and economic development
natural environment changes
and human social activities. As a commonly used method for multi-dimensional data visualization
parallel coordinates do not work well for the visual exploration of geospatial multi-dimensional data because of the lack of spatial information and uncertainty of spatial correlation. Therefore
analysis and understanding of geospatial multidimensional data are highly important in establishing an effective association between spatial locations and multiple attributes.
Method
2
In this study
we propose a novel geospatial multi-dimensional data visualization method that uses geographical maps to display spatial locations
visualizes multi-dimensional attributes via parallel coordinates
and associates map and parallel coordinates through data lines. We design a corresponding visual analysis system that allows users to explore and analyze the spatial distribution of geospatial multi-dimensional data and its associated feature patterns interactively on the basis of the initial geospatial multidimensional data
including different spatial locations and their corresponding multi-dimensional attribute information. Spatial areas are classified into different clusters according to multi-dimensional attributes and spatial distance
and Voronoi diagrams and color mappings are designed to represent different clusters visually. The attribute information of the geospatial multi-dimensional data is represented by parallel coordinates
and the data on different attribute axes are clustered and analyzed. Mutual information is used to calculate the correlation between the geospatial clustering and attribute categories dynamically
and the ordering of the parallel coordinate plot is adaptively determined. Then
the map is embedded into the parallel coordinates on the basis of the axis alignment results
and the map view and parallel coordinate systems are effectively correlated through data lines. Furthermore
the binding position of the data line between the attribute axis and the map is dynamically calculated according to the geospatial clustering
and the layout of the data line is optimized to reduce the disorder of the data line distribution between the map and parallel coordinate system. We design and implement a geospatial multi-dimensional data visualization analysis system that integrates the above visual designs and data analysis methods. To demonstrate the validity and practicability of the proposed visual analysis system
a convenient user interaction mode is provided
and two case studies are conducted based on the datasets with multi-dimensional geospatial attributes. GDP data containing 11 attributes and 32 spatial locations are visualized using our visual analysis system.
Result
2
Comparison of the geospatial clustering and actual urban development in the map view proves that the proposed geospatial clustering algorithm that comprehensively considers data attribute and spatial location information is useful. By observing the arrangement of parallel axes
we confirm that the dynamic arrangement of parallel axes based on mutual information exhibits a certain rationality. In the second case based on geospatial multi-dimensional data
we explore the spatial distribution of attribute information in a certain spatial cluster. When a user clicks on a geospatial clustering of interest
the system rearranges the parallel coordinate axes.
Conclusion
2
By comparing the distributions of attributes of the same geospatial clustering at different times
we find that the proposed method is highly sensitive to data. When the data change slightly
the order of the parallel axis changes
making the map embedded in parallel coordinates match the spatial distribution of multi-dimensional attribute information well. We invite experts from different fields
such as geography and economics
to use and evaluate the system. The validity and practicability of the geospatial multidimensional data visual analysis system are further verified through one-on-one interviews. A set of case studies and expert feedback shows that the visual analysis methods and tools proposed in this study can help users quickly analyze the spatial distribution characteristics and associated patterns of geospatial multi-dimensional attributes and provide domain experts with an effective means of exploring geospatial multi-dimensional data.
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