A spatial heterogeneity-based rough set extension for spatial data

ABSTRACT

When classical rough set (CRS) theory is used to analyze spatial data, there is an underlying assumption that objects in the universe are completely randomly distributed over space. However, this assumption conflicts with the actual situation of spatial data. Generally, spatial heterogeneity and spatial autocorrelation are two important characteristics of spatial data. These two characteristics are important information sources for improving the modeling accuracy of spatial data. This paper extends CRS theory by introducing spatial heterogeneity and spatial autocorrelation. This new extension adds spatial adjacency information into the information table. Many fundamental concepts in CRS theory, such as the indiscernibility relation, equivalent classes, and lower and upper approximations, are improved by adding spatial adjacency information into these concepts. Based on these fundamental concepts, a new reduct and an improved rule matching method are proposed. The new reduct incorporates spatial heterogeneity in selecting the feature subset which can preserve the local discriminant power of all features, and the new rule matching method uses spatial autocorrelation to improve the classification ability of rough set-based classifiers. Experimental results show that the proposed extension significantly increased classification or segmentation accuracy, and the spatial reduct required much less time than classical reduct.

KEYWORDS:

• Rough set model
• spatial information table
• spatial heterogeneity
• spatial autocorrelation
• feature selection

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by the Strategic Priority Research Program of the Chinese Academy of Science under Grant [XDA19040501], the National Natural Science Foundation of China under Grant [41871286], the National Natural Science Foundation for Distinguished Young Scholars of China under Grant [41725006] and the Natural Science Foundation of Shanxi Province of China under Grant [201701D121055].

Notes on contributors

Hexiang Bai

Hexiang Bai is an associate professor in Computer Science at the school of computer and informatin technology, Shanxi University. His research interests include rough set based granular computing and spatial statistics. E-mail: [email protected].

Deyu Li

Deyu Li is a professor in Computer Science at the school of computer and informatin technology, Shanxi University. His research interests include rough set based granular computing and computational intelligence. E-mail: [email protected].

Yong Ge

Yong Ge is a professor in Geograhphical Information Sciences at the Institute of Geograhpic Sciences and Natural Resources Research, Chinese Academy of Science. Her research interests include spatial statistics spatial scale transformation. E-mail: [email protected].

Jinfeng Wang

Jinfeng Wang is a professor in Geograhphical Information Sciences at the Institute of Geograhpic Sciences and Natural Resources Research, Chinese Academy of Science. His research interest is spatial statistics. E-mail: [email protected].