The Study on Trinary Join-Counts for Spatial Autocorrelation

Songlin Zhang 1, Kun Zhang 2
1 Department of Surveying and Geomatics, Tongji University, Shanghai, 200092, China
2 Lab. of Geographic Information Science, East China Normal University, Shanghai 200062, China

Abstract. Spatial autocorrelation must handle two kinds of geographic data. One is continuous valued variables in which the observations are real numbers. Another is nominal variables which consist of a set of discrete categories. The frequently used spatial autocorrelation statistic for nominal variable is “join-counts”, which deals with two categories that are often referred to as “black” and “white”. However, three categories are also common case in present world. For example, as to land cover, the attribute of each parcel may be changed, unchanged or uncertain which represents parcels not belonging to the first two categories. In three valued logic, values could be true, false or unknown. This paper extended join-counts to trinary join-count. The trinary categories are referred as “black”, “white” and “gray” in this paper and the possible type of joins are limited to black-black (BB), white-white (WW), gray-gray (GG), black-white (BW), black-gray (BG) and white-gray (WG). In order to calculating joins, we assign a trinary variable xi to each region with xi=1 if region is “black”, xi=0 if region is “white”, and xi=-1 if region is “gray”. Formulas for counting six kinds of joins are deduced. The aim of trinary join-counts is to test the null hypothesis that the values are assigned to the regions randomly and independently. Means and variance of trinary join-counts are calculated under sampling without replacement assumption. The tests statistic is computed by transforming the join-counts into standardized value. At last, two kinds of examples are designed. The first one is regular grid with trinary values, the selection of regular grid is particularly motivated by widely use of remote sensing data. The second one is irregular spatial regions, such as land cover statues. The results suggest that the trinary joincount is useful and could be used in spatial autocorrelation analysis.

Keywords: trinary variable, join-counts statistics, spatial autocorrelation

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).

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