Spatial Contiguity Matrices
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Practical Handbook of Spatial Statistics, pp. 65–82, CRC, Boca Raton, Florida, USA (1995)
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Spatial Autocorrelation Measures S UMEETA S RINIVASAN School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Definition
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and the off-diagonal non-zero elements indicating contiguity of locations i and j are used to code proximities. The most commonly used of global indicators of spatial autocorrelation are Moran’s I and Geary’s C which are defined as: N i j Wij Zi Zj (1) I= 2, i i Wij i Zi (N − 1) i j Wij (xi − xj )2 . C= 2 2 i j Wij i Zi
(2)
Z i is the deviation of the variable of interest xi from the mean x¯ at location i, and N is the number of data points. Recommended Reading 1. Cliff, A., Ord, J.K.: Autocorrelation, Spatial. Pion, London (1973)
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Spatial Contiguity Matrices S UMEETA S RINIVASAN School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Synonyms
A statistic that assesses the global clustering of spatial data.
Spatial weight matrices
Main Text
Definition
Moran’s I and Geary’s C are indices of spatial autocorrelation. A spatial contiguity matrix W ij , with a zero diagonal,
These are spatial matrices that are used to define spatial contiguity.
S
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Spatial Correlation
Main Text The contiguity relations used for spatial autocorrelation measures such as Moran and Geary are in terms of sets of neighbors of location i. These are coded in the form of a weights matrix W, with a zero diagonal, and the offdiagonal non-zero elements. The off-diagonal elements are often scaled to sum to unity in each row. They indicate the proximity of locations either through distance measures or by equaling 1 when the locations are proximate and 0 otherwise. Cross References Autocorrelation, Spatial Spatial Autocorrelation Measures
Recommended Reading 1. Cliff, A., Ord, J.K.: Autocorrelation, Spatial. Pion, London (1973)
called probability threshold queries, which return answers whose probabilities are higher than a user-defined value. The main idea of the PTI is to precompute information for each uncertain object, and augment this information in the nodes of an R-tree. The PTI provides early filtering opportunities and reduces the need to perform expensive integration operations that are required for computing probabilities. The PTI supports various types of probability threshold queries. This chapter studies the use of PTI to answer two types of que
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