Entropy uncertainty of multi-dimensional random variable

Da-jun Li; Xia Yang; Jian-ya Gong

doi:10.1117/12.813130

10 November 2008 Entropy uncertainty of multi-dimensional random variable

Da-jun Li, Xia Yang, Jian-ya Gong

Proceedings Volume 7146, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses; 714613 (2008) https://doi.org/10.1117/12.813130
Event: Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Geo-Simulation and Virtual GIS Environments, 2008, Guangzhou, China

Abstract

Research on positional uncertainty of point is the basis of modeling uncertainty of line segment and polygon. The positional uncertainty indices of point have been widely studied in topography and metrology. In this paper, the exist entropy uncertainty interval of one-dimensional random variable is extended to the circumstances of two-dimensional, three-dimensional and N-dimensional by introducing the theory of information entropy. The indices of entropy uncertainty ellipse, entropy uncertainty ellipsoid and entropy uncertainty super ellipsoid are presented, which can be considered as the indices of uncertainty degree of the random point in two-dimensional, three-dimensional and multidimensional. The entropy indices presented in this paper are unaffected by the objective selection of the confidence level. And they are especially suitable for uncertainty measurement of the random points with unknown distribution in GIS.

Citation Download Citation

Da-jun Li, Xia Yang, and Jian-ya Gong "Entropy uncertainty of multi-dimensional random variable", Proc. SPIE 7146, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Advanced Spatial Data Models and Analyses, 714613 (10 November 2008); https://doi.org/10.1117/12.813130

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