Directed Acyclic Graphs
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16. Zhong, Z.-N., Jing, N., Chen, L., Wu, Q.-Y.: Representing topological relationships among heterogeneous geometry-collection features. Journal of Computer Science and Technology archive, Institute of Computing Technology, Beijing, China 19(3), 280–289 (2004)
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Distance Metrics JAMES M. K ANG Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA Synonyms
Directed Acyclic Graphs
D
Euclidean distance; Manhattan distance
Bayesian Network Integration with GIS
Definition
Directory Rectangles R*-tree
Dirichlet Tessellation Voronoi Diagram
The Euclidean distance is the direct measure between two points in some spatial space. These points can be represented in any n-dimensional space. Formally, the Euclidean distance can be mathematically expressed as: (a1 − b1 )2 + (a2 − b3 )2 + · · · + (an − bn ) (1) where a and b are two points in some spatial space and n is the dimension. The Manhattan distance can be mathematically described as: |x1 − x2| + |y1 − y2|
Discord or Non-Specificity in Spatial Data Uncertainty, Semantic
Discretization of Quatitative Attributes Geosensor Networks, Qualitative Monitoring of
Dynamic Fields
Disease Mapping Public Health and Spatial Modeling
Disk Page Indexing Schemes for Multi-dimensional Moving
Objects
Distance Measures Indexing and Mining Time Series Data
(2)
where A and B are the following points (x1 , y1 ) and (x2 , y2 ), respectively. Notice that it does not matter which order the difference is taken from because of the absolute value condition. Main Text The Euclidean distance can be measured at a various number of dimensions. For dimensions above three, other feature sets corresponding to each point could be added as more dimensions within a data set. Thus, there can be an infinite number of dimensions used for the Euclidean distance. For a Voronoi Diagram in a two dimensional space, a distance metric that can be used is the Euclidean distance where the number of dimensions n would be two. A common distance metric that uses the Euclidean distance is the Manhattan distance. This measure is similar to finding the exact distance by car from one corner to another corner in a city. Just using the Euclidean distance could not be used since we are trying to find the distance where a person can physically drive from the starting to the ending point. However, if we measure the distances between intersections using the Euclidean distance and add these values together, this would be the Manhattan distance. Cross References Voronoi Diagram
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