GGR276H5 Chapter Notes - Chapter 4: Euclidean Distance, Taxicab Geometry, Central Tendency
4.1-4.2
The central feature is the feature (point or area) whose total distance to all other
features in the study area is the shortest.
If we are evaluating a point pattern, the central point is the point with the lowest
total distance to all other points.
Similarly, if evaluating an area pattern, the central area is the area whose total
distance to all other areas is the shortest.
Notice that the definition of distance in this example is Euclidean (or straight-
line) distance.
If this concept of central tendency is now extended to the same set of seven points
as shown in figure 4.1, the mean center (or average location), can be determined.
The mean center may be considered the center of gravity of a point pattern or
spatial distribution.
Perhaps the most widely known application of the mean center is the decennial
calculation of the geographic center of population by the U.S. Bureau of the
census.
The weighted mean center is defined as follows:
This location, which minimizes the sum of Euclidean distances from all other points
in a spatial distribution to that central location, is called the median center (Xe, Ye)
or Euclidean median.
If this Euclidean distance metric is now generalized to allow non-Euclidean
distance measurement, the result is a general distance metric:
The term Manhattan distance describes the restrictive movement typical of travel
in the New York City borough of Manhattan.
However, one of the many possible network distance routes (traveling along
interstate highways through Indianapolis, Indiana) seems reasonable from both
travel time and travel convenience perspectives.
The linear directional mean (or simply directional mean) identifies the typical or
general (mean) direction for a set of lines.
Just as the mean center serves as a location analogue to the mean, standard
distance is the spatial equivalent of standard deviation (table 4.1).
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Document Summary
The central feature is the feature (point or area) whose total distance to all other features in the study area is the shortest. If we are evaluating a point pattern, the central point is the point with the lowest total distance to all other points. Similarly, if evaluating an area pattern, the central area is the area whose total distance to all other areas is the shortest. Notice that the definition of (cid:498)distance(cid:499) in this example is euclidean (or straight- line) distance. If this concept of central tendency is now extended to the same set of seven points as shown in figure 4. 1, the mean center (or average location), can be determined. The mean center may be considered the center of gravity of a point pattern or spatial distribution. Perhaps the most widely known application of the mean center is the decennial calculation of the geographic (cid:498)center of population(cid:499) by the u. s. bureau of the census.
