ST_GeometricMedian

Description

Computes the approximate geometric median of a MultiPoint geometry using the Weiszfeld algorithm. The geometric median provides a centrality measure that is less sensitive to outlier points than the centroid.

The algorithm will iterate until the distance change between successive iterations is less than the supplied tolerance parameter. If this condition has not been met after max_iterations iterations, the function will produce an error and exit, unless fail_if_not_converged is set to false.

If a tolerance value is not provided, a default tolerance value will be calculated based on the extent of the input geometry.

M value of points, if present, is interpreted as their relative weight.

Availability: 2.3.0

Enhanced: 2.5.0 Added support for M as weight of points.

This function supports 3d and will not drop the z-index.

This function supports M coordinates.

Examples

Comparison of the centroid (turquoise point) and geometric median (red point) of a four-point MultiPoint (yellow points).

WITH test AS (
SELECT 'MULTIPOINT((0 0), (1 1), (2 2), (200 200))'::geometry geom)
SELECT
  ST_AsText(ST_Centroid(geom)) centroid,
  ST_AsText(ST_GeometricMedian(geom)) median
FROM test;
      centroid      |                 median
--------------------+----------------------------------------
 POINT(50.75 50.75) | POINT(1.9761550281255 1.9761550281255)
(1 row)
	  

See Also

ST_Centroid