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# Principal coordinates analysis

is a multivariate technique that operates on a symmetric matrix A of similarities or associations between a set of objects. It aims to find a set of points for the n units in a multidimensional space so that the squared distance between the ith and jth points is given by:

dij = aii + ajj2aij.

The coordinates of the points are arranged so that their centroid, or mean position, is at the origin. Furthermore they are arranged relative to their principal axes, so that the first dimension of the solution gives the best one-dimensional fit to the full set of points, the first two dimensions give the best two-dimensional fit, and so on. The analysis also gives the distances of the points from their centroid, the origin. Associated with each dimension (or principal coordinate) is a latent root which is the sum of squares of the coordinates of all the points in that dimension. (See `PCO`.)

Updated on December 4, 2017