HIERARCHICAL CLUSTERING FROM PRINCIPAL COORDINATES - AN EFFICIENT METHOD FOR SMALL TO VERY LARGE NUMBERS OF OBJECTS

A divisive method for hierarchical clustering, having certian optimal properties, is derived from the properties of matrices of ultrametric distances. Computationally there is 1 main step, the estimation of the principal coordinates of the objects, which is little more than the computation of the eigenvalues and eigenvectors of a matrix. For many types of data, including variables which may be described as dichotomies, alternatives, multistate unordered or ordered, and continuous, advantage can be taken of the smaller of the 2 matrix products, XX'' or X''X, where X is the matrix of the appropriately transformed data. Since the number of variables is often much less than 200, the number of objects which can be clustered using even a medium sized computer is virtuallly unlimited.