Computational Resources

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The VARCLUS Procedure

Computational Resources

Let

$n &=& {number of observations}\v &=& {number of variables}\c &=& {number of clusters}$

It is assumed that, at each stage of clustering, the clusters all contain the same number of variables.

Time

The time required for PROC VARCLUS to analyze a given data set varies greatly depending on the number of clusters requested, the number of iterations in both the alternating least-squares and search phases, and whether centroid or principal components are used.

The time required to compute the correlation matrix is roughly proportional to nv².

Default cluster initialization requires time roughly proportional to v³. Any other method of initialization requires time roughly proportional to cv².

In the alternating least-squares phase, each iteration requires time roughly proportional to cv² if centroid components are used or

(c+5[v/(c²)])v²

if principal components are used.

In the search phase, each iteration requires time roughly proportional to v³/c if centroid components are used or v⁴/c² if principal components are used. The HIERARCHY option speeds up each iteration after the first split by as much as c/2.

Memory

The amount of memory, in bytes, needed by PROC VARCLUS is approximately

v²+2vc+20v+15c

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