Modeling and Multivariate Methods - SAS

Chapter 18 Clustering Data 479
Self Organizing Maps
The Cluster Comparison report gives fit statistics to compare different numbers of clusters. For KMeans
Clustering and Self Organizing Maps, the fit statistic is CCC (Cubic Clustering Criterion). For Normal
Mixtures, the fit statistic is BIC or AICc. Robust Normal Mixtures does not provide a fit statistic.
For details on the red-triangle options for Self Organizing Maps, see “K-Means Platform Options” on
page 472.
Implementation Technical Details
The SOM implementation in JMP proceeds as follows:
• The first step is to obtain good initial cluster seeds that provide a good coverage of the multidimensional
space. JMP uses principal components to determine the two directions which capture the most variation
in the data.
• JMP then lays out a grid in this principal component space with its edges 2.5 standard deviations from
the middle in each direction. The clusters seeds are formed by translating this grid back into the original
space of the variables.
• The cluster assignment proceeds as with k-means, with each point assigned to the cluster closest to it.
• The means are estimated for each cluster as in k-means. JMP then uses these means to set up a weighted
regression with each variable as the response in the regression, and the SOM grid coordinates as the
regressors. The weighting function uses a ‘kernel’ function that gives large weight to the cluster whose
center is being estimated, with smaller weights given to clusters farther away from the cluster in the
SOM grid. The new cluster means are the predicted values from this regression.
• These iterations proceed until the process has converged.