Description of SOM Algorithm

The SOM implementation in JMP proceeds as follows:

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Initial cluster seeds are selected in a way that provides a good coverage of the multidimensional space. JMP uses principal components to determine the two directions that capture the most variation in the data.

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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 determined by translating this grid back into the original space of the variables.

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The cluster assignment proceeds as with k-means. Each point is assigned to the cluster closest to it.

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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. Smaller weights are given to clusters farther away from the cluster in the SOM grid. The new cluster means are the predicted values from this regression.

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These iterations proceed until the process has converged.