Modeling and Multivariate Methods - SAS

Chapter 18 Clustering Data 477
Self Organizing Maps
So, in the limit as k becomes arbitrarily large, Φ k
( x) tends toward the normal PDF. As k → 0 , Φ k
( x)
tends
toward the exponential (Laplace) distribution.
The regularization parameter k is set so that P(Normal(x) < k) = Huber Coverage, where Normal(x)
indicates a multivariate normal variate. Huber Coverage is a user field, which defaults to 0.90.
Self Organizing Maps
The Self-Organizing Maps (SOMs) technique was developed by Teuvo Kohonen (1989) and further
extended by a number of other neural network enthusiasts and statisticians. The original SOM was cast as a
learning process, like the original neural net algorithms, but the version implemented here is done in a
much more straightforward way as a simple variation on k-means clustering. In the SOM literature, this
would be called a batch algorithm using a locally weighted linear smoother.
The goal of a SOM is to not only form clusters, but form them in a particular layout on a cluster grid, such
that points in clusters that are near each other in the SOM grid are also near each other in multivariate
space. In classical k-means clustering, the structure of the clusters is arbitrary, but in SOMs the clusters have
the grid structure. This grid structure helps to interpret the clusters in two dimensions: clusters that are close
are more similar than distant clusters.
To create a Self Organizing Map, select that option on the Method menu of the Iterative Clustering Control
Panel (Figure 18.5). After selecting Self Organizing Map, the control panel looks like Figure 18.10.
Figure 18.10 Self Organizing Map Control Panel
Some of the options on the panel are described in “K-Means Control Panel” on page 470. The other options
are described below:
N Rows
is the number of rows in the cluster grid.
N Columns
is the number of columns in the cluster grid.