Modeling and Multivariate Methods - SAS

Chapter 18 Clustering Data 473
Normal Mixtures
Normal Mixtures
Normal mixtures is an iterative technique, but rather than being a clustering method to group rows, it is
more of an estimation method to characterize the cluster groups. Rather than classifying each row into a
cluster, it estimates the probability that a row is in each cluster. See McLachlan and Krishnan (1997).
The normal mixtures approach to clustering predicts the proportion of responses expected within each
cluster. The assumption is that the joint probability distribution of the measurement columns can be
approximated using a mixture of multivariate normal distributions, which represent different clusters. The
distributions have mean vectors and covariance matrices for each cluster.
Hierarchical and k-means clustering methods work well when clusters are well separated, but when clusters
overlap, assigning each point to one cluster is problematic. In the overlap areas, there are points from several
clusters sharing the same space. It is especially important to use normal mixtures rather than k-means
clustering if you want an accurate estimate of the total population in each group, because it is based on
membership probabilities, rather than arbitrary cluster assignments based on borders.
To perform Normal Mixtures, select that option on the Method menu of the Iterative Clustering Control
Panel (Figure 18.5). After selecting Normal Mixtures, the control panel looks like Figure 18.7.
Figure 18.7 Normal Mixtures 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:
Diagonal Variance is used to constrain the off-diagonal elements of the covariance matrix to zero. In this
case, the platform fits multivariate normal distributions that have no correlations between the variables.
This is sometimes necessary in order to avoid getting a singular covariance matrix, when there are fewer
observations than columns.