Modeling and Multivariate Methods - SAS

Chapter 18 Clustering Data 463
Hierarchical Clustering
Select Data is distance matrix if you have a data table of distances instead of raw data. If your raw data
consists of n observations, the distance table should have n rows and n columns, with the values being the
distances between the observations. The distance table needs to have an additional column giving a unique
identifier (such as row number) that matches the column names of the other n columns. The diagonal
elements of the table should be zero, since the distance between a point and itself is zero. The table can be
square (both upper and lower elements), or it can be upper or lower triangular. If using a square table, the
platform gives a warning if the table is not symmetric. For an example of what the distance table should look
like, use the option “Save Distance Matrix” on page 467.
To sort clusters by their mean value, specify an Ordering column. One way to use this feature is to complete
a Principal Components analysis (using Multivariate) and save the first principal component to use as an
Ordering column. The clusters are then sorted by these values.
Use the Missing value imputation option to impute missing values in the data. Missing value imputation is
done assuming that there are no clusters, that the data come from a single multivariate normal distribution,
and that the missing values are completely at random. These assumptions are usually not reasonable in
practice. Thus this feature must be used with caution, but it may produce more informative results than
throwing away most of your data.
Using the Pairwise method, a single covariance matrix is formed for all the data. Then each missing value is
imputed by a method that is equivalent to regression prediction using all the non-missing variables as
predictors. If you have categorical variables, it uses the category indices as dummy variables. If regression
prediction fails due to a non-positive-definite covariance for the non-missing values, JMP uses univariate
means.
Hierarchical clustering supports character columns as follows. K-Means clustering only supports numeric
columns.
• For Ordinal columns, the data value used for clustering is just the index of the ordered category, treated
as if it were continuous data. These data values are standardized like continuous columns.
• For Nominal columns, the categories must either match to contribute a distance of zero, or contribute a
standardized distance of 1.
Hierarchical Clustering
The Hierarchical option clusters rows that group the points (rows) of a JMP table into clusters whose values
are close to each other relative to those of other clusters. Hierarchical clustering is a process that starts with
each point in its own cluster. At each step, the two clusters that are closest together are combined into a
single cluster. This process continues until there is only one cluster containing all the points. This type of
clustering is good for smaller data sets (a few hundred observations).
To see a simple example of hierarchical clustering, select the Birth Death Subset.jmp data table. The data
are the 1976 crude birth and death rates per 100,000 people.
When you select the Cluster command, the Cluster Launch dialog (shown previously in Figure 18.1)
appears. In this example the birth and death columns are used as cluster variables in the default method,
Ward’s minimum variance, for hierarchical clustering.