Modeling and Multivariate Methods - SAS

Chapter 18 Clustering Data 467
Hierarchical Clustering
Save Cluster Hierarchy saves information needed if you are going to do a custom dendrogram with
scripting. For each clustering, it outputs three rows, the joiner, the leader, and the result, with the cluster
centers, size, and other information.
Save Distance Matrix
makes a new data table containing the distances between the observations.
Parallel Coord Plots creates a parallel coordinate plot for each cluster. For details about the plots, see
Basic Analysis and Graphing.
Script
contains options that are available to all platforms. See Using JMP.
Technical Details for Hierarchical Clustering
The following description of hierarchical clustering methods gives distance formulas that use the following
notation. Lowercase symbols generally pertain to observations and uppercase symbols to clusters.
n is the number of observations
v is the number of variables
x i is the ith observation
C K is the Kth cluster, subset of {1, 2,..., n}
N K is the number of observations in C K
x
is the sample mean vector
x K
x
x)
is the mean vector for cluster C K
is the square root of the sum of the squares of the elements of x (the Euclidean length of the vector
d(x i , x j ) is
x 2
Average Linkage In average linkage, the distance between two clusters is the average distance between
pairs of observations, or one in each cluster. Average linkage tends to join clusters with small variances
and is slightly biased toward producing clusters with the same variance. See Sokal and Michener (1958).
Distance for the average linkage cluster method is
D KL
=
d( x i
, x j
)
------------------
i ∈ C K j ∈ C L
N K
N L
Centroid Method In the centroid method, the distance between two clusters is defined as the squared
Euclidean distance between their means. The centroid method is more robust to outliers than most
other hierarchical methods but in other respects might not perform as well as Ward’s method or average
linkage. See Milligan (1980).
Distance for the centroid method of clustering is
2
D KL
= x K – x L