Cluster Analysis

1
Cluster Analysis

• Single Link Cluster Analysis
• Wards Minimum Sum of Squares
• k-Means Cluster Analysis
• SPSS TwoStep Cluster Analysis

2
Single-Link Clustering (most popular method)
Cost (Importance)
.
Right
Left
C
.
.
.
B
Single Link Join item to cluster which has
the single closest member. Since Bltq, join the
star to the Left cluster, even though Agtq and
Cgtq.
A
q
Complete Pain Relief (Importance)
3
Cluster AnalysisSingle Chain Agglomerative
Procedure(most popular method)
Part-Worth Coefficients of Complete Pain Relief
D
Therapy A
Therapy E
Therapy B
Therapies C
5
9 10
15
2
Single Link Join item to cluster which has the
single closest member.

• First Stage A 2 B5 C9 D10 E15
• Second Stage AB 3 BD5
• (Euclidian Distance) AC6 BE10
• AD8 CD 1
• AE13 CE6
• BC 4 DE5
• Third Stage CDA7 CDB4 CDE5 AB 3
• AE 13 BE 10
• Fourth Stage ABCD4 ABE10 CDE5
• Fifth Stage ABCDE5

4
Single Chain Agglomerative Clustering Output
Dendogram
5 4 3 1
A B C D E
5
Wards Clustering
Strength (Importance)
.
Right
Left
D
.
.
.
C
Wards Cluster Join item to cluster which has
the smallest distance ESS. In this case, if
star is joined to left cluster, ESSA2B2C2D2
A
B
mean location of points in proposed cluster
Water Resistance (Importance)
6
Wards Minimum Variance Agglomerative Clustering
Procedure

• First Stage A 2 B5 C9 D10 E15
• Second Stage AB 4.5 BD12.5
• AC24.5 BE50.0
• AD32.0 CD 0.5
• AE84.5 CE18.0
• BC 8.0 DE12.5
• Third Stage CDA38.0 CDB14 CDE20.66 AB 5.0
• AE 85 BE 50.5
• Fourth Stage ABCD41.0 ABE93.17 CDE25.18
• Fifth Stage ABCDE98.8

7
Wards Minimum Variance Agglomerative Clustering
Output
98.8 25.18 5 0.5
A B C D E
8
k-Means Clustering
1. Begin with two starting center points and
allocate each item to nearest cluster
center. 2. Recalculate center of clusters.
Stop if center hasnt changed. 3. Allocate
items to nearest cluster center. Goto 2.
9
k-Means Clustering
1
4
A
A
B
B
2
5
A
A
B
B
3
A
B
10
SPSS TwoStep Cluster Method

• -scalable cluster analysis algorithm designed to
  handle
• very large data sets.
• can handle both continuous and categorical
  variables or attributes.
• automatically select the number of clusters.

Step 1 pre-cluster the cases (or records) into
many small sub-clusters Step 2 cluster the
sub-clusters resulting from pre-cluster step into
the desired number of clusters.