Interaction Matrix
This is a simple example of
Cluster Tools
using a small interaction matrix of 21 elements.
An interaction matrix is used to define relationships
between the elements.
A filledin cell indicates that the element represented by
the column interacts with the element represented by the row.
For example, if the elements are of design insights or factors,
a filledin square could represent which ones should be
considered together because of some critical relationship.
(The cells along the diagonal represent that the elements interact
with themselves.)
Each time the user clicks on a cell its color toggles.
When a cell in column 'x' row 'y' is clicked, the cell color
for column 'y' row 'x' also toggles. (If 'x' interacts with
'y' then 'y' interacts with 'x'.)
NonDirected Graph
This nondirected graph is
another way to represent the interactions
between elements in the matrix.
For example, we can see that element 2 interacts with
1, 3, 10 and 12.
It belongs to the cluster or set arbitrarily labeled "103"
because it interacts with two of the other four (1/2 of them).
It's relationship to set "101" is weaker because it only
interacts with 2 out of the other 6 (1/3 of them).
Cluster analysis is a mathematical
technique to find the strongest cluster sets in a graph of such
relationships.
Compare the cluster sets in this nondirected graph to the
sets found and plotted by
Cluster Tools below.
Cluster Set Plots
A simple graph of interactions like this can be easily
"untangled" but a graph of dozens of elements
would be very large and complex.
Cluster Tools plots the cluster sets
with lines representing the interactions between
elements. The connection ratios (CR) show the ratios of
possible to existing interactions. If the user specified fewer
sets the connection ratios would be higher, e.g., 100%.
Cluster Hierarchies
Cluster Tools
reports clusters found within clusters.
In this simple example
the cluster sets further decompose as follows.
Note that sets with a connection ratio of 100% cannot be
decomposed further.

Set 101 Subsets:
5, 6, 10
3
14, 21

Set 102 Subsets:
13, 18

Set 103 Subsets:
2
1, 8, 12, 17

Set 104 Subsets:
7, 11, 19, 20

Set 105 Subsets:
15
4, 9, 16

Cluster Weights
Cluster weights ("centers") plotted by
Cluster Tools
shows the relative strength of
each element in each cluster set. The row in the forground shows the
weights of the elements in set 101. Elements 3, 5, 6, 10 14 and
21 have the greatest weights. If the threshold allowing elements
into a set is raised or lowered, fewer or more would be included
respectively.
For screenshots of more complex examples
and for information about its features
go to the
Cluster Tools
page.