Cluster Tools
A Simple Example

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 filled-in 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 filled-in 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'.)

Interaction Matrix

Non-Directed Graph

This non-directed 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 non-directed graph to the sets found and plotted by Cluster Tools below.

Non-directed Graph

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 Set Plots

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
14, 21
Set 102 Subsets:
13, 18
Set 103 Subsets:
1, 8, 12, 17
Set 104 Subsets:
7, 11, 19, 20
Set 105 Subsets:
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.
Cluster Weights