Clustering and Visualization of Retail Market Baskets - Advanced Techniques in Knowledge Discovery and Data Mining - page 84

3.4 CLUSION: Cluster Visualization

In this section, we present our visualization tool, highlight some of its proper-
ties, and compare it with some popular visualization methods. Applications
of this tool are illustrated in Section 3.5.

3.4.1 Coarse Seriation

When data are limited to two or three dimensions, the most powerful tool
for judging cluster quality is usually the human eye. , our CLUSter

visualizatION toolkit, allows us to convert high-dimensional data into a per-
ceptually more suitable format and to employ the human vision system to
explore the relationships in the data, guide the clustering process, and verify
the quality of the results. In our experience with two years of Dell customer
data, we found

Clusion

effective for getting clusters balanced with respect
to number of customers or net dollar amount, and even more so for conveying
the results to marketing management.
Clusion

Clusion

looks at the output of a clustering routine, reorders the data
points such that points with the same cluster label are contiguous, and then
visualizes the resulting permuted similarity matrix, S . More formally, the
original n × n similarity matrix S is permuted with an n × n permutation

matrix P defined as follows:
p i,j = 1ifj = i a=1

l a,λ i + λ i −1 n

=1

(3.5)

0 otherwise,

where l areentriesinthebinaryn × k cluster membership indicator matrix

L :

l i,j = 1ifλ i = j (3.6)

0 otherwise.

In other words, p i,j is 1 if j isthenumberofpointsamongthefirsti points
that belong to the cluster λ i plus the number of points in the clusters 1 to

λ i − 1. This is easily understood with an example. Let there be four points

with the following labeling:

⎛ ⎞

3
2
1
2

⎝ ⎠

λ = . (3.7)

Then the binary cluster membership matrix is

⎛
⎝

⎞
⎠

001
010
100
010

L = . (3.8)