Efficient Clustering for Orders - Mining Complex Data - page 260

frequently shown to respondents. Objects were selected independently with probabil-
ities ranging from 3 . 2% to 0 . 13%. Therefore, the assumption of the uniformity of the
sampling distribution, introduced by the EBC method, was violated. The best result in
terms of Equation (15.8) ware selected from 10 trials. The number of clusters, K ,was
set to 2. Note that responses of both authors were clustered into Cluster 1.

15.5.2 Qualitative Analysis of Order Clusters

In [8], we proposed a technique to interpret the acquired clusters based on the relation
between attributes of objects and central orders. We applied this method to clusters
derived by the EBC and TMSE methods. Table 15.2 shows Spearman's ρ between
central orders of each cluster and an order of objects sorted according to the specific
object attributes. For example, the third row presents the ρ between the central order
and the sorted object sequence according to their price. Based on these correlations,
we were able to learn what kind of object attributes affected the preferences of the
respondents in each cluster. We will comment next on each of the object attributes.
Almost the same observations were obtained by both EBC and TMSE . The attribute
A1 shows whether the object tasted heavy (i.e., high in fat) or light (i.e., low in fat). The
positive correlation indicate a preference for heavy testing. The cluster 2 respondents
preferred heavy-tasting sushi. The attribute A2 shows how frequently the respondent
eats the sushi. The positive correlation indicates a preference for the sushi that the re-
spondent infrequently eats. Respondents in both clusters preferred the sushi they usually
eat. No clear difference was observed between clusters. The attribute A3 is the prices
of the objects. The positive correlation indicates a preference for economical sushi.
The cluster 2 respondents preferred more expensive sushi. The attribute A4 shows how
frequently the objects are supplied at sushi shops. The positive correlation indicates a
preference for the objects that fewer shops supply. Though the correlation of cluster 1
was rather larger, the difference was not very clear. Roughly speaking, the members of
cluster 2 preferred more heavy-tasting and expensive sushi than those of cluster 1.
In this paper, we propose a new technique based on the changes in object ranks. First,
a central order of all the sample orders was calculated, and was denoted by O ∗ .Next,
for each cluster, the central orders were also calculated, and were denoted by O k . Then,
for each object x j in X ∗ , the difference of ranks,

rankup( x j )= r ( O ∗ ,x j ) r ( O k ,x j ) , − (15.18)

Table 15.2. Relations between clusters and attributes of objects

Attribute Cluster 1 Cluster 2

EBC TMSE EBC TMSE

A1 0 . 0999 0 . 0349 0 . 3656 0 . 2634

A2 − 0 . 5662 − 0 . 7852 − 0 . 4228 − 0 . 6840

A3 − 0 . 0012 − 0 . 0724 − 0 . 4965 − 0 . 6403

A4 − 0 . 1241 − 0 . 4555 − 0 . 1435 − 0 . 5838