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sushi categorized as a
red fish meat
, e.g., fatty tuna, were not listed in the table, because
the preference of sushi in this category were similar in both clusters. We can say that
the respondents in cluster 2 preferred rather oily sushi, especially blue fish, clam/shell,
or liver. The sushi marked by
are very economical. Though these sushi were fairly
ranked up in cluster 1, this would not indicate a preference for economical sushi. These
would be ranked up because these respondents had sushi that they disliked more than
these inexpensive types of sushi. Therefore, to interpret the acquired cluster of orders,
not only should the values of equation (15.18) be observed, but also the kind of objects
that were ranked up or ranked down.
♣
15.6
Conclusions
We developed a new algorithm for clustering orders called the
k
-o'means-EBC method.
This algorithm is far more efficient in computation and memory usage than
k
-o'means-
TMSE. Therefore, this new algorithm can be applied even if the number of objects
L
∗
is
large. In the experiments on artificial data, our
k
-o'means outperformed the traditional
hierarchical clustering. For artificial data, the prediction ability of
k
-o'means-TMSE
is almost equal to that of
k
-o'means-EBC. Therefore, by taking computational cost
into account, it could be concluded that the
k
-o'means-EBC method was superior to
the
k
-o'means-TMSE for clustering orders. Additionally, we advocated the method to
interpret the acquired ordinal clusters.
We plan to improve this method in the following ways. During clustering orders,
undesired merges of clusters more frequently occur than in clustering of real value vec-
tors. To overcome this defect, it is necessary to improve the initial clusters. For applying
ordinal clustering to DNA microarray data, the curse of dimensionality must be solved.
We want to develop a dimension reduction technique for orders like PCA. In the case
of an Euclidean space, there are many points far from one point. However, in a case
of a space of orders (a permutation group), the order most distant from one order is
unique, i.e., the reverse order. Therefore, there are biases for central orders to become
exact reversals of themselves. We also would like to lessen this bias.
Acknowledgments.
This work is supported by the grants-in-aid 14658106 and
16700157 of the Japan society for the promotion of science.
References
1. Luaces, O., Bayon, G.F., Quevedo, J.R., Dıez, J., del Coz, J.J., Bahamonde, A.: Analyzing
sensory data using non-linear preference learning with feature subset selection. In: Boulicaut,
J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol. 3201,
pp. 286-297. Springer, Heidelberg (2004)
2. Fujibuchi, W., Kiseleva, L., Horton, P.: Searching for similar gene expression profiles across
platforms. In: Proc. of the 16th Int'l Conf. on Genome Informatics, p. 143 (2005)
3. Everitt, B.S.: Cluster Analysis, 3rd edn. Edward Arnold (1993)
4. Marden, J.I.: Analyzing and Modeling Rank Data. Monographs on Statistics and Applied
Probability, vol. 64. Chapman & Hall, Boca Raton (1995)
