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IPS273 Tomoki Tokuda et al.

board’ where both objects and features are exclusively partitioned (Fig.1A;
features are partitioned based on their distribution patterns). Yet, the co-
clustering method (as well as conventional clustering methods) does not
always work well for real data, because real data may have different ‘views’
that characterize multiple clustering structures (Fig. 1B; Muller et al., 2012; Niu
et al., 2010).
To find the underlying multiple clustering structures, however,
determination of the number of views is not straightforward. A promising
approach is based on nonparametric mixture models assuming multivariate
Gaussian mixtures for each view proposed by Guan (2010). In this approach,
the full Gaussian model for covariance matrices is considered, and the
numbers of views and of object clusters are inferred in a data-driven way via
the Dirichlet process. Such a method is quite useful to discover possible
multiple cluster structures by screening out irrelevant features, when these
numbers are not known in advance. However, this method suffers from the
drawback that features need to belong to the same distribution family, which
severely limits its application, because real data often include both numerical
and categorical features. Further, its application is rather limited to low
dimensional cases (p < n), because in high-dimensional cases, sample size to
infer the full covariance matrix of Gaussian distribution may be insufficient,
resulting in overfitting.

Figure 1. Illustration of clustering structures. In each panel, the horizontal axis denotes
feature index, while the vertical axis subject index. Subjects and features are sorted in
the order of their cluster memberships. Dashed lines denote boundaries between
subject clusters or between feature clusters. Note that in Panels (B) and (C), subjects
members in view 1 and view 2 are the same, but they are differently sorted following
their cluster memberships in each view.

To address the aforementioned problems, we consider a multiple
clustering framework in which we can make the best use of co-clustering
structure that is not prone to overfitting. We propose a novel multiple
clustering method (referred to hereafter as the multiple co-clustering method)

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