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Advisor(s)
Abstract(s)
Cluster analysis for categorical data has been an active area of research. A well-known
problem in this area is the determination of the number of clusters, which is unknown
and must be inferred from the data.
In order to estimate the number of clusters, one often resorts to information criteria,
such as BIC (Bayesian information criterion), MML (minimum message length, proposed
by Wallace and Boulton, 1968), and ICL (integrated classification likelihood). In
this work, we adopt the approach developed by Figueiredo and Jain (2002) for clustering
continuous data. They use an MML criterion to select the number of clusters and a
variant of the EM algorithm to estimate the model parameters. This EM variant seamlessly
integrates model estimation and selection in a single algorithm. For clustering
categorical data, we assume a finite mixture of multinomial distributions and implement
a new EM algorithm, following a previous version (Silvestre et al., 2008).
Results obtained with synthetic datasets are encouraging. The main advantage of the
proposed approach, when compared to the above referred criteria, is the speed of execution,
which is especially relevant when dealing with large data sets.
Description
Keywords
Cluster analysis Model selection Categorical variables
Citation
Silvestre, Cláudia; Cardoso, Margarida; Figueiredo, Mário - Determining the Number of Clusters in Categorical Data. In CONFERENCE OF THE INTERNATIONAL FEDERATION OF CLASSICATION SOCIETIES - IFCS-2013, Tilburg, (Netherlands), 14-17 July 2013