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Abstract:
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Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. In general, it is not possible to use statistical inferences or select the appropriateness of a model via information criteria with these techniques because there is no underlying probability model. Additionally, the use of ordinal data is very common (e.g. Likert or Braun-Blanquet scale). Recent research has developed a set of likelihood-based finite mixture models for a data matrix of ordinal data (Fernández et al., 2016). This approach applies fuzzy clustering via finite mixtures to the stereotype model. Fuzzy allocation of rows, columns and rows, and columns simultaneously to corresponding clusters is obtained by performing a Reversible-Jump MCMC sampler. Examples with ordinal data sets will be shown to illustrate the application of this approach. Finally, different visualisation tools for depicting the fuzziness of the clustering results for ordinal data will be demonstrated.
Fernandez, D., Arnold, R. and Pledger, S. (2016). Mixture-based clustering for the ordered stereotype
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