Simultaneous Method of Orthogonal Non-metric Non-negative Matrix Factorization and Constrained Non-hierarchical Clustering

For multivariate categorical data, it is important to detect both clustering structures and low dimensions such that clusters are discriminated. This is because it is easy to interpret the features of clusters through the estimated low dimensions. It is sure that these existing methods for dimensional reduction clustering are useful to achieve such purpose; however, the interpretation sometimes becomes complicated due to the sign of the estimated parameters. Thus, we propose new dimensional reduction clustering with non-negativity constraints for all parameters. The proposed method has several advantages. First, when the features of clusters are interpreted, it is easier to interpret the clusters since effects of sign should not be considered. In addition, from the non-negativity and orthogonality constraints, the estimated components become perfect simple structure, which is interpretable descriptions. Second, we showed that the clustering results are not inferior to these existing methods through the simulations, although the constraints for the proposed method are strong.