A clustering procedure

In this paper we propose a procedure to obtain an optimal clustering solution for a given set of data. The main idea that runs through this thesis is the clustering of a data set with the consideration of multiple clustering solutions. This is achieved through first finding multiple clustering solutions through the k-means and/or spectral clustering algorithm. With the clustering solutions a cluster ensemble is formed. In order to avoid losing sight of the original data matrix, a hybrid bipartite graph formulation is applied to the ensemble. To obtain a clustering solution from the resulting bipartite graph we may consider a linear deterministic programming algorithm and/or the PivotBiCluster algorithm. Upon the selection of the PivotBiCluster algorithm we are finally able to obtain what can be considered an optimal clustering solution.The example carried throughout the thesis illustrates the process used. The example shows that the procedure can be used to obtain a clustering solution that has a cost closely related to the true clustering solution. Furthermore, an example that classifies wheat seeds, presented in Chapter 5, exposes the procedures dependence on the clustering solutions within the ensemble. Although k-means outperforms the procedure in terms of the cost of the clustering solution, the procedure theoretically holds for multiple values of k and can consider solutions from different algorithms that may expose different structures within the data set, which can potentially give a better clustering in terms of the data set