Global optimization, Meta Clustering and consensus clustering for class prediction

Clustering of real-world data is often ill-posed. Because of noise and intrinsic ambiguity in data, optimization models attempting to maximize a fitness function can be misled by the assumption of uniqueness of the solution. In this work we present a methodology including classic and novel techniques to approach clustering in a systematic way, with two application examples to biological data sets. The methodology is based on a process that generates multiple clustering solutions (using global optimization), performs cluster analysis on such clusterings (i.e. meta clustering) and analyzes the obtained clusterings by the appropriate application of different consensus techniques. In order to validate the method, we seek for the solutions that best match the real class labels, exploiting only a random sample of them. Finally, we guess the class labels of the remaining patterns using cluster enrichment information and verify the percentage of correct assignments for each class. The optimization of clustering objective functions together with the use of partial labeling puts the described approach in between unsupervised and semi-supervised methods.