Application of nonsmooth optimisation to data analysis

The research presented in this thesis is two-fold: on the one hand, major data mining problems are reformulated as mathematical programming problems. These problems should be carefully designed, since from their formulation depends the efficiency, perhaps the existence, of the solvers. On the other hand, optimisation methods are adapted to solve these problems, most of which are nonsmooth and nonconvex. This part is delicate, as the solution is often required to be good and obtained fast. Numerical experiments on real-world datasets are presented and analysed.Doctor of Philosoph

Classes and clusters in data analysis

We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. (c) 2005 Elsevier B.V. All rights reserved.C

Abstract Classes and clusters in data analysis

We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. Key words: data mining, dataset with classes, point-based clustering, optimization clustering model, comparison of classes and clusters.