Clustering in Relational Data and Ontologies

This dissertation studies the problem of clustering objects represented by relational data. This is a pertinent problem as many real-world data sets can only be represented by relational data for which object-based clustering algorithms are not designed. Relational data are encountered in many fields including biology, management, industrial engineering, and social sciences. Unlike numerical object data, which are represented by a set of feature values (e.g. height, weight, shoe size) of an object, relational object data are the numerical values of (dis)similarity between objects. For this reason, conventional cluster analysis methods such as k-means and fuzzy c-means cannot be used directly with relational data. I focus on three main problems of cluster analysis of relational data: (i) tendency prior to clustering—how many clusters are there?; (ii) partitioning of objects—which objects belong to which cluster?; and (iii) validity of the resultant clusters—are the partitions “good”? Analyses are included in this dissertation that prove that the Visual Assessment of cluster Tendency (VAT) algorithm has a direct relation to single-linkage hierarchical clustering and Dunn’s cluster validity index. These analyses are important to the development of two novel clustering algorithms, CLODD-CLustering in Ordered Dissimilarity Data and ReSL-Rectangular SingleLinkage clustering. Also presented in my analysis of VAT is a recursive formulation of the improved VAT (iVAT) algorithm. iVAT is shown to improve the visual evidence of cluster tendency on some types of data for which VAT fails. The computational complexity of my recursive formulation of iVAT is O(n), as opposed to O(n) of the original formulation—n is the number of objects considered. CLODD is a clustering algorithm that works on reordered dissimilarity data. Typically, the dissimilarity matrix is reordered with the VAT algorithm; although, I