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In short, clustering is the process of partitioning a given set of objects into groups containing highly related instances. This relation is determined by a specific distance metric with which the intra-cluster similarity is estimated. Finding an optimal number of such partitions is usually the key step in the entire process, yet a rather difficult one. Selecting an unsuitable number of clusters might lead to incorrect conclusions and, consequently, to wrong decisions: the term "optimal" is quite ambiguous. Furthermore, various inherent characteristics of the datasets, such as clusters that overlap or clusters containing subclusters, will most often increase the level of difficulty of the task. Thus, the methods used to detect similarities and the parameter selection of the partition algorithm have a major impact on the quality of the groups and the identification of their optimal number. Given that each dataset constitutes a rather distinct case, validity indices are indicators introduced to address the problem of selecting such an optimal number of clusters. In this work, an extensive set of well-known validity indices, based on the approach of the so-called relative criteria, are examined comparatively. A total of 26 cluster validation measures were investigated in two distinct case studies: one in real-world and one in artificially generated data. To ensure a certain degree of difficulty, both real-world and generated data were selected to exhibit variations and inhomogeneity. Each of the indices is being deployed under the schemes of 9 different clustering methods, which incorporate 5 different distance metrics. All results are presented in various explanatory forms. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of extracting fundamental learning style stereotypes through the exploitation of the biologically-inspired pattern recognition paradigm of Artificial Immune Systems (AIS). We present an unsupervised computational mechanism which exhibits the ability to reveal the inherent group structure of learning patterns that pervade a given set of educational profiles. We rely on the construction of an Artificial Immune Network (AIN) of learning style exemplars by proposing a correlation-based distance metric. This choice is actually imposed by the categoric nature of the underlying data. Our work utilizes an original dataset which was derived during the conduction of an extended empirical study involving students of the Hellenic Open University. The educational profiles of the students were built by collecting their answers on a thoroughly designed questionnaire taking into account a wide range of personal characteristics and skills. The efficiency of the proposed approach was assessed in terms of cluster compactness. Specifically, we measured the average correlation deviation of the students' education profiles from the corresponding artificial memory antibodies that represent the acquired learning style stereotypes. Finally, the unsupervised learning procedure adopted in this paper was tested against a correlation-based version of the k-means algorithm indicating a significant improvement in performance for the AIS-based clustering approach. [ABSTRACT FROM AUTHOR]