In this paper a new cluster validity index is introduced, which assesses the average compactness and separation of fuzzy partitions generated by the fuzzy c-means algorithm. To compare the performance of this new index with a number of known validation indices, the fuzzy partitioning of two data sets was carried out. Our validation performed favorably in all studies, even in those where other v...

Many real-world and man-made objects are symmetry, therefore, it is reasonable to assume that some kind of symmetry may exist in data clusters. In this paper a new cluster validity measure which adopts a non-metric distance measure based on the idea of “line symmetry” is presented. The proposed validity measure can be applied in finding the number of clusters of different geometrical structures...

This correspondence proposes parallel algorithms on SIMD machines for hierarchical clustering and cluster validity computation. The machine model uses a parallel memory system and an alignment network to facilitate parallel access of both pattern matrix and proximity matrix. For a problem with N patterns, the number of memory accesses is reduced from 0 ( N 3 ) on a sequential machine to 0 ( N 2...

Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions. The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni, and exten...

STUDY OBJECTIVES To examine the internal validity of a dietary pattern analysis and its ability to discriminate clusters of people with similar dietary patterns using independently assessed nutrient intakes and heart disease risk factors. DESIGN AND PARTICIPANTS Population based study characterising dietary patterns using cluster analysis applied to data from the semiquantitative Framingham f...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

This paper investigates validity analysis of alternative clustering results obtained using the algorithm named Multiobjective K-Means Genetic Algorithm (MOKGA). The reported results are promising. MOKGA gives the optimal number of clusters as a solution set. The achieved clustering results are then analyzed and validated under several cluster validity techniques proposed in the literature. The ...

To generalize from one experience to the next in a world where the underlying structures are ever-changing, people construct clusters that group their observations and enable information to be pooled within a cluster in an efficient and effective manner. Despite substantial computational work describing potential domain-general processes for how people construct these clusters, there has been l...

In the field of information retrieval, clustering algorithms are used to analyze large collections of documents with the objective to form groups of similar documents. Clustering a document collection is an ambiguous task: A clustering, i. e. a set of document groups, depends on the chosen clustering algorithm as well as on the algorithm’s parameter settings. To find the best among several clus...

Many validity measures have been proposed for evaluating clustering results. Most of these popular validity measures do not work well for clusters with different densities and/or sizes. They usually have a tendency of ignoring clusters with low densities. In this paper, we propose a new validity measure, which can deal with this situation. The performance evaluation of the validity measure comp...