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A geometric approach to cluster validity for normal mixtures

A geometric approach to cluster validity for normal mixtures,10.1007/s005000050019,Soft Computing,James C. Bezdek,Wanqing Li,Yianni Attikiouzel,Michae

A geometric approach to cluster validity for normal mixtures   (Citations: 42)
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We study indices for choosing the correct number of components in a mixture of normal distributions. Previous studies have been confined to indices based wholly on probabilistic models. Viewing mixture decomposition as probabilistic clustering (where the emphasis is on partitioning for geometric substructure) as opposed to parametric estimation enables us to introduce both fuzzy and crisp measures of cluster validity for this problem. We presume the underlying samples to be unlabeled, and use the expectation-maximization (EM) algorithm to find clusters in the data. We test 16 probabilistic, 3 fuzzy and 4 crisp indices on 12 data sets that are samples from bivariate normal mixtures having either 3 or 6 components. Over three run averages based on different initializations of EM, 10 of the 23 indices tested for choosing the right number of mixture components were correct in at least 9 of the 12 trials. Among these were the fuzzy index of Xie-Beni, the crisp Davies-Bouldin index, and two crisp indices that are recent generalizations of Dunn’s index.
Journal: Soft Computing - SOCO , vol. 1, no. 4, pp. 166-179, 1997
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    • ...Another possibility is to create relational duals of nonpoint-prototype [7], [20]–[26] and hyperellipsoidal [72] clustering algorithms and cluster validity indices [73], [74]...

    Isaac J. Sledgeet al. Relational Generalizations of Cluster Validity Indices

    • ...5 As an alternative, we propose that relational duals of nonhyperspherical clustering algorithms, like the Gaussian mixture model [2], [26], c-varieties [27], [28], and c-quadratics [29], [30], be created, along with relational duals of indices suited for these types of clusters [31], [32]...
    • ...We explicitly recommend dual-relational indices, since the validity functions in [31] and [32] incorporate additional detailsintodistancecalculations,e.g.,covarianceinformation,thatcannot be modeled by relational generalizations...

    Isaac J. Sledgeet al. Relational Duals of Cluster-Validity Functions for the c Means Family

    • ...Index-based methods for cluster validity usually emphasize the intracluster compactness and intercluster separation and consider the effects of other factors such as the geometric or statistical properties of the data [17], [19], [23], [18], [29], [28], [30], [35]...
    • ...Comparative studies such as [15] and [29] provided experimental comparisons of many criteria such as AIC, MDL, and BYY for determining the number of clusters based on a Gaussian mixture model...

    Liang Wanget al. Automatically Determining the Number of Clusters in Unlabeled Data Set...

    • ...This possibility has been deeply explored in the literature, and different indices based on these and similar criteria have been proposed to validate clustering partitions and assess the number of components in clustering problems using mixture models [7,8,20]...

    Luis F. Lago-fernándezet al. Fuzzy Cluster Validation Using the Partition Negentropy Criterion

    • ...To compare the quality of the different cluster analyses the Dunn index has been found a useful instrument (Bezdek et al. 1997)...

    Peter Rittgen. Self-organization of interorganizational process design

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