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• W77462712 abstract "The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copulafunctions with particular emphasis on microarray data. Copula functions are a popular multivariate modelingtool in each field where the multivariate dependence is of great interest and their use in clustering has notbeen still investigated.The first part of this work contains the review of the literature of clustering methods, copula functionsand microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong,1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007)clustering techniques because their performance is compared. Then, the probabilistic interpretation of theSklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe andXu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications ofclustering methods and copulas to the genetic and microarray experiments are highlighted.The second part contains the original contribution proposed. A simulation study is performed in order toevaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifyingclusters according to the dependence structure of the data generating process. Different simulations areperformed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) andthe value of the dependence parameter ) and the results are evaluated by means of different measures ofperformance.In light of the simulation results and of the limits of the two investigated clustering methods, a newclustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterativeprocedure of the CoClust and the description of the written R functions with their output are given. TheCoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, thedependence parameter value and the degree of overlap of margins) and is compared with the performanceof model–based clustering by using different measures of performance, like the percentage of well–identifiednumber of clusters and the not rejection percentage of H0 on .It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigatedclustering techniques and is able to identify clusters according to the dependence structure of the dataindependently of the degree of overlap of margins and the strength of the dependence. The CoClust usesa criterion based on the maximized log–likelihood function of the copula and can virtually account forany possible dependence relationship between observations. Many peculiar characteristics are shown for theCoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require astarting classification.Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both tothe gene expressions observed in three different cancer samples and to the columns (tumor samples) of thewhole data matrix." @default.
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• W77462712 date "2008-04-02" @default.
• W77462712 modified "2023-10-17" @default.
• W77462712 title "Analyzing the dependence structure of microarray data: a copula–based approach" @default.
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• W77462712 doi "https://doi.org/10.6092/unibo/amsdottorato/670" @default.
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