Dimension Reduction for Model-based Clustering via Mixtures of ...

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Table 4.11: Variable description for the banknotes data.VariableStatusRange of values0 (genuine) or 1 (counterfeit)Length [213.8, 216.3]Left [129, 131]Right [129, 131.1]Bottom [7.2, 12.7]Top [7.7, 12.3]Diagonal [137.8, 142.4]Table 4.12: Model-based clustering results for the banknotes data.Method Model Clusters (G) Degrees of freedom Features ARIGMMDR EEI 4 - 3 0.6739tMMDR CICU 3 {13, 10.1, 63.6} 6 0.8603The tMMDR method (ARI = 0.86) produces a better clustering than the GMMDRmethod (ARI = 0.67) on the banknotes data, although neither is able to classify correctlythe data into its two known clusters. The resulting classification is presented inTable 4.13.Table 4.13: A classification table for the best tMMDR model fitted to the banknotesdata.ClusterStatus 1 21 99 02 1 153 0 85While we expect genuine bank notes to present as one identifiable cluster, counterfeitnotes may well appear in two clusters depending on the number of different sources of36
those notes. The results may indicate that there were two different kinds of counterfeitnotes.Figure 4.7 illustrates a scatterplot of the tMMDR directions corresponding to thethree clusters found by the procedure. The separation between the types of banknote ismost clear in the plots of direction one against directions two and three, as they do notoverlap.Figure 4.7: Plots of tMMDR directions for the banknotes data. The shape of theobservations indicates their true cluster classification and the colour gives their tMMDRcluster allocation.4.2.5 Diabetes DataReaven and Miller (1979) examined the relationship between measures of blood plasmaglucose and insulin in order to classify people as normal, overt diabetic or chemicaldiabetic. This data set consists of observations from 145 adult patients at the StanfordClinical Research Centre, as described in Table 4.14, and is available through the Rpackage locfit (Loader, 2012).37
Page 1: Dimension Reduction for Model-based
Page 5 and 6: List of Tables2.1 Nomenclature for
Page 7: Chapter 1IntroductionClustering alg
Page 10 and 11: 2.1 Gaussian Mixture ModelsFrom McL
Page 12 and 13: • λ g is a scalar which specifie
Page 14 and 15: In the M-step of the algorithm, the
Page 16 and 17: simple example. McLachlan and Peel
Page 18: For the tEIGEN models, parameter es
Page 21 and 22: onto the reduced subspace and their
Page 23 and 24: to the others. Specifically, we nee
Page 25 and 26: Definition 3.2 The tMMDR variables,
Page 27 and 28: • the forward step evaluates the
Page 29 and 30: Chapter 4ApplicationsWe now focus o
Page 31 and 32: Figure 4.2: Pairs plot for the thre
Page 33 and 34: Table 4.1: Average ARI (with standa
Page 35 and 36: The known classification of the cof
Page 37 and 38: Table 4.5: Variable description for
Page 39 and 40: 4.2.3 Australian Crabs DataCampbell
Page 41: Figure 4.6: Plots of tMMDR directio
Page 45 and 46: Table 4.16: A classification table
Page 47 and 48: Chapter 5ConclusionThis thesis intr
Page 49 and 50: Forina, M., C. Armanino, M. Castino
Page 51: Meng, X. L. and D. B. Rubin (1993).

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