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

More documents

Recommendations

Info

Figure 4.4: Plots of tMMDR directions for the coffee data. The shape of the observationsindicates their true cluster classification and the colour gives their tMMDR clusterallocation.4.2.2 Italian Wines DataForina et al. (1986) recorded twenty-eight chemical and physical properties for threetypes of Italian wines, namely Barolo, Grignolino and Barbera. For our analysis, weused a subset of 13 of these variables, as shown in Table 4.5. These data, comprising178 observations, are available through the R package gclus (Hurley, 2010).30
Table 4.5: Variable description for the wines data.VariableTypeRange of values1 (Barolo), 2 (Grignolino) or 3 (Barbera)Alcohol [11.03, 14.83]Malic acid [0.74, 5.8]Ash [1.36, 3.23]Alcalinity of ash [10.6, 30]Magnesium [70, 162]Total phenols [0.98, 3.88]Flavanoids [0.34, 5.08]Nonflavanoid phenols [0.13, 0.66]Proanthocyanins [0.41, 3.58]Color intensity [1.28, 13]Hue [0.48, 1.71]OD280/OD315 of diluted wines [1.27, 4]Proline [278, 1680]The known classification of the wine data by type has three groups: Barolo with 59observations, Grignolino with 71 observations and Barbera with 48 observations. Weran the GMMDR and tMMDR algorithms on the scaled version of the data using theMCLUST hierarchical agglomerative procedure for initialization. The results of themodel-based clustering are shown in Table 4.6.Table 4.6: Model-based clustering results for the wine data.Method Model Clusters (G) Degrees of freedom Features ARIGMMDR VEV 3 - 5 0.85tMMDR CUCC 3 57.8 4 0.9309The tMMDR method (ARI = 0.93) produces a better clustering than the GMMDRmethod (ARI = 0.85) on the wine data and uses less features in the process. The31
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: The known classification of the cof
Page 39 and 40: 4.2.3 Australian Crabs DataCampbell
Page 41 and 42: Figure 4.6: Plots of tMMDR directio
Page 43 and 44: those notes. The results may indica
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).

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

Create successful ePaper yourself

Delete template?

Save as template?