9.5 Kmeans Clustering
In this section, we explore clustering techniques. These are different from the PCA applied above as these are unsupervised learning algorithms. For the PCA, we told the algorithm that there are two groups in our outcome context. Here, we let the algorithm decide how many clusters there are.
9.5.1 Nb Clusters
We compute number of clusters via hierarchical clustering, after applying 500 Monte Carlo (“bootstrap”) samples. We specify 10 as our maximum number of clusters
dat1Clust <- dfPharPCA[-1]
set.seed(123)
gap_stat <- clusGap(dat1Clust, FUN = hcut, nstart = 20, K.max = 10, B = 500, spaceH0 = "scaledPCA")
print(gap_stat, method = "Tibs2001SEmax")## Clustering Gap statistic ["clusGap"] from call:
## clusGap(x = dat1Clust, FUNcluster = hcut, K.max = 10, B = 500, spaceH0 = "scaledPCA", nstart = 20)
## B=500 simulated reference sets, k = 1..10; spaceH0="scaledPCA"
## --> Number of clusters (method 'Tibs2001SEmax', SE.factor=1): 8
## logW E.logW gap SE.sim
## [1,] 8.407623 8.661800 0.2541775 0.010937959
## [2,] 8.131417 8.519075 0.3876578 0.013833464
## [3,] 7.961471 8.421735 0.4602642 0.011830234
## [4,] 7.843640 8.347227 0.5035878 0.012692611
## [5,] 7.722050 8.308187 0.5861367 0.011315080
## [6,] 7.634004 8.276993 0.6429896 0.010594202
## [7,] 7.588294 8.250448 0.6621539 0.010205889
## [8,] 7.533120 8.226987 0.6938672 0.009925265
## [9,] 7.503556 8.205583 0.7020276 0.009794064
## [10,] 7.467433 8.186055 0.7186212 0.009604244
The results in the plot above show that the optimal number of clusters is 10! This is not helpful at all; for the moment, this is for demonstration.
9.5.1.1 Computing clusters
Although optimal number of clusters is 10, we perform a kMeans clustering with 2, 3, 4, 5, 6, 7, 8, and 9 clusters. The aim is to evaluate how close (or far) our groups are, and whether the the two contexts cluster together.
We use the function hcut from the package factoextra. This will compute Hierarchical Clustering and Cut the Tree into k clusters. By default, it uses hc_method = “ward.D2”, hc_metric = “euclidean”. stand = TRUE allows for the data to be normalised (z-scored)
km.resdat1_2 <- hcut(dat1Clust, 2, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_3 <- hcut(dat1Clust, 3, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_4 <- hcut(dat1Clust, 4, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_5 <- hcut(dat1Clust, 5, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_6 <- hcut(dat1Clust, 6, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_7 <- hcut(dat1Clust, 7, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_8 <- hcut(dat1Clust, 8, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_9 <- hcut(dat1Clust, 9, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_10 <- hcut(dat1Clust, 10, hc_method = "ward.D2", stand = TRUE, graph = TRUE)
km.resdat1_2##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 402##
## Call:
## stats::hclust(d = x, method = hc_method)
##
## Cluster method : ward.D2
## Distance : euclidean
## Number of objects: 4029.5.1.2 Dendograms
fviz_dend(km.resdat1_2, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 2 clusters")
fviz_dend(km.resdat1_3, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 3 clusters")
fviz_dend(km.resdat1_4, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 4 clusters")
fviz_dend(km.resdat1_5, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 5 clusters")
fviz_dend(km.resdat1_6, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 6 clusters")
fviz_dend(km.resdat1_7, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 7 clusters")
fviz_dend(km.resdat1_8, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 8 clusters")
fviz_dend(km.resdat1_9, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 9 clusters")
fviz_dend(km.resdat1_10, show_labels = TRUE, rect = TRUE, repel = TRUE, main = "Cluster Dendrogram - 10 clusters")
9.5.1.3 Plots
fviz_cluster(km.resdat1_2, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 2 clusters")
fviz_cluster(km.resdat1_3, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 3 clusters")
fviz_cluster(km.resdat1_4, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 4 clusters")
fviz_cluster(km.resdat1_5, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 5 clusters")
fviz_cluster(km.resdat1_6, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 6 clusters")
fviz_cluster(km.resdat1_7, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 7 clusters")
fviz_cluster(km.resdat1_8, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 8 clusters")
fviz_cluster(km.resdat1_9, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 9 clusters")
fviz_cluster(km.resdat1_10, data = dat1Clust,
ellipse.type = "convex",
palette = "jco",
ggtheme = theme_minimal(),
show.clust.cent = TRUE,
main = "Cluster plot - 10 clusters")
9.5.1.4 Individual Clusters
## G_01 G_02 G_03 G_04 G_05 G_06 G_07 G_08 G_09 G_10 G_11
## 1 1 1 1 1 1 1 1 1 1 1
## G_12 G_13 G_14 G_15 G_16 G_17 G_18 G_19 G_20 G_21 G_22
## 1 1 1 1 1 1 1 1 1 1 1
## G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_32 G_33
## 1 1 1 1 1 1 1 1 1 1 1
## G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_41 G_42 G_43 G_44
## 1 1 1 1 1 1 1 1 1 1 1
## G_45 G_46 G_47 G_48 G_49 G_50 G_51 G_52 G_53 G_54 G_55
## 1 1 1 1 1 1 1 1 1 1 1
## G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63 G_64 G_65 G_66
## 1 1 1 1 1 1 1 1 1 1 1
## G_67 G_68 G_69 G_70 G_71 G_72 G_73 G_74 G_75 G_76 G_77
## 1 1 1 1 1 1 1 1 1 1 1
## G_78 G_79 G_80 G_81 G_82 G_83 G_84 G_85 G_86 G_87 G_88
## 1 1 1 1 1 1 1 1 1 1 1
## G_89 G_90 G_91 G_92 G_93 G_94 G_95 G_96 NG_01 NG_02 NG_03
## 1 1 1 1 1 1 1 1 1 1 1
## NG_04 NG_05 NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14
## 1 1 1 1 1 1 1 1 1 1 1
## NG_15 NG_16 NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25
## 1 1 1 1 1 1 1 1 1 1 1
## NG_26 NG_27 NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_34 NG_35 NG_36
## 1 1 1 1 1 1 1 1 1 1 1
## NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44 NG_45 NG_46 NG_47
## 1 1 1 1 1 1 1 1 1 1 1
## NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55 NG_56 NG_57 NG_58
## 1 1 1 1 1 1 1 1 1 1 1
## NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66 NG_67 NG_68 NG_69
## 1 1 1 1 1 1 1 1 1 1 1
## NG_70 NG_71 NG_72 NG_73 NG_74 NG_75 NG_76 NG_77 NG_78 NG_79 NG_80
## 1 1 1 1 1 1 1 1 1 1 1
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 1 1 1 1 1 1 1 1 1 1 1
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 1 1 1 1 1 1 1 1 1 1 1
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 1 1 1 1 1 1 1 1 1 1 1
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 1 2 2 2 2 2 2 2 2 2 2
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 2 2 2 2 2 2 2 2 2 2 2
## G_118 G_119 G_120 G_121 G_122 G_123 G_124 G_125 G_126 G_127 G_128
## 2 2 2 2 2 2 2 2 2 2 2
## G_129 G_130 G_131 G_132 G_133 G_134 G_135 G_136 G_137 G_138 G_139
## 2 2 2 2 2 2 2 2 2 2 2
## G_140 G_141 G_142 G_143 G_144 G_145 G_146 G_147 G_148 G_149 G_150
## 2 2 2 2 2 2 2 2 2 2 2
## G_151 G_152 G_153 G_154 G_155 G_156 G_157 G_158 G_159 G_160 G_161
## 2 2 2 2 2 2 2 2 2 2 2
## G_162 G_163 G_164 G_165 G_166 G_167 G_168 G_169 G_170 G_171 G_172
## 2 2 2 2 2 2 2 2 2 2 2
## G_173 G_174 G_175 G_176 G_177 G_178 G_179 G_180 NG_115 NG_116 NG_117
## 2 2 2 2 2 2 2 2 2 2 2
## NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127 NG_128
## 2 2 2 2 2 2 2 2 2 2 2
## NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138 NG_139
## 2 2 2 2 2 2 2 2 2 2 2
## NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149 NG_150
## 2 2 2 2 2 2 2 2 2 2 2
## NG_151 NG_152 NG_153 NG_154 NG_155 NG_156 NG_157 NG_158 NG_159 NG_160 NG_161
## 2 2 2 2 2 2 2 2 2 2 2
## NG_162 NG_163 NG_164 NG_165 NG_166 NG_167 NG_168 NG_169 NG_170 NG_171 NG_172
## 2 2 2 2 2 2 2 2 2 2 2
## NG_173 NG_174 NG_175 NG_176 NG_177 NG_178 NG_179 NG_180 NG_181 NG_182 NG_183
## 2 2 2 2 2 2 2 2 2 2 2
## NG_184 NG_185 NG_186 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 2 2 2 2 2 2 2 2 2 2 2
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 2 2 2 2 2 2 2 2 2 2 2
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 2 2 2 2 2 2 2 2 2 2 2
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 2 2 2 2 2 2## G_01 G_02 G_03 G_04 G_05 G_06 G_07 G_08 G_09 G_10 G_11
## 1 1 1 1 1 1 1 1 1 1 1
## G_12 G_13 G_14 G_15 G_16 G_17 G_18 G_19 G_20 G_21 G_22
## 1 1 1 1 1 1 1 1 1 1 1
## G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_32 G_33
## 1 1 1 1 1 1 1 1 1 1 1
## G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_41 G_42 G_43 G_44
## 1 1 1 1 1 1 1 1 1 1 1
## G_45 G_46 G_47 G_48 G_49 G_50 G_51 G_52 G_53 G_54 G_55
## 1 1 1 1 1 1 1 1 1 1 1
## G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63 G_64 G_65 G_66
## 1 1 1 1 1 1 1 1 1 1 1
## G_67 G_68 G_69 G_70 G_71 G_72 G_73 G_74 G_75 G_76 G_77
## 1 1 1 1 1 1 1 1 1 1 1
## G_78 G_79 G_80 G_81 G_82 G_83 G_84 G_85 G_86 G_87 G_88
## 1 1 1 1 1 1 1 1 1 1 1
## G_89 G_90 G_91 G_92 G_93 G_94 G_95 G_96 NG_01 NG_02 NG_03
## 1 1 1 1 1 1 1 1 1 1 1
## NG_04 NG_05 NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14
## 1 1 1 1 1 1 1 1 1 1 1
## NG_15 NG_16 NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25
## 1 1 1 1 1 1 1 1 1 1 1
## NG_26 NG_27 NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_34 NG_35 NG_36
## 1 1 1 1 1 1 1 1 1 1 1
## NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44 NG_45 NG_46 NG_47
## 1 1 1 1 1 1 1 1 1 1 1
## NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55 NG_56 NG_57 NG_58
## 1 1 1 1 1 1 1 1 1 1 1
## NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66 NG_67 NG_68 NG_69
## 1 1 1 1 1 1 1 1 1 1 1
## NG_70 NG_71 NG_72 NG_73 NG_74 NG_75 NG_76 NG_77 NG_78 NG_79 NG_80
## 1 1 1 1 1 1 1 1 1 1 1
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 1 1 1 1 1 1 1 1 1 1 1
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 1 1 1 1 1 1 1 1 1 1 1
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 1 1 1 1 1 1 1 1 1 1 1
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 1 2 2 2 2 2 2 2 2 2 2
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 2 2 2 2 2 2 2 2 2 2 2
## G_118 G_119 G_120 G_121 G_122 G_123 G_124 G_125 G_126 G_127 G_128
## 2 2 2 2 2 2 2 2 2 2 2
## G_129 G_130 G_131 G_132 G_133 G_134 G_135 G_136 G_137 G_138 G_139
## 2 2 2 2 2 2 2 2 2 2 2
## G_140 G_141 G_142 G_143 G_144 G_145 G_146 G_147 G_148 G_149 G_150
## 2 2 2 2 2 2 2 2 2 2 2
## G_151 G_152 G_153 NG_115 NG_116 NG_117 NG_118 NG_119 NG_120 NG_121 NG_122
## 2 2 2 2 2 2 2 2 2 2 2
## NG_123 NG_124 NG_125 NG_126 NG_127 NG_128 NG_129 NG_130 NG_131 NG_132 NG_133
## 2 2 2 2 2 2 2 2 2 2 2
## NG_134 NG_135 NG_136 NG_137 NG_138 NG_139 NG_140 NG_141 NG_142 NG_143 NG_144
## 2 2 2 2 2 2 2 2 2 2 2
## NG_145 NG_146 NG_147 NG_148 NG_149 NG_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 2 2 2 2 2 2 2 2 2 2 2
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 2 2 2 2 2 2 2 2 2 2 2
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 2 2 2 2 2 2 2 2 2 2 2
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 2 2 2 2 2 2 2 2 2 3 3
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 3 3 3 3 3 3 3 3 3 3 3
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 3 3 3 3 3 3 3 3 3 3 3
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 3 3 3 3 3 3 3 3 3 3 3
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 3 3 3 3 3 3 3 3 3 3 3
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 3 3 3 3 3 3 3 3 3 3 3
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 3 3 3 3 3 3## G_01 G_02 G_03 G_04 G_05 G_06 G_07 G_08 G_09 G_10 G_11
## 1 1 1 1 1 1 1 1 1 1 1
## G_12 G_13 G_14 G_15 G_16 G_17 G_18 G_19 G_20 G_21 G_22
## 1 1 1 1 1 1 1 1 1 1 1
## G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_32 G_33
## 1 1 1 1 1 1 1 1 1 1 1
## G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_41 G_42 G_43 G_44
## 1 1 1 1 1 1 1 1 1 1 1
## G_45 G_46 G_47 G_48 G_49 G_50 G_51 G_52 G_53 G_54 G_55
## 1 1 1 1 1 1 1 1 1 1 1
## G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63 G_64 G_65 G_66
## 1 1 1 1 1 1 1 1 1 1 1
## G_67 G_68 G_69 G_70 G_71 G_72 G_73 G_74 G_75 G_76 G_77
## 1 1 1 1 1 1 1 1 1 1 1
## G_78 G_79 G_80 G_81 G_82 G_83 G_84 G_85 G_86 G_87 G_88
## 1 1 1 1 1 1 1 1 1 1 1
## G_89 G_90 G_91 G_92 G_93 G_94 G_95 G_96 NG_01 NG_02 NG_03
## 1 1 1 1 1 1 1 1 1 1 1
## NG_04 NG_05 NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14
## 1 1 1 1 1 1 1 1 1 1 1
## NG_15 NG_16 NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25
## 1 1 1 1 1 1 1 1 1 1 1
## NG_26 NG_27 NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_34 NG_35 NG_36
## 1 1 1 1 1 1 1 1 1 1 1
## NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44 NG_45 NG_46 NG_47
## 1 1 1 1 1 1 1 1 1 1 1
## NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55 NG_56 NG_57 NG_58
## 1 1 1 1 1 1 1 1 1 1 1
## NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66 NG_67 NG_68 NG_69
## 1 1 1 1 1 1 1 1 1 1 1
## NG_70 NG_71 NG_72 NG_73 NG_74 NG_75 NG_76 NG_77 NG_78 NG_79 NG_80
## 1 1 1 1 1 1 1 1 1 1 1
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 1 1 1 1 1 1 1 1 1 1 1
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 1 1 1 1 1 1 1 1 1 1 1
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 1 1 1 1 1 1 1 1 1 1 1
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 1 2 2 2 2 2 2 2 2 2 2
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 2 2 2 2 2 2 2 2 2 2 2
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 2 2 2 2 2 2 2 2 2 2 2
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 2 2 2 2 2 2 2 2 2 2 2
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 2 2 2 2 2 2 2 2 2 2 2
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 2 2 2 2 2 2 2 2 2 2 2
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 2 3 3 3 3 3 3 3 3 3 3
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 3 3 3 3 3 3 3 3 3 3 3
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 3 3 3 3 3 3 3 3 3 3 3
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 3 3 3 3 3 3 3 3 3 3 3
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 3 3 3 3 3 3 3 3 3 3 3
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 3 3 3 3 3 3 3 3 3 4 4
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 4 4 4 4 4 4 4 4 4 4 4
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 4 4 4 4 4 4 4 4 4 4 4
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 4 4 4 4 4 4 4 4 4 4 4
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 4 4 4 4 4 4 4 4 4 4 4
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 4 4 4 4 4 4 4 4 4 4 4
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 4 4 4 4 4 4## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_67 G_68 G_69 G_70
## 1 1 1 1 1 1 1 1 1 1 1
## G_71 G_72 G_73 G_74 G_75 G_76 G_77 G_78 G_79 G_80 G_81
## 1 1 1 1 1 1 1 1 1 1 1
## G_82 G_83 G_84 G_85 G_86 G_87 G_88 G_89 G_90 G_91 G_92
## 1 1 1 1 1 1 1 1 1 1 1
## G_93 G_94 G_95 G_96 NG_76 NG_77 NG_78 NG_79 NG_80 NG_81 NG_82
## 1 1 1 1 1 1 1 1 1 1 1
## NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91 NG_92 NG_93
## 1 1 1 1 1 1 1 1 1 1 1
## NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102 NG_103 NG_104
## 1 1 1 1 1 1 1 1 1 1 1
## NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113 NG_114 G_03
## 1 1 1 1 1 1 1 1 1 1 2
## G_08 G_11 G_14 G_15 G_16 G_17 G_18 G_19 G_20 G_21 G_22
## 2 2 2 2 2 2 2 2 2 2 2
## G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_32 G_33
## 2 2 2 2 2 2 2 2 2 2 2
## G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_49 G_50 G_51 G_52
## 2 2 2 2 2 2 2 2 2 2 2
## G_53 G_54 G_55 G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63
## 2 2 2 2 2 2 2 2 2 2 2
## G_64 G_65 G_66 NG_01 NG_02 NG_03 NG_04 NG_05 NG_06 NG_07 NG_08
## 2 2 2 2 2 2 2 2 2 2 2
## NG_09 NG_10 NG_11 NG_12 NG_13 NG_14 NG_15 NG_16 NG_17 NG_18 NG_19
## 2 2 2 2 2 2 2 2 2 2 2
## NG_20 NG_21 NG_22 NG_23 NG_24 NG_25 NG_26 NG_27 NG_28 NG_29 NG_30
## 2 2 2 2 2 2 2 2 2 2 2
## NG_31 NG_32 NG_33 NG_34 NG_35 NG_36 NG_37 NG_38 NG_39 NG_40 NG_41
## 2 2 2 2 2 2 2 2 2 2 2
## NG_42 NG_43 NG_44 NG_45 NG_46 NG_47 NG_48 NG_49 NG_50 NG_51 NG_52
## 2 2 2 2 2 2 2 2 2 2 2
## NG_53 NG_54 NG_55 NG_56 NG_57 NG_58 NG_59 NG_60 NG_61 NG_62 NG_63
## 2 2 2 2 2 2 2 2 2 2 2
## NG_64 NG_65 NG_66 NG_67 NG_68 NG_69 NG_70 NG_71 NG_72 NG_73 NG_74
## 2 2 2 2 2 2 2 2 2 2 2
## NG_75 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 2 3 3 3 3 3 3 3 3 3 3
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 3 3 3 3 3 3 3 3 3 3 3
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 3 3 3 3 3 3 3 3 3 3 3
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 3 3 3 3 3 3 3 3 3 3 3
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 3 3 3 3 3 3 3 3 3 3 3
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 3 3 3 3 3 3 3 3 3 3 3
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 3 4 4 4 4 4 4 4 4 4 4
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 4 4 4 4 4 4 4 4 4 4 4
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 4 4 4 4 4 4 4 4 4 4 4
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 4 4 4 4 4 4 4 4 4 4 4
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 4 4 4 4 4 4 4 4 4 4 4
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 4 4 4 4 4 4 4 4 4 5 5
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 5 5 5 5 5 5 5 5 5 5 5
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 5 5 5 5 5 5 5 5 5 5 5
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 5 5 5 5 5 5 5 5 5 5 5
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 5 5 5 5 5 5 5 5 5 5 5
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 5 5 5 5 5 5 5 5 5 5 5
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 5 5 5 5 5 5## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_67 G_68 G_69 G_70
## 1 1 1 1 1 1 1 1 1 1 1
## G_71 G_73 G_76 G_77 G_78 G_79 G_80 G_81 G_91 G_92 G_93
## 1 1 1 1 1 1 1 1 1 1 1
## G_96 G_03 G_08 G_11 G_14 G_15 G_16 G_17 G_18 G_19 G_20
## 1 2 2 2 2 2 2 2 2 2 2
## G_21 G_22 G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31
## 2 2 2 2 2 2 2 2 2 2 2
## G_32 G_33 G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_49 G_50
## 2 2 2 2 2 2 2 2 2 2 2
## G_51 G_52 G_53 G_54 G_55 G_56 G_57 G_58 G_59 G_60 G_61
## 2 2 2 2 2 2 2 2 2 2 2
## G_62 G_63 G_64 G_65 G_66 NG_01 NG_02 NG_03 NG_04 NG_05 NG_06
## 2 2 2 2 2 2 2 2 2 2 2
## NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14 NG_15 NG_16 NG_17
## 2 2 2 2 2 2 2 2 2 2 2
## NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25 NG_26 NG_27 NG_28
## 2 2 2 2 2 2 2 2 2 2 2
## NG_29 NG_30 NG_31 NG_32 NG_33 NG_34 NG_35 NG_36 NG_37 NG_38 NG_39
## 2 2 2 2 2 2 2 2 2 2 2
## NG_40 NG_41 NG_42 NG_43 NG_44 NG_45 NG_46 NG_47 NG_48 NG_49 NG_50
## 2 2 2 2 2 2 2 2 2 2 2
## NG_51 NG_52 NG_53 NG_54 NG_55 NG_56 NG_57 NG_58 NG_59 NG_60 NG_61
## 2 2 2 2 2 2 2 2 2 2 2
## NG_62 NG_63 NG_64 NG_65 NG_66 NG_67 NG_68 NG_69 NG_70 NG_71 NG_72
## 2 2 2 2 2 2 2 2 2 2 2
## NG_73 NG_74 NG_75 G_72 G_74 G_75 G_82 G_83 G_84 G_85 G_86
## 2 2 2 3 3 3 3 3 3 3 3
## G_87 G_88 G_89 G_90 G_94 G_95 NG_76 NG_77 NG_78 NG_79 NG_80
## 3 3 3 3 3 3 3 3 3 3 3
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 3 3 3 3 3 3 3 3 3 3 3
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 3 3 3 3 3 3 3 3 3 3 3
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 3 3 3 3 3 3 3 3 3 3 3
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 3 4 4 4 4 4 4 4 4 4 4
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 4 4 4 4 4 4 4 4 4 4 4
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 4 4 4 4 4 4 4 4 4 4 4
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 4 4 4 4 4 4 4 4 4 4 4
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 4 4 4 4 4 4 4 4 4 4 4
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 4 4 4 4 4 4 4 4 4 4 4
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 4 5 5 5 5 5 5 5 5 5 5
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 5 5 5 5 5 5 5 5 5 5 5
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 5 5 5 5 5 5 5 5 5 5 5
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 5 5 5 5 5 5 5 5 5 5 5
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 5 5 5 5 5 5 5 5 5 5 5
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 5 5 5 5 5 5 5 5 5 6 6
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 6 6 6 6 6 6 6 6 6 6 6
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 6 6 6 6 6 6 6 6 6 6 6
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 6 6 6 6 6 6 6 6 6 6 6
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 6 6 6 6 6 6 6 6 6 6 6
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 6 6 6 6 6 6 6 6 6 6 6
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 6 6 6 6 6 6## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_67 G_68 G_69 G_70
## 1 1 1 1 1 1 1 1 1 1 1
## G_71 G_73 G_76 G_77 G_78 G_79 G_80 G_81 G_91 G_92 G_93
## 1 1 1 1 1 1 1 1 1 1 1
## G_96 G_03 G_08 G_11 G_14 G_15 G_16 G_17 G_18 G_19 G_20
## 1 2 2 2 2 2 2 2 2 2 2
## NG_01 NG_02 NG_03 NG_04 NG_05 NG_06 NG_07 NG_08 NG_09 NG_10 NG_11
## 2 2 2 2 2 2 2 2 2 2 2
## NG_12 NG_13 NG_14 NG_15 NG_16 NG_17 NG_18 NG_19 NG_20 NG_21 NG_22
## 2 2 2 2 2 2 2 2 2 2 2
## NG_23 NG_24 NG_25 NG_26 NG_27 NG_28 NG_29 NG_30 NG_31 NG_32 NG_33
## 2 2 2 2 2 2 2 2 2 2 2
## NG_70 NG_71 NG_72 G_21 G_22 G_23 G_24 G_25 G_26 G_27 G_28
## 2 2 2 3 3 3 3 3 3 3 3
## G_29 G_30 G_31 G_32 G_33 G_34 G_35 G_36 G_37 G_38 G_39
## 3 3 3 3 3 3 3 3 3 3 3
## G_40 G_49 G_50 G_51 G_52 G_53 G_54 G_55 G_56 G_57 G_58
## 3 3 3 3 3 3 3 3 3 3 3
## G_59 G_60 G_61 G_62 G_63 G_64 G_65 G_66 NG_34 NG_35 NG_36
## 3 3 3 3 3 3 3 3 3 3 3
## NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44 NG_45 NG_46 NG_47
## 3 3 3 3 3 3 3 3 3 3 3
## NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55 NG_56 NG_57 NG_58
## 3 3 3 3 3 3 3 3 3 3 3
## NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66 NG_67 NG_68 NG_69
## 3 3 3 3 3 3 3 3 3 3 3
## NG_73 NG_74 NG_75 G_72 G_74 G_75 G_82 G_83 G_84 G_85 G_86
## 3 3 3 4 4 4 4 4 4 4 4
## G_87 G_88 G_89 G_90 G_94 G_95 NG_76 NG_77 NG_78 NG_79 NG_80
## 4 4 4 4 4 4 4 4 4 4 4
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 4 4 4 4 4 4 4 4 4 4 4
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 4 4 4 4 4 4 4 4 4 4 4
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 4 4 4 4 4 4 4 4 4 4 4
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 4 5 5 5 5 5 5 5 5 5 5
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 5 5 5 5 5 5 5 5 5 5 5
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 5 5 5 5 5 5 5 5 5 5 5
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 5 5 5 5 5 5 5 5 5 5 5
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 5 5 5 5 5 5 5 5 5 5 5
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 5 5 5 5 5 5 5 5 5 5 5
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 5 6 6 6 6 6 6 6 6 6 6
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 6 6 6 6 6 6 6 6 6 6 6
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 6 6 6 6 6 6 6 6 6 6 6
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 6 6 6 6 6 6 6 6 6 6 6
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 6 6 6 6 6 6 6 6 6 6 6
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 6 6 6 6 6 6 6 6 6 7 7
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 7 7 7 7 7 7 7 7 7 7 7
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 7 7 7 7 7 7 7 7 7 7 7
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 7 7 7 7 7 7 7 7 7 7 7
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 7 7 7 7 7 7 7 7 7 7 7
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 7 7 7 7 7 7 7 7 7 7 7
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 7 7 7 7 7 7## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_03 G_08 G_11 G_14
## 1 1 1 1 1 1 1 2 2 2 2
## G_15 G_16 G_17 G_18 G_19 G_20 NG_01 NG_02 NG_03 NG_04 NG_05
## 2 2 2 2 2 2 2 2 2 2 2
## NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14 NG_15 NG_16
## 2 2 2 2 2 2 2 2 2 2 2
## NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25 NG_26 NG_27
## 2 2 2 2 2 2 2 2 2 2 2
## NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_70 NG_71 NG_72 G_21 G_22
## 2 2 2 2 2 2 2 2 2 3 3
## G_23 G_24 G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_32 G_33
## 3 3 3 3 3 3 3 3 3 3 3
## G_34 G_35 G_36 G_37 G_38 G_39 G_40 G_49 G_50 G_51 G_52
## 3 3 3 3 3 3 3 3 3 3 3
## G_53 G_54 G_55 G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63
## 3 3 3 3 3 3 3 3 3 3 3
## G_64 G_65 G_66 NG_34 NG_35 NG_36 NG_37 NG_38 NG_39 NG_40 NG_41
## 3 3 3 3 3 3 3 3 3 3 3
## NG_42 NG_43 NG_44 NG_45 NG_46 NG_47 NG_48 NG_49 NG_50 NG_51 NG_52
## 3 3 3 3 3 3 3 3 3 3 3
## NG_53 NG_54 NG_55 NG_56 NG_57 NG_58 NG_59 NG_60 NG_61 NG_62 NG_63
## 3 3 3 3 3 3 3 3 3 3 3
## NG_64 NG_65 NG_66 NG_67 NG_68 NG_69 NG_73 NG_74 NG_75 G_67 G_68
## 3 3 3 3 3 3 3 3 3 4 4
## G_69 G_70 G_71 G_73 G_76 G_77 G_78 G_79 G_80 G_81 G_91
## 4 4 4 4 4 4 4 4 4 4 4
## G_92 G_93 G_96 G_72 G_74 G_75 G_82 G_83 G_84 G_85 G_86
## 4 4 4 5 5 5 5 5 5 5 5
## G_87 G_88 G_89 G_90 G_94 G_95 NG_76 NG_77 NG_78 NG_79 NG_80
## 5 5 5 5 5 5 5 5 5 5 5
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 5 5 5 5 5 5 5 5 5 5 5
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 5 5 5 5 5 5 5 5 5 5 5
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 5 5 5 5 5 5 5 5 5 5 5
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 5 6 6 6 6 6 6 6 6 6 6
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 6 6 6 6 6 6 6 6 6 6 6
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 6 6 6 6 6 6 6 6 6 6 6
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 6 6 6 6 6 6 6 6 6 6 6
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 6 6 6 6 6 6 6 6 6 6 6
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 6 6 6 6 6 6 6 6 6 6 6
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 6 7 7 7 7 7 7 7 7 7 7
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 7 7 7 7 7 7 7 7 7 7 7
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 7 7 7 7 7 7 7 7 7 7 7
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 7 7 7 7 7 7 7 7 7 7 7
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 7 7 7 7 7 7 7 7 7 7 7
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 7 7 7 7 7 7 7 7 7 8 8
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 8 8 8 8 8 8 8 8 8 8 8
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 8 8 8 8 8 8 8 8 8 8 8
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 8 8 8 8 8 8 8 8 8 8 8
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 8 8 8 8 8 8 8 8 8 8 8
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 8 8 8 8 8 8 8 8 8 8 8
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 8 8 8 8 8 8## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_03 G_08 G_11 G_14
## 1 1 1 1 1 1 1 2 2 2 2
## G_15 G_16 G_17 G_18 G_19 G_20 NG_01 NG_02 NG_03 NG_04 NG_05
## 2 2 2 2 2 2 2 2 2 2 2
## NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14 NG_15 NG_16
## 2 2 2 2 2 2 2 2 2 2 2
## NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25 NG_26 NG_27
## 2 2 2 2 2 2 2 2 2 2 2
## NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_70 NG_71 NG_72 G_21 G_24
## 2 2 2 2 2 2 2 2 2 3 3
## G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_33 G_34 G_35 G_36
## 3 3 3 3 3 3 3 3 3 3 3
## G_37 G_38 G_39 G_40 G_51 G_52 G_53 G_54 G_64 G_65 G_66
## 3 3 3 3 3 3 3 3 3 3 3
## NG_34 NG_35 NG_36 NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44
## 3 3 3 3 3 3 3 3 3 3 3
## NG_45 NG_46 NG_47 NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55
## 3 3 3 3 3 3 3 3 3 3 3
## NG_56 NG_57 NG_58 NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66
## 3 3 3 3 3 3 3 3 3 3 3
## NG_67 NG_68 NG_69 NG_73 NG_74 NG_75 G_22 G_23 G_32 G_49 G_50
## 3 3 3 3 3 3 4 4 4 4 4
## G_55 G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63 G_67 G_68
## 4 4 4 4 4 4 4 4 4 5 5
## G_69 G_70 G_71 G_73 G_76 G_77 G_78 G_79 G_80 G_81 G_91
## 5 5 5 5 5 5 5 5 5 5 5
## G_92 G_93 G_96 G_72 G_74 G_75 G_82 G_83 G_84 G_85 G_86
## 5 5 5 6 6 6 6 6 6 6 6
## G_87 G_88 G_89 G_90 G_94 G_95 NG_76 NG_77 NG_78 NG_79 NG_80
## 6 6 6 6 6 6 6 6 6 6 6
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 6 6 6 6 6 6 6 6 6 6 6
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 6 6 6 6 6 6 6 6 6 6 6
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 6 6 6 6 6 6 6 6 6 6 6
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 6 7 7 7 7 7 7 7 7 7 7
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 7 7 7 7 7 7 7 7 7 7 7
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 7 7 7 7 7 7 7 7 7 7 7
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 7 7 7 7 7 7 7 7 7 7 7
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 7 7 7 7 7 7 7 7 7 7 7
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 7 7 7 7 7 7 7 7 7 7 7
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 7 8 8 8 8 8 8 8 8 8 8
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 8 8 8 8 8 8 8 8 8 8 8
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 8 8 8 8 8 8 8 8 8 8 8
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 8 8 8 8 8 8 8 8 8 8 8
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 8 8 8 8 8 8 8 8 8 8 8
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 8 8 8 8 8 8 8 8 8 9 9
## G_156 G_157 G_158 G_159 G_160 G_161 G_162 G_163 G_164 G_165 G_166
## 9 9 9 9 9 9 9 9 9 9 9
## G_167 G_168 G_169 G_170 G_171 G_172 G_173 G_174 G_175 G_176 G_177
## 9 9 9 9 9 9 9 9 9 9 9
## G_178 G_179 G_180 NG_187 NG_188 NG_189 NG_190 NG_191 NG_192 NG_193 NG_194
## 9 9 9 9 9 9 9 9 9 9 9
## NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202 NG_203 NG_204 NG_205
## 9 9 9 9 9 9 9 9 9 9 9
## NG_206 NG_207 NG_208 NG_209 NG_210 NG_211 NG_212 NG_213 NG_214 NG_215 NG_216
## 9 9 9 9 9 9 9 9 9 9 9
## NG_217 NG_218 NG_219 NG_220 NG_221 NG_222
## 9 9 9 9 9 9## G_01 G_02 G_04 G_05 G_06 G_07 G_09 G_10 G_12 G_13 G_41
## 1 1 1 1 1 1 1 1 1 1 1
## G_42 G_43 G_44 G_45 G_46 G_47 G_48 G_03 G_08 G_11 G_14
## 1 1 1 1 1 1 1 2 2 2 2
## G_15 G_16 G_17 G_18 G_19 G_20 NG_01 NG_02 NG_03 NG_04 NG_05
## 2 2 2 2 2 2 2 2 2 2 2
## NG_06 NG_07 NG_08 NG_09 NG_10 NG_11 NG_12 NG_13 NG_14 NG_15 NG_16
## 2 2 2 2 2 2 2 2 2 2 2
## NG_17 NG_18 NG_19 NG_20 NG_21 NG_22 NG_23 NG_24 NG_25 NG_26 NG_27
## 2 2 2 2 2 2 2 2 2 2 2
## NG_28 NG_29 NG_30 NG_31 NG_32 NG_33 NG_70 NG_71 NG_72 G_21 G_24
## 2 2 2 2 2 2 2 2 2 3 3
## G_25 G_26 G_27 G_28 G_29 G_30 G_31 G_33 G_34 G_35 G_36
## 3 3 3 3 3 3 3 3 3 3 3
## G_37 G_38 G_39 G_40 G_51 G_52 G_53 G_54 G_64 G_65 G_66
## 3 3 3 3 3 3 3 3 3 3 3
## NG_34 NG_35 NG_36 NG_37 NG_38 NG_39 NG_40 NG_41 NG_42 NG_43 NG_44
## 3 3 3 3 3 3 3 3 3 3 3
## NG_45 NG_46 NG_47 NG_48 NG_49 NG_50 NG_51 NG_52 NG_53 NG_54 NG_55
## 3 3 3 3 3 3 3 3 3 3 3
## NG_56 NG_57 NG_58 NG_59 NG_60 NG_61 NG_62 NG_63 NG_64 NG_65 NG_66
## 3 3 3 3 3 3 3 3 3 3 3
## NG_67 NG_68 NG_69 NG_73 NG_74 NG_75 G_22 G_23 G_32 G_49 G_50
## 3 3 3 3 3 3 4 4 4 4 4
## G_55 G_56 G_57 G_58 G_59 G_60 G_61 G_62 G_63 G_67 G_68
## 4 4 4 4 4 4 4 4 4 5 5
## G_69 G_70 G_71 G_73 G_76 G_77 G_78 G_79 G_80 G_81 G_91
## 5 5 5 5 5 5 5 5 5 5 5
## G_92 G_93 G_96 G_72 G_74 G_75 G_82 G_83 G_84 G_85 G_86
## 5 5 5 6 6 6 6 6 6 6 6
## G_87 G_88 G_89 G_90 G_94 G_95 NG_76 NG_77 NG_78 NG_79 NG_80
## 6 6 6 6 6 6 6 6 6 6 6
## NG_81 NG_82 NG_83 NG_84 NG_85 NG_86 NG_87 NG_88 NG_89 NG_90 NG_91
## 6 6 6 6 6 6 6 6 6 6 6
## NG_92 NG_93 NG_94 NG_95 NG_96 NG_97 NG_98 NG_99 NG_100 NG_101 NG_102
## 6 6 6 6 6 6 6 6 6 6 6
## NG_103 NG_104 NG_105 NG_106 NG_107 NG_108 NG_109 NG_110 NG_111 NG_112 NG_113
## 6 6 6 6 6 6 6 6 6 6 6
## NG_114 G_97 G_98 G_99 G_100 G_101 G_102 G_103 G_104 G_105 G_106
## 6 7 7 7 7 7 7 7 7 7 7
## G_107 G_108 G_109 G_110 G_111 G_112 G_113 G_114 G_115 G_116 G_117
## 7 7 7 7 7 7 7 7 7 7 7
## G_118 G_119 G_120 G_121 G_122 G_123 G_151 G_152 G_153 NG_115 NG_116
## 7 7 7 7 7 7 7 7 7 7 7
## NG_117 NG_118 NG_119 NG_120 NG_121 NG_122 NG_123 NG_124 NG_125 NG_126 NG_127
## 7 7 7 7 7 7 7 7 7 7 7
## NG_128 NG_129 NG_130 NG_131 NG_132 NG_133 NG_134 NG_135 NG_136 NG_137 NG_138
## 7 7 7 7 7 7 7 7 7 7 7
## NG_139 NG_140 NG_141 NG_142 NG_143 NG_144 NG_145 NG_146 NG_147 NG_148 NG_149
## 7 7 7 7 7 7 7 7 7 7 7
## NG_150 G_124 G_125 G_126 G_127 G_128 G_129 G_130 G_131 G_132 G_133
## 7 8 8 8 8 8 8 8 8 8 8
## G_134 G_135 G_136 G_137 G_138 G_139 G_140 G_141 G_142 G_143 G_144
## 8 8 8 8 8 8 8 8 8 8 8
## G_145 G_146 G_147 G_148 G_149 G_150 NG_151 NG_152 NG_153 NG_154 NG_155
## 8 8 8 8 8 8 8 8 8 8 8
## NG_156 NG_157 NG_158 NG_159 NG_160 NG_161 NG_162 NG_163 NG_164 NG_165 NG_166
## 8 8 8 8 8 8 8 8 8 8 8
## NG_167 NG_168 NG_169 NG_170 NG_171 NG_172 NG_173 NG_174 NG_175 NG_176 NG_177
## 8 8 8 8 8 8 8 8 8 8 8
## NG_178 NG_179 NG_180 NG_181 NG_182 NG_183 NG_184 NG_185 NG_186 G_154 G_155
## 8 8 8 8 8 8 8 8 8 9 9
## G_156 G_165 G_172 G_173 G_174 G_175 G_176 G_177 NG_187 NG_188 NG_189
## 9 9 9 9 9 9 9 9 9 9 9
## NG_190 NG_191 NG_192 NG_195 NG_196 NG_197 NG_198 NG_199 NG_200 NG_201 NG_202
## 9 9 9 9 9 9 9 9 9 9 9
## NG_203 NG_204 NG_205 NG_206 NG_207 NG_208 NG_209 NG_210 NG_215 NG_216 NG_218
## 9 9 9 9 9 9 9 9 9 9 9
## NG_219 NG_220 NG_221 NG_222 G_157 G_158 G_159 G_160 G_161 G_162 G_163
## 9 9 9 9 10 10 10 10 10 10 10
## G_164 G_166 G_167 G_168 G_169 G_170 G_171 G_178 G_179 G_180 NG_193
## 10 10 10 10 10 10 10 10 10 10 10
## NG_194 NG_211 NG_212 NG_213 NG_214 NG_217
## 10 10 10 10 10 109.5.2 Conclusion
Cluster analysis is useful in many cases as it provides insights into how the various predictors interact with each other to allow for clusters to emerge. Given that these are independent of the actual groupings of your dependent variable (context), one can use them to interpret the results in a more in-depth way and allow you to be critical about the original grouping. Do not forget that the two guttural and non-guttural are composed each of three contexts (guttural = uvula, pharyngealised and pharyngeal; non-guttural = plain coronal, velar and glottal). Each of the contexts is produced in an /i: a: u:/ contexts. Hence, cluster analysis, which was restricted to a maximum of 10 clusters, picked this up.