Projet The multi-feature digit dataset Pixel
STA211 - 2019/2020
L.RANT
04 juillet, 2020
1 Introduction
Ce jeu de données est constitué de caractéristiques de chiffres manuscrits (0'--9’) extrait d’une collection de cartes d’utilité publique néerlandaises. Les modèles ont été numérisés en images binaire. Ces chiffres sont représentés par les six des ensembles de fonctionnalités suivantes :
- mfeat-fou: 76 Fourier coefficients of the character shapes;
- mfeat-fac: 216 profile correlations;
- mfeat-kar: 64 Karhunen-Love coefficients;
- mfeat-pix: 240 pixel averages in 2 x 3 windows;
- mfeat-zer: 47 Zernike moments;
- mfeat-mor: 6 morphological features.
Nous n’avons pas de valeurs manquantes. La problématique: en analysant les 6 groupes séparement on gardera dans chaque groupe les variables qui influence le plus le choix des classes et cherchera le meilleur algorithme qui peut predire les classes.
2 Importation des données
## Warning: package 'factoextra' was built under R version 3.6.3## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 3.6.3## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa## Warning: package 'data.table' was built under R version 3.6.3## class pix_1 pix_2 pix_3 pix_4 pix_5 pix_6 pix_7 pix_8 pix_9 pix_10 pix_11
## 1 0 0 3 4 4 4 4 4 4 4 4 4
## 2 0 0 0 3 6 6 6 6 6 6 5 4
## 3 0 0 0 0 2 5 5 4 6 4 4 1
## 4 0 0 0 0 0 0 0 0 0 1 3 5
## 5 0 0 5 6 6 6 6 6 6 6 5 2
## 6 0 0 0 0 0 1 3 4 4 4 3 2
## 7 0 0 0 0 1 5 6 6 6 6 5 3
## 8 0 0 5 6 6 6 6 6 6 6 6 4
## 9 0 0 3 4 6 6 5 2 0 0 0 0
## 10 0 0 3 6 6 6 6 6 6 5 1 0
## pix_12 pix_13 pix_14 pix_15 pix_16 pix_17 pix_18 pix_19 pix_20 pix_21 pix_22
## 1 1 0 0 0 0 6 6 6 6 6 4
## 2 3 0 0 0 0 3 6 6 6 6 6
## 3 0 0 0 0 0 1 5 6 6 6 6
## 4 6 4 4 1 0 0 0 0 1 5 6
## 5 0 0 0 0 3 6 6 6 6 5 4
## 6 4 1 0 0 0 0 0 3 6 3 0
## 7 1 0 0 0 0 1 4 6 6 6 6
## 8 1 0 0 0 4 6 6 6 6 6 6
## 9 0 0 0 0 5 6 6 6 6 6 6
## 10 0 0 0 0 0 6 6 6 6 6 6
## pix_23 pix_24 pix_25 pix_26 pix_27 pix_28 pix_29 pix_30 pix_31 pix_32 pix_33
## 1 6 6 6 6 4 0 0 0 0 6 6
## 2 6 6 6 6 6 1 0 0 2 6 6
## 3 6 6 6 3 0 0 0 0 1 6 6
## 4 6 6 6 6 6 6 6 5 0 0 0
## 5 5 6 6 6 5 3 0 0 3 6 6
## 6 0 3 6 6 6 6 1 0 0 0 3
## 7 6 6 6 6 6 2 0 0 0 6 6
## 8 6 6 6 6 4 0 0 0 5 6 6
## 9 6 3 0 0 0 0 0 0 6 6 6
## 10 6 6 5 1 0 0 0 0 0 6 6
## pix_34 pix_35 pix_36 pix_37 pix_38 pix_39 pix_40 pix_41 pix_42 pix_43 pix_44
## 1 6 6 1 0 1 5 6 6 6 2 0
## 2 6 6 4 2 2 2 5 6 6 5 1
## 3 6 6 6 6 6 6 6 6 1 0 0
## 4 0 5 6 6 3 0 0 0 4 6 6
## 5 6 4 0 0 0 2 5 6 6 6 4
## 6 6 6 0 0 0 0 2 6 6 6 3
## 7 6 6 5 2 2 4 6 6 6 3 0
## 8 6 6 1 0 0 1 6 6 6 5 0
## 9 6 4 5 6 6 6 4 0 0 0 0
## 10 6 6 5 3 6 6 6 6 0 0 0
## pix_45 pix_46 pix_47 pix_48 pix_49 pix_50 pix_51 pix_52 pix_53 pix_54 pix_55
## 1 0 0 3 6 6 6 0 0 0 0 5
## 2 0 4 6 6 6 1 0 0 0 0 3
## 3 0 3 6 6 6 6 3 3 6 6 6
## 4 3 0 0 0 4 6 6 3 0 0 0
## 5 0 2 6 6 6 3 0 0 0 0 0
## 6 0 0 5 6 6 6 0 0 0 0 0
## 7 0 0 6 6 6 4 0 0 0 0 3
## 8 0 3 6 6 6 6 0 0 0 0 6
## 9 0 6 6 6 3 0 0 3 6 6 6
## 10 0 2 6 6 6 5 1 0 3 6 6
## pix_56 pix_57 pix_58 pix_59 pix_60 pix_61 pix_62 pix_63 pix_64 pix_65 pix_66
## 1 6 6 5 0 0 0 3 6 6 6 0
## 2 6 6 6 2 0 6 6 6 6 5 1
## 3 6 5 1 0 0 4 6 6 6 3 0
## 4 0 3 6 6 6 0 0 0 6 6 6
## 5 5 6 6 6 0 0 3 6 6 3 0
## 6 6 6 6 4 0 0 4 6 6 6 0
## 7 6 6 6 3 0 0 6 6 6 6 2
## 8 6 6 6 1 0 5 6 6 5 1 0
## 9 6 2 0 0 0 6 6 6 5 0 0
## 10 6 4 0 0 0 6 6 6 6 0 0
## pix_67 pix_68 pix_69 pix_70 pix_71 pix_72 pix_73 pix_74 pix_75 pix_76 pix_77
## 1 0 0 0 1 6 6 6 0 0 0 3
## 2 0 0 0 1 5 6 6 2 0 3 6
## 3 0 5 6 6 6 6 6 0 0 5 6
## 4 0 0 0 0 0 3 6 6 4 0 0
## 5 0 0 0 0 2 6 6 6 1 0 5
## 6 0 0 0 0 3 6 6 5 0 1 6
## 7 0 0 0 3 6 6 6 6 0 0 6
## 8 0 0 0 5 6 6 6 3 0 3 6
## 9 0 2 6 6 6 4 0 0 0 2 6
## 10 0 2 6 6 6 6 0 0 0 5 6
## pix_78 pix_79 pix_80 pix_81 pix_82 pix_83 pix_84 pix_85 pix_86 pix_87 pix_88
## 1 6 6 6 0 0 0 0 2 6 6 6
## 2 6 6 6 3 0 0 0 0 5 6 6
## 3 6 6 3 0 0 1 6 6 6 6 6
## 4 0 6 6 6 0 0 0 0 0 3 6
## 5 6 6 3 0 0 0 0 0 0 6 6
## 6 6 6 5 0 0 0 0 2 6 6 6
## 7 6 6 6 3 0 0 1 5 6 6 6
## 8 6 4 0 0 0 0 0 1 6 6 6
## 9 6 6 0 0 0 0 2 6 6 6 3
## 10 6 6 0 0 0 0 4 6 6 6 1
## pix_89 pix_90 pix_91 pix_92 pix_93 pix_94 pix_95 pix_96 pix_97 pix_98 pix_99
## 1 0 0 0 6 6 6 6 0 0 0 0
## 2 6 2 4 6 6 6 3 0 0 0 0
## 3 0 0 1 6 6 6 5 0 0 0 6
## 4 6 3 0 1 5 6 6 2 0 0 0
## 5 6 3 0 6 6 6 3 0 0 0 0
## 6 3 0 3 6 6 6 4 0 0 0 0
## 7 6 0 1 6 6 6 3 0 0 0 1
## 8 4 0 4 6 6 6 3 0 0 0 0
## 9 0 0 0 6 6 6 0 0 0 0 0
## 10 0 0 1 6 6 6 0 0 0 0 1
## pix_100 pix_101 pix_102 pix_103 pix_104 pix_105 pix_106 pix_107 pix_108
## 1 2 6 6 6 0 0 0 3 6
## 2 0 3 6 6 6 2 6 6 6
## 3 6 6 6 6 2 0 0 6 6
## 4 0 0 3 6 6 3 0 1 6
## 5 0 0 6 6 6 5 0 6 6
## 6 1 6 6 6 3 0 3 6 6
## 7 5 6 6 6 1 0 2 6 6
## 8 0 6 6 6 6 3 5 6 6
## 9 4 6 6 6 0 0 0 4 6
## 10 6 6 6 5 0 0 2 6 6
## pix_109 pix_110 pix_111 pix_112 pix_113 pix_114 pix_115 pix_116 pix_117
## 1 6 3 0 0 0 0 0 6 6
## 2 6 0 0 0 0 0 0 0 6
## 3 6 6 2 0 0 5 6 6 6
## 4 6 6 0 0 0 0 0 1 6
## 5 6 6 1 0 0 0 0 0 5
## 6 6 5 0 0 0 0 0 6 6
## 7 6 1 0 0 0 0 4 6 6
## 8 6 0 0 0 0 0 0 6 6
## 9 6 3 0 0 0 0 3 6 6
## 10 6 0 0 0 0 0 3 6 6
## pix_118 pix_119 pix_120 pix_121 pix_122 pix_123 pix_124 pix_125 pix_126
## 1 6 3 0 0 3 6 6 0 0
## 2 6 6 2 6 6 6 6 0 0
## 3 6 6 0 0 6 6 6 4 0
## 4 6 5 0 0 1 6 6 3 0
## 5 6 6 6 0 5 6 6 6 3
## 6 6 6 1 3 6 6 6 1 0
## 7 6 5 0 1 6 6 6 6 2
## 8 6 6 1 3 6 6 6 5 0
## 9 6 0 0 0 0 6 6 6 3
## 10 6 0 0 6 6 6 6 0 0
## pix_127 pix_128 pix_129 pix_130 pix_131 pix_132 pix_133 pix_134 pix_135
## 1 0 0 0 0 6 6 6 3 0
## 2 0 0 0 0 0 6 6 6 3
## 3 0 0 1 6 6 6 6 6 0
## 4 0 0 0 0 3 6 6 3 0
## 5 0 0 0 0 0 5 6 6 6
## 6 0 0 0 0 6 6 6 6 3
## 7 0 0 2 6 6 6 6 6 1
## 8 0 0 0 0 6 6 6 6 2
## 9 0 0 0 0 4 6 6 3 0
## 10 0 0 0 3 6 6 6 0 0
## pix_136 pix_137 pix_138 pix_139 pix_140 pix_141 pix_142 pix_143 pix_144
## 1 0 3 6 6 3 0 0 0 0
## 2 6 6 6 6 0 0 0 0 0
## 3 3 6 6 6 6 1 0 0 1
## 4 0 3 6 6 2 0 0 0 0
## 5 0 3 6 6 6 5 0 0 0
## 6 3 6 6 6 6 0 0 0 0
## 7 5 6 6 6 5 1 0 0 0
## 8 3 6 6 6 6 0 0 0 0
## 9 0 0 5 6 6 4 0 0 0
## 10 2 6 6 6 0 0 0 0 0
## pix_145 pix_146 pix_147 pix_148 pix_149 pix_150 pix_151 pix_152 pix_153
## 1 0 6 6 6 3 0 0 3 6
## 2 0 3 6 6 6 0 6 6 6
## 3 5 6 6 6 6 1 0 5 6
## 4 0 3 6 6 0 0 0 3 6
## 5 0 0 4 6 6 6 0 3 6
## 6 0 6 6 6 6 3 3 6 6
## 7 3 6 6 6 6 3 6 6 6
## 8 0 6 6 6 6 5 1 6 6
## 9 0 5 6 6 3 0 0 0 1
## 10 3 6 6 6 4 0 0 6 6
## pix_154 pix_155 pix_156 pix_157 pix_158 pix_159 pix_160 pix_161 pix_162
## 1 6 6 0 0 0 0 0 6 6
## 2 6 0 0 0 0 0 3 6 6
## 3 6 6 5 1 0 0 3 6 6
## 4 4 0 0 0 0 0 2 6 6
## 5 6 6 4 0 0 0 0 0 3
## 6 6 6 0 0 0 0 0 6 6
## 7 6 5 1 0 0 0 3 6 6
## 8 6 6 1 0 0 0 2 6 6
## 9 6 6 6 2 0 0 0 0 6
## 10 6 0 0 0 0 0 3 6 6
## pix_163 pix_164 pix_165 pix_166 pix_167 pix_168 pix_169 pix_170 pix_171
## 1 6 4 0 0 3 6 6 6 0
## 2 6 6 0 6 6 6 6 0 0
## 3 6 6 3 0 0 6 6 6 6
## 4 6 0 0 1 6 6 3 0 0
## 5 6 6 6 0 0 6 6 6 4
## 6 6 6 3 3 6 6 6 6 0
## 7 6 6 0 3 6 6 6 6 4
## 8 6 6 3 0 6 6 6 6 5
## 9 6 5 0 0 0 0 2 6 6
## 10 6 6 2 2 6 6 6 0 0
## pix_172 pix_173 pix_174 pix_175 pix_176 pix_177 pix_178 pix_179 pix_180
## 1 0 0 0 0 6 6 6 6 0
## 2 0 0 0 5 6 6 6 4 0
## 3 6 3 0 4 6 6 6 6 5
## 4 0 0 0 6 6 5 1 0 0
## 5 0 0 0 0 0 4 6 6 6
## 6 0 0 0 2 6 6 6 6 2
## 7 0 0 0 4 6 6 6 6 0
## 8 0 0 0 3 6 6 6 6 5
## 9 6 1 0 0 0 5 6 6 0
## 10 0 0 0 5 6 6 6 6 2
## pix_181 pix_182 pix_183 pix_184 pix_185 pix_186 pix_187 pix_188 pix_189
## 1 0 3 6 6 6 3 0 0 0
## 2 6 6 6 6 0 0 0 0 4
## 3 0 0 5 6 6 6 6 6 6
## 4 3 6 6 3 0 0 0 0 3
## 5 0 0 6 6 6 6 5 0 0
## 6 1 6 6 6 6 1 0 0 1
## 7 5 6 6 6 6 6 3 0 3
## 8 0 5 6 6 6 6 0 0 0
## 9 0 0 0 0 3 6 6 4 0
## 10 3 6 6 6 0 0 0 0 3
## pix_190 pix_191 pix_192 pix_193 pix_194 pix_195 pix_196 pix_197 pix_198
## 1 1 6 6 6 5 0 0 3 6
## 2 6 6 6 6 0 0 6 6 6
## 3 6 6 6 6 6 6 0 0 0
## 4 6 6 2 0 0 0 3 6 6
## 5 0 2 6 6 6 6 0 0 5
## 6 6 6 6 6 2 0 0 6 6
## 7 6 6 6 6 3 0 4 6 6
## 8 5 6 6 6 6 1 0 1 6
## 9 0 0 3 6 6 1 0 0 0
## 10 6 6 6 6 3 0 2 6 6
## pix_199 pix_200 pix_201 pix_202 pix_203 pix_204 pix_205 pix_206 pix_207
## 1 6 6 5 1 0 1 5 6 6
## 2 6 3 2 2 5 6 6 6 6
## 3 4 6 6 6 6 6 6 6 6
## 4 6 3 3 4 5 6 5 1 0
## 5 6 6 6 6 3 2 2 5 6
## 6 6 6 6 4 4 6 6 6 6
## 7 6 6 6 5 2 5 6 6 6
## 8 6 6 6 1 1 3 6 6 6
## 9 0 0 3 6 6 5 2 3 6
## 10 6 5 4 4 4 6 6 6 6
## pix_208 pix_209 pix_210 pix_211 pix_212 pix_213 pix_214 pix_215 pix_216
## 1 6 0 0 0 3 6 6 6 6
## 2 5 0 0 6 6 6 6 6 6
## 3 6 6 3 0 0 0 0 3 6
## 4 0 0 0 3 6 6 6 6 6
## 5 6 6 5 0 0 0 3 6 6
## 6 3 0 0 0 5 6 6 6 6
## 7 5 0 0 0 5 6 6 6 6
## 8 6 6 0 0 0 5 6 6 6
## 9 6 6 5 0 0 0 0 0 0
## 10 6 0 0 0 5 6 6 6 6
## pix_217 pix_218 pix_219 pix_220 pix_221 pix_222 pix_223 pix_224 pix_225
## 1 6 4 6 6 6 6 5 0 0
## 2 6 6 6 6 6 5 1 0 0
## 3 6 6 6 6 6 6 5 1 0
## 4 6 6 4 0 0 0 0 0 0
## 5 6 6 6 6 6 6 6 3 0
## 6 6 6 6 6 4 4 1 0 0
## 7 6 6 6 6 5 3 0 0 0
## 8 6 6 6 6 6 6 6 3 0
## 9 5 6 6 6 6 6 6 5 1
## 10 6 6 6 6 6 6 5 0 0
## pix_226 pix_227 pix_228 pix_229 pix_230 pix_231 pix_232 pix_233 pix_234
## 1 0 1 2 4 4 4 4 4 4
## 2 3 4 4 4 4 4 4 4 4
## 3 0 0 0 0 0 1 4 4 4
## 4 0 2 4 4 4 4 4 4 1
## 5 0 0 0 0 1 4 4 4 4
## 6 0 0 1 4 4 4 4 3 2
## 7 0 0 2 4 4 4 4 4 4
## 8 0 0 0 3 4 4 4 4 4
## 9 0 0 0 0 0 0 2 4 4
## 10 0 0 3 4 4 4 4 4 4
## pix_235 pix_236 pix_237 pix_238 pix_239 pix_240
## 1 4 4 1 0 0 0
## 2 4 3 0 0 0 0
## 3 4 4 3 0 0 0
## 4 0 0 0 0 0 0
## 5 4 3 0 0 0 0
## 6 0 0 0 0 0 0
## 7 2 0 0 0 0 0
## 8 4 4 2 0 0 0
## 9 4 3 1 0 0 0
## 10 4 4 3 0 0 03 Aperçu général
##
## factor numeric
## 1 240## [1] 1500## [1] 241## NULL## [1] 150## [1] 150REPRESENTATION GRAPHIQUE DES GROUPES DE PIXELS
4 Exploration
4.1 Analyse univariée
Representation des 240 groupes de pixels: sur chaque groupe, supprimer ce qui ne servent à rien.on supprime les colonnes selon le résultat du fichier excel sélection de variables
4.2 Analyse bivariée
- pix
## pix_153 pix_138 pix_57 pix_72 pix_152 pix_168 pix_139 pix_154
## 0.7113043 0.6790212 0.6727874 0.6534527 0.6477325 0.6397767 0.6393719 0.6325938
## pix_58 pix_123
## 0.6222215 0.6032054## pix_36 pix_37 pix_204 pix_205 pix_203 pix_202 pix_131
## 0.02720639 0.03493618 0.08567808 0.09472063 0.10449521 0.12044912 0.12727255
## pix_38 pix_186 pix_51
## 0.13499050 0.17389801 0.18931691Voici la matrice des corrélations :
Nous observons de tres fortes corrélations
Voici la matrice des corrélations avec coefficient de spearman par rang :
4.3 Analyse multivariée
4.3.1 Analyse factorielle
4.3.2 ACP sur les données quantitatives
Transformation de variables
## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
Exploitation de l’acp garder les 50 premieres composante principales
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 16.2462 12.4069 11.95148 9.82256 9.18245 7.87848 7.37105
## Proportion of Variance 0.1783 0.1040 0.09651 0.06519 0.05697 0.04194 0.03671
## Cumulative Proportion 0.1783 0.2823 0.37885 0.44405 0.50102 0.54296 0.57967
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 6.88477 6.62678 5.93165 5.27942 5.01733 4.79990 4.6481
## Proportion of Variance 0.03203 0.02967 0.02377 0.01883 0.01701 0.01557 0.0146
## Cumulative Proportion 0.61169 0.64137 0.66514 0.68397 0.70098 0.71655 0.7311
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 4.35925 4.30979 3.95707 3.78329 3.69746 3.63423 3.41547
## Proportion of Variance 0.01284 0.01255 0.01058 0.00967 0.00924 0.00892 0.00788
## Cumulative Proportion 0.74398 0.75654 0.76712 0.77679 0.78602 0.79495 0.80283
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 3.34112 3.15763 3.1261 2.92363 2.88227 2.82266 2.64167
## Proportion of Variance 0.00754 0.00674 0.0066 0.00578 0.00561 0.00538 0.00472
## Cumulative Proportion 0.81037 0.81711 0.8237 0.82949 0.83510 0.84048 0.84520
## PC29 PC30 PC31 PC32 PC33 PC34 PC35
## Standard deviation 2.53246 2.47004 2.4323 2.32352 2.29095 2.25418 2.15915
## Proportion of Variance 0.00433 0.00412 0.0040 0.00365 0.00355 0.00343 0.00315
## Cumulative Proportion 0.84953 0.85365 0.8577 0.86130 0.86485 0.86828 0.87143
## PC36 PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 2.13652 2.1084 2.00353 1.97731 1.94658 1.92636 1.88226
## Proportion of Variance 0.00308 0.0030 0.00271 0.00264 0.00256 0.00251 0.00239
## Cumulative Proportion 0.87451 0.8775 0.88023 0.88287 0.88543 0.88794 0.89033
## PC43 PC44 PC45 PC46 PC47 PC48 PC49
## Standard deviation 1.85614 1.83292 1.8055 1.75732 1.71123 1.69259 1.68218
## Proportion of Variance 0.00233 0.00227 0.0022 0.00209 0.00198 0.00194 0.00191
## Cumulative Proportion 0.89266 0.89493 0.8971 0.89922 0.90120 0.90313 0.90505
## PC50 PC51 PC52 PC53 PC54 PC55 PC56
## Standard deviation 1.66331 1.65462 1.61436 1.60210 1.57443 1.56411 1.5383
## Proportion of Variance 0.00187 0.00185 0.00176 0.00173 0.00167 0.00165 0.0016
## Cumulative Proportion 0.90692 0.90876 0.91053 0.91226 0.91394 0.91559 0.9172
## PC57 PC58 PC59 PC60 PC61 PC62 PC63
## Standard deviation 1.51217 1.50537 1.46663 1.44998 1.4374 1.41689 1.40245
## Proportion of Variance 0.00155 0.00153 0.00145 0.00142 0.0014 0.00136 0.00133
## Cumulative Proportion 0.91873 0.92026 0.92172 0.92314 0.9245 0.92589 0.92722
## PC64 PC65 PC66 PC67 PC68 PC69 PC70
## Standard deviation 1.3894 1.3873 1.37731 1.37151 1.3338 1.32533 1.31292
## Proportion of Variance 0.0013 0.0013 0.00128 0.00127 0.0012 0.00119 0.00116
## Cumulative Proportion 0.9285 0.9298 0.93111 0.93238 0.9336 0.93476 0.93593
## PC71 PC72 PC73 PC74 PC75 PC76 PC77
## Standard deviation 1.30214 1.28515 1.27198 1.26555 1.24697 1.2174 1.20583
## Proportion of Variance 0.00115 0.00112 0.00109 0.00108 0.00105 0.0010 0.00098
## Cumulative Proportion 0.93708 0.93819 0.93928 0.94037 0.94142 0.9424 0.94340
## PC78 PC79 PC80 PC81 PC82 PC83 PC84
## Standard deviation 1.19493 1.18509 1.17186 1.16930 1.16256 1.13641 1.13202
## Proportion of Variance 0.00096 0.00095 0.00093 0.00092 0.00091 0.00087 0.00087
## Cumulative Proportion 0.94437 0.94531 0.94624 0.94717 0.94808 0.94895 0.94982
## PC85 PC86 PC87 PC88 PC89 PC90 PC91
## Standard deviation 1.12732 1.09692 1.08397 1.07456 1.06498 1.05839 1.05702
## Proportion of Variance 0.00086 0.00081 0.00079 0.00078 0.00077 0.00076 0.00075
## Cumulative Proportion 0.95068 0.95149 0.95228 0.95306 0.95383 0.95459 0.95534
## PC92 PC93 PC94 PC95 PC96 PC97 PC98
## Standard deviation 1.04942 1.04068 1.02956 1.0207 1.01104 1.00178 0.98958
## Proportion of Variance 0.00074 0.00073 0.00072 0.0007 0.00069 0.00068 0.00066
## Cumulative Proportion 0.95609 0.95682 0.95753 0.9582 0.95893 0.95961 0.96027
## PC99 PC100 PC101 PC102 PC103 PC104 PC105
## Standard deviation 0.98133 0.97493 0.96711 0.96005 0.95249 0.94900 0.9422
## Proportion of Variance 0.00065 0.00064 0.00063 0.00062 0.00061 0.00061 0.0006
## Cumulative Proportion 0.96092 0.96156 0.96219 0.96282 0.96343 0.96404 0.9646
## PC106 PC107 PC108 PC109 PC110 PC111 PC112
## Standard deviation 0.93331 0.92744 0.92434 0.91707 0.91334 0.90579 0.89454
## Proportion of Variance 0.00059 0.00058 0.00058 0.00057 0.00056 0.00055 0.00054
## Cumulative Proportion 0.96523 0.96581 0.96638 0.96695 0.96752 0.96807 0.96861
## PC113 PC114 PC115 PC116 PC117 PC118 PC119
## Standard deviation 0.88852 0.88538 0.88153 0.87332 0.8604 0.85586 0.85356
## Proportion of Variance 0.00053 0.00053 0.00053 0.00052 0.0005 0.00049 0.00049
## Cumulative Proportion 0.96914 0.96967 0.97020 0.97071 0.9712 0.97171 0.97220
## PC120 PC121 PC122 PC123 PC124 PC125 PC126
## Standard deviation 0.84424 0.84106 0.83472 0.82672 0.81983 0.81178 0.80954
## Proportion of Variance 0.00048 0.00048 0.00047 0.00046 0.00045 0.00045 0.00044
## Cumulative Proportion 0.97268 0.97316 0.97363 0.97409 0.97455 0.97499 0.97544
## PC127 PC128 PC129 PC130 PC131 PC132 PC133
## Standard deviation 0.80687 0.79798 0.78907 0.78571 0.77906 0.7726 0.7664
## Proportion of Variance 0.00044 0.00043 0.00042 0.00042 0.00041 0.0004 0.0004
## Cumulative Proportion 0.97588 0.97631 0.97673 0.97714 0.97755 0.9780 0.9784
## PC134 PC135 PC136 PC137 PC138 PC139 PC140
## Standard deviation 0.75974 0.75402 0.74896 0.74257 0.73827 0.73179 0.72864
## Proportion of Variance 0.00039 0.00038 0.00038 0.00037 0.00037 0.00036 0.00036
## Cumulative Proportion 0.97874 0.97913 0.97951 0.97988 0.98025 0.98061 0.98097
## PC141 PC142 PC143 PC144 PC145 PC146 PC147
## Standard deviation 0.72688 0.71970 0.71734 0.71193 0.70752 0.70174 0.69439
## Proportion of Variance 0.00036 0.00035 0.00035 0.00034 0.00034 0.00033 0.00033
## Cumulative Proportion 0.98133 0.98168 0.98202 0.98237 0.98270 0.98304 0.98336
## PC148 PC149 PC150 PC151 PC152 PC153 PC154
## Standard deviation 0.69355 0.69161 0.68868 0.68024 0.67937 0.6688 0.6680
## Proportion of Variance 0.00033 0.00032 0.00032 0.00031 0.00031 0.0003 0.0003
## Cumulative Proportion 0.98369 0.98401 0.98433 0.98464 0.98496 0.9853 0.9856
## PC155 PC156 PC157 PC158 PC159 PC160 PC161
## Standard deviation 0.6636 0.65940 0.65025 0.64626 0.64167 0.63747 0.63302
## Proportion of Variance 0.0003 0.00029 0.00029 0.00028 0.00028 0.00027 0.00027
## Cumulative Proportion 0.9859 0.98615 0.98644 0.98672 0.98700 0.98727 0.98754
## PC162 PC163 PC164 PC165 PC166 PC167 PC168
## Standard deviation 0.63157 0.62512 0.62030 0.61510 0.61181 0.60843 0.60701
## Proportion of Variance 0.00027 0.00026 0.00026 0.00026 0.00025 0.00025 0.00025
## Cumulative Proportion 0.98781 0.98808 0.98834 0.98859 0.98884 0.98909 0.98934
## PC169 PC170 PC171 PC172 PC173 PC174 PC175
## Standard deviation 0.60405 0.59925 0.59291 0.58859 0.58481 0.58138 0.57603
## Proportion of Variance 0.00025 0.00024 0.00024 0.00023 0.00023 0.00023 0.00022
## Cumulative Proportion 0.98959 0.98983 0.99007 0.99030 0.99054 0.99076 0.99099
## PC176 PC177 PC178 PC179 PC180 PC181 PC182
## Standard deviation 0.56909 0.56546 0.56319 0.56158 0.55628 0.55334 0.5450
## Proportion of Variance 0.00022 0.00022 0.00021 0.00021 0.00021 0.00021 0.0002
## Cumulative Proportion 0.99121 0.99142 0.99164 0.99185 0.99206 0.99227 0.9925
## PC183 PC184 PC185 PC186 PC187 PC188 PC189
## Standard deviation 0.5415 0.5379 0.53412 0.52771 0.52553 0.52172 0.52104
## Proportion of Variance 0.0002 0.0002 0.00019 0.00019 0.00019 0.00018 0.00018
## Cumulative Proportion 0.9927 0.9929 0.99305 0.99324 0.99343 0.99361 0.99380
## PC190 PC191 PC192 PC193 PC194 PC195 PC196
## Standard deviation 0.51663 0.51228 0.50635 0.50376 0.49755 0.49705 0.49496
## Proportion of Variance 0.00018 0.00018 0.00017 0.00017 0.00017 0.00017 0.00017
## Cumulative Proportion 0.99398 0.99415 0.99433 0.99450 0.99467 0.99483 0.99500
## PC197 PC198 PC199 PC200 PC201 PC202 PC203
## Standard deviation 0.48958 0.48522 0.48007 0.47901 0.47490 0.47040 0.46737
## Proportion of Variance 0.00016 0.00016 0.00016 0.00016 0.00015 0.00015 0.00015
## Cumulative Proportion 0.99516 0.99532 0.99547 0.99563 0.99578 0.99593 0.99608
## PC204 PC205 PC206 PC207 PC208 PC209 PC210
## Standard deviation 0.46213 0.46063 0.45533 0.45011 0.44806 0.44477 0.44147
## Proportion of Variance 0.00014 0.00014 0.00014 0.00014 0.00014 0.00013 0.00013
## Cumulative Proportion 0.99622 0.99637 0.99651 0.99664 0.99678 0.99691 0.99704
## PC211 PC212 PC213 PC214 PC215 PC216 PC217
## Standard deviation 0.44125 0.43295 0.43249 0.42971 0.42664 0.42398 0.41954
## Proportion of Variance 0.00013 0.00013 0.00013 0.00012 0.00012 0.00012 0.00012
## Cumulative Proportion 0.99718 0.99730 0.99743 0.99755 0.99768 0.99780 0.99792
## PC218 PC219 PC220 PC221 PC222 PC223 PC224
## Standard deviation 0.41708 0.41416 0.40623 0.40573 0.40359 0.39570 0.3882
## Proportion of Variance 0.00012 0.00012 0.00011 0.00011 0.00011 0.00011 0.0001
## Cumulative Proportion 0.99803 0.99815 0.99826 0.99837 0.99848 0.99859 0.9987
## PC225 PC226 PC227 PC228 PC229 PC230 PC231
## Standard deviation 0.3858 0.3834 0.3817 0.3756 0.36407 0.36243 0.35816
## Proportion of Variance 0.0001 0.0001 0.0001 0.0001 0.00009 0.00009 0.00009
## Cumulative Proportion 0.9988 0.9989 0.9990 0.9991 0.99917 0.99926 0.99935
## PC232 PC233 PC234 PC235 PC236 PC237 PC238
## Standard deviation 0.34993 0.34789 0.33923 0.33563 0.32923 0.32161 0.31592
## Proportion of Variance 0.00008 0.00008 0.00008 0.00008 0.00007 0.00007 0.00007
## Cumulative Proportion 0.99943 0.99951 0.99959 0.99967 0.99974 0.99981 0.99988
## PC239 PC240
## Standard deviation 0.30991 0.28882
## Proportion of Variance 0.00006 0.00006
## Cumulative Proportion 0.99994 1.00000
Exploitation de l’acp garder les 10 premieres composante principales. Pertes d’information mais gain de temps. Sur des gros datasets? 
Exploitation de l’acp garder les 40 premieres composante principales. Pertes d’information mais gain de temps. Sur des gros datasets? test a 30 non concluant. 
5 Pré-traitement
La récupération dataSET basé sur l’acp a 40 dimensions. Cela permet une reduction du nombre de variable, passant de 240 à 40 avec une perte d’information acceptable:87,6% de l’information est résumée
On transforme notre dataset Test grace aux 40 composantes principales on passe de 375241 Ă 40241
##
## Attaching package: 'reshape'## The following object is masked from 'package:data.table':
##
## melton tente la préduction avec les fameuses méthodes :
6 prédiction
Arbre de décision /Tree CART
utilisation de la librairie CARET
## Loading required package: lattice## Time difference of 5.151615 secsexploitataion des RĂ©sultats du CART
Voici le resultat de l’apprentissage :
## CART
##
## 1125 samples
## 40 predictor
## 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 1125, 1125, 1125, 1125, 1125, 1125, ...
## Resampling results across tuning parameters:
##
## maxdepth Accuracy Kappa
## 1 0.2354981 0.1593970
## 2 0.3657610 0.3010154
## 3 0.3950741 0.3327888
## 4 0.4213976 0.3614760
## 5 0.4884847 0.4341967
## 6 0.5576086 0.5095610
## 7 0.6114697 0.5688294
## 8 0.6596813 0.6219046
## 9 0.6993625 0.6657589
## 10 0.7223685 0.6913621
## 11 0.7351236 0.7055100
## 12 0.7469353 0.7185980
## 13 0.7527365 0.7250121
## 14 0.7544709 0.7269815
## 15 0.7553395 0.7279727
## 16 0.7559220 0.7286162
## 17 0.7559220 0.7286162
## 18 0.7559220 0.7286162
## 19 0.7559220 0.7286162
## 20 0.7559220 0.7286162
## 21 0.7559220 0.7286162
## 22 0.7559220 0.7286162
## 23 0.7559220 0.7286162
## 24 0.7559220 0.7286162
## 25 0.7559220 0.7286162
## 26 0.7559220 0.7286162
## 27 0.7559220 0.7286162
## 28 0.7559220 0.7286162
## 29 0.7559220 0.7286162
## 30 0.7559220 0.7286162
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was maxdepth = 16.Nous avons une faible erreur d’apprentissage.
Voici les paramètres choisis :
## Best parameter pour maxdepth est : 16
## Warning: package 'rattle' was built under R version 3.6.3## Loading required package: tibble## Warning: package 'tibble' was built under R version 3.6.3## Loading required package: bitops## Rattle: A free graphical interface for data science with R.
## Version 5.4.0 Copyright (c) 2006-2020 Togaware Pty Ltd.
## Entrez 'rattle()' pour secouer, faire vibrer, et faire défiler vos données.
Voici le resultat de la validation:
## Accuracy Kappa
## 0.7520000 0.7242407## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3 4 5 6 7 8 9
## 0 34 1 0 1 1 4 0 0 1 0
## 1 1 27 2 8 3 5 0 0 2 0
## 2 0 4 28 0 0 0 0 3 0 1
## 3 0 2 0 26 0 1 1 1 6 0
## 4 1 3 0 1 21 1 2 0 0 0
## 5 1 0 0 0 0 26 2 0 2 0
## 6 1 0 0 0 8 0 31 0 0 0
## 7 0 0 2 0 0 0 0 27 0 0
## 8 6 0 0 0 0 1 1 0 25 0
## 9 0 0 7 2 0 2 0 2 0 37
##
## Overall Statistics
##
## Accuracy : 0.752
## 95% CI : (0.7051, 0.7949)
## No Information Rate : 0.1173
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7242
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity 0.77273 0.72973 0.71795 0.68421 0.63636 0.65000
## Specificity 0.97583 0.93787 0.97619 0.96736 0.97661 0.98507
## Pos Pred Value 0.80952 0.56250 0.77778 0.70270 0.72414 0.83871
## Neg Pred Value 0.96997 0.96942 0.96755 0.96450 0.96532 0.95930
## Prevalence 0.11733 0.09867 0.10400 0.10133 0.08800 0.10667
## Detection Rate 0.09067 0.07200 0.07467 0.06933 0.05600 0.06933
## Detection Prevalence 0.11200 0.12800 0.09600 0.09867 0.07733 0.08267
## Balanced Accuracy 0.87428 0.83380 0.84707 0.82578 0.80649 0.81754
## Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity 0.83784 0.81818 0.69444 0.97368
## Specificity 0.97337 0.99415 0.97640 0.96142
## Pos Pred Value 0.77500 0.93103 0.75758 0.74000
## Neg Pred Value 0.98209 0.98266 0.96784 0.99692
## Prevalence 0.09867 0.08800 0.09600 0.10133
## Detection Rate 0.08267 0.07200 0.06667 0.09867
## Detection Prevalence 0.10667 0.07733 0.08800 0.13333
## Balanced Accuracy 0.90561 0.90617 0.83542 0.96755Confusion Table
| Durée | Accuracy | Taux.Erreur | |
|---|---|---|---|
| CART | 5.151615 secs | 0.752 | 0.248 |
Random Forest
## Time difference of 8.021825 secsVoici le resultat de l’apprentissage :
## Random Forest
##
## 1125 samples
## 40 predictor
## 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
##
## No pre-processing
## Resampling: Cross-Validated (2 fold)
## Summary of sample sizes: 562, 563
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 8 0.9439960 0.9377693
## 12 0.9351024 0.9278872
## 16 0.9306603 0.9229501
## 20 0.9244341 0.9160343
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 8.## Best parameter pour mtry est : 8
Apply model to the test set
## Accuracy Kappa
## 0.9546667 0.9495956Nous avons une faible taux d’erreur de validation et elle est équivalant à l’erreur d’apprentissage.
Le kappa est faible donc accord faible sur la prédiction par rapport à une prédiction au hasard.
Confusion Table
La matrice de confusion suivante se lit alors comme suit :
Resultat de la prédiction
## Durée Accuracy Taux.Erreur
## Random Forest 8.021825 secs 0.9546667 0.04533333| Durée | Accuracy | Taux.Erreur | |
|---|---|---|---|
| Random Forest | 8.021825 secs | 0.9546667 | 0.0453333 |
Nous avons une bonne accuracy pour la prédiction mais le temps d’excution est long.
Neural Networks/reseau de neurones
size (#Hidden Units)
- decay (Weight Decay)
## Neural Network
##
## 1125 samples
## 240 predictor
## 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 899, 900, 900, 902, 899
## Resampling results across tuning parameters:
##
## size decay Accuracy Kappa
## 1 0.2 0.1982072 0.1085044
## 1 0.5 0.2044136 0.1135094
## 1 0.8 0.2061953 0.1180197
## 1 1.0 0.2177711 0.1285361
## 1 1.5 0.2079969 0.1162543
## 1 2.0 0.2044216 0.1131601
## 1 3.0 0.2062232 0.1148697
## 1 4.0 0.2070923 0.1161503
## 1 5.0 0.1999851 0.1086338
## 1 6.0 0.2026676 0.1108840
## 1 7.0 0.1963777 0.1042397
## 1 8.0 0.1991198 0.1072330
## 1 9.0 0.2062152 0.1149637
## 1 10.0 0.2071160 0.1159913
## 2 0.2 0.3117654 0.2344433
## 2 0.5 0.3324372 0.2574485
## 2 0.8 0.3706043 0.3004798
## 2 1.0 0.3475567 0.2736767
## 2 1.5 0.3565281 0.2836019
## 2 2.0 0.3029884 0.2238356
## 2 3.0 0.3608654 0.2891083
## 2 4.0 0.3467543 0.2731350
## 2 5.0 0.3724253 0.3013228
## 2 6.0 0.3635408 0.2914259
## 2 7.0 0.3733223 0.3023708
## 2 8.0 0.3635331 0.2914859
## 2 9.0 0.3812275 0.3116442
## 2 10.0 0.3866917 0.3172668
## 3 0.2 0.4630706 0.4032565
## 3 0.5 0.4907383 0.4335734
## 3 0.8 0.5163024 0.4622074
## 3 1.0 0.4472515 0.3843496
## 3 1.5 0.4936711 0.4366590
## 3 2.0 0.5128003 0.4588307
## 3 3.0 0.5982488 0.5533686
## 3 4.0 0.5510805 0.5005550
## 3 5.0 0.5875774 0.5408950
## 3 6.0 0.5548598 0.5048778
## 3 7.0 0.5598879 0.5103469
## 3 8.0 0.5725146 0.5247476
## 3 9.0 0.5786932 0.5313794
## 3 10.0 0.5547268 0.5050427
## 4 0.2 NaN NaN
## 4 0.5 NaN NaN
## 4 0.8 NaN NaN
## 4 1.0 NaN NaN
## 4 1.5 NaN NaN
## 4 2.0 NaN NaN
## 4 3.0 NaN NaN
## 4 4.0 NaN NaN
## 4 5.0 NaN NaN
## 4 6.0 NaN NaN
## 4 7.0 NaN NaN
## 4 8.0 NaN NaN
## 4 9.0 NaN NaN
## 4 10.0 NaN NaN
## 5 0.2 NaN NaN
## 5 0.5 NaN NaN
## 5 0.8 NaN NaN
## 5 1.0 NaN NaN
## 5 1.5 NaN NaN
## 5 2.0 NaN NaN
## 5 3.0 NaN NaN
## 5 4.0 NaN NaN
## 5 5.0 NaN NaN
## 5 6.0 NaN NaN
## 5 7.0 NaN NaN
## 5 8.0 NaN NaN
## 5 9.0 NaN NaN
## 5 10.0 NaN NaN
##
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were size = 3 and decay = 3.## Best parameter pour size est : 3## Best parameter pour decay est : 3
#### Apply model to the test set
## Accuracy Kappa
## 0.6026667 0.5597759## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3 4 5 6 7 8 9
## 0 0 0 0 1 0 0 1 0 0 0
## 1 0 30 4 0 1 1 0 1 0 1
## 2 1 1 30 0 0 0 0 0 0 0
## 3 1 1 1 34 0 31 22 3 0 0
## 4 1 2 0 0 32 1 5 0 2 0
## 5 1 0 0 1 0 0 3 0 0 0
## 6 0 0 0 0 0 2 4 0 0 0
## 7 0 1 3 2 0 4 0 28 0 0
## 8 39 0 0 0 0 1 2 0 33 2
## 9 1 2 1 0 0 0 0 1 1 35
##
## Overall Statistics
##
## Accuracy : 0.6027
## 95% CI : (0.5512, 0.6525)
## No Information Rate : 0.1173
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5598
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity 0.000000 0.81081 0.76923 0.89474 0.96970 0.00000
## Specificity 0.993958 0.97633 0.99405 0.82493 0.96784 0.98507
## Pos Pred Value 0.000000 0.78947 0.93750 0.36559 0.74419 0.00000
## Neg Pred Value 0.882038 0.97923 0.97376 0.98582 0.99699 0.89189
## Prevalence 0.117333 0.09867 0.10400 0.10133 0.08800 0.10667
## Detection Rate 0.000000 0.08000 0.08000 0.09067 0.08533 0.00000
## Detection Prevalence 0.005333 0.10133 0.08533 0.24800 0.11467 0.01333
## Balanced Accuracy 0.496979 0.89357 0.88164 0.85983 0.96877 0.49254
## Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity 0.10811 0.84848 0.9167 0.92105
## Specificity 0.99408 0.97076 0.8702 0.98220
## Pos Pred Value 0.66667 0.73684 0.4286 0.85366
## Neg Pred Value 0.91057 0.98516 0.9899 0.99102
## Prevalence 0.09867 0.08800 0.0960 0.10133
## Detection Rate 0.01067 0.07467 0.0880 0.09333
## Detection Prevalence 0.01600 0.10133 0.2053 0.10933
## Balanced Accuracy 0.55110 0.90962 0.8934 0.95162Plus proche voisins KNN
## Time difference of 1.249782 secs## k-Nearest Neighbors
##
## 1125 samples
## 40 predictor
## 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 1012, 1012, 1013, 1012, 1013, 1014, ...
## Resampling results across tuning parameters:
##
## k Accuracy Kappa
## 1 0.9733399 0.9703721
## 4 0.9733716 0.9704072
## 7 0.9688910 0.9654280
## 10 0.9617796 0.9575240
## 13 0.9591325 0.9545800
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 4.## Best parameter pour k est : 4
#### Apply model to the test set
## Accuracy Kappa
## 0.9733333 0.9703452## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3 4 5 6 7 8 9
## 0 43 0 0 0 0 0 0 0 1 0
## 1 0 36 0 0 0 1 0 0 0 0
## 2 0 0 39 0 0 0 0 1 0 0
## 3 1 0 0 38 0 1 0 0 1 0
## 4 0 0 0 0 33 0 0 0 0 0
## 5 0 1 0 0 0 38 2 0 0 0
## 6 0 0 0 0 0 0 34 0 0 0
## 7 0 0 0 0 0 0 0 32 0 0
## 8 0 0 0 0 0 0 1 0 34 0
## 9 0 0 0 0 0 0 0 0 0 38
##
## Overall Statistics
##
## Accuracy : 0.9733
## 95% CI : (0.9515, 0.9871)
## No Information Rate : 0.1173
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9703
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity 0.9773 0.97297 1.0000 1.0000 1.000 0.9500
## Specificity 0.9970 0.99704 0.9970 0.9911 1.000 0.9910
## Pos Pred Value 0.9773 0.97297 0.9750 0.9268 1.000 0.9268
## Neg Pred Value 0.9970 0.99704 1.0000 1.0000 1.000 0.9940
## Prevalence 0.1173 0.09867 0.1040 0.1013 0.088 0.1067
## Detection Rate 0.1147 0.09600 0.1040 0.1013 0.088 0.1013
## Detection Prevalence 0.1173 0.09867 0.1067 0.1093 0.088 0.1093
## Balanced Accuracy 0.9871 0.98501 0.9985 0.9955 1.000 0.9705
## Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity 0.91892 0.96970 0.94444 1.0000
## Specificity 1.00000 1.00000 0.99705 1.0000
## Pos Pred Value 1.00000 1.00000 0.97143 1.0000
## Neg Pred Value 0.99120 0.99708 0.99412 1.0000
## Prevalence 0.09867 0.08800 0.09600 0.1013
## Detection Rate 0.09067 0.08533 0.09067 0.1013
## Detection Prevalence 0.09067 0.08533 0.09333 0.1013
## Balanced Accuracy 0.95946 0.98485 0.97075 1.0000Confusion Table
| Durée | Accuracy | Taux.Erreur | |
|---|---|---|---|
| KNN | 1.249782 secs | 0.9733333 | 0.0266667 |
Perceptron multicouche
## Multi-Layer Perceptron, with multiple layers
##
## 1125 samples
## 240 predictor
## 10 classes: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 899, 900, 900, 902, 899
## Resampling results:
##
## Accuracy Kappa
## 0.9715311 0.9683643
##
## Tuning parameter 'layer1' was held constant at a value of 240
## Tuning
## parameter 'layer2' was held constant at a value of 10
## Tuning
## parameter 'layer3' was held constant at a value of 0Apply model to the test set
## Accuracy Kappa
## 0.9680000 0.9644198## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3 4 5 6 7 8 9
## 0 43 0 0 0 0 0 0 0 0 0
## 1 1 35 0 1 0 2 0 0 1 0
## 2 0 0 38 0 0 0 0 0 0 0
## 3 0 0 0 37 0 1 0 0 0 0
## 4 0 0 0 0 33 0 0 0 0 0
## 5 0 1 0 0 0 37 2 0 0 0
## 6 0 1 0 0 0 0 35 0 0 0
## 7 0 0 1 0 0 0 0 32 0 0
## 8 0 0 0 0 0 0 0 0 35 0
## 9 0 0 0 0 0 0 0 1 0 38
##
## Overall Statistics
##
## Accuracy : 0.968
## 95% CI : (0.9448, 0.9834)
## No Information Rate : 0.1173
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9644
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
## Sensitivity 0.9773 0.94595 0.9744 0.97368 1.000 0.92500
## Specificity 1.0000 0.98521 1.0000 0.99703 1.000 0.99104
## Pos Pred Value 1.0000 0.87500 1.0000 0.97368 1.000 0.92500
## Neg Pred Value 0.9970 0.99403 0.9970 0.99703 1.000 0.99104
## Prevalence 0.1173 0.09867 0.1040 0.10133 0.088 0.10667
## Detection Rate 0.1147 0.09333 0.1013 0.09867 0.088 0.09867
## Detection Prevalence 0.1147 0.10667 0.1013 0.10133 0.088 0.10667
## Balanced Accuracy 0.9886 0.96558 0.9872 0.98536 1.000 0.95802
## Class: 6 Class: 7 Class: 8 Class: 9
## Sensitivity 0.94595 0.96970 0.97222 1.0000
## Specificity 0.99704 0.99708 1.00000 0.9970
## Pos Pred Value 0.97222 0.96970 1.00000 0.9744
## Neg Pred Value 0.99410 0.99708 0.99706 1.0000
## Prevalence 0.09867 0.08800 0.09600 0.1013
## Detection Rate 0.09333 0.08533 0.09333 0.1013
## Detection Prevalence 0.09600 0.08800 0.09333 0.1040
## Balanced Accuracy 0.97149 0.98339 0.98611 0.9985