Wolfram Language

Réseaux neuronaux

Apprentissage non supervisé avec les auto-encodeurs

Entraînez un réseau auto-encodeur pour reconstruire des images de chiffres manuscrits après les avoir projetés à un "code" espace vectoriel de dimensions inférieures. Utilisez ces vecteurs de code pour effectuer des regroupements et des visualisations.

Tout d'abord obtenez les données d'entraînement, puis sélectionnez les images correspondant aux chiffres de 0 à 4.

In[1]:=
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resource = ResourceObject["MNIST"]; trainingData = ResourceData[resource, "TrainingData"]; trainingSubset = Select[trainingData, Last[#] <= 4 &]; testData = ResourceData[resource, "TestData"]; testSubset = Select[testData, Last[#] <= 4 &]; RandomSample[trainingSubset, 8]
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Obtenez la "l'image moyenne" pour soustraire des données d'entraînement.

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trainingImages = Keys[trainingSubset]; meanImage = Image[Mean@Map[ImageData, trainingImages]]
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Créez un réseau pour entraîner qui produit à la fois la reconstruction et l'erreur de reconstruction.

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net = NetGraph[ {FlattenLayer[], 50, Ramp, 784, Tanh, ReshapeLayer[{1, 28, 28}], MeanSquaredLossLayer[]}, {1 -> 2 -> 3 -> 4 -> 5 -> 6 -> NetPort["Output"], 6 -> NetPort[7, "Input"], NetPort["Input"] -> NetPort[7, "Target"]}, "Input" -> NetEncoder[{"Image", {28, 28}, "Grayscale", "MeanImage" -> meanImage}], "Output" -> NetDecoder[{"Image", "Grayscale"}] ]
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Entraînez le réseau afin de minimiser l'erreur de reconstruction.

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trained = NetTrain[net, <|"Input" -> trainingImages|>, "Loss"];
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Obtenez un sous-réseau qui exécute seulement les reconstructions.

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reconstructor = Take[trained, {NetPort["Input"], NetPort["Output"]}]
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Reconstruisez quelques exemples d'images.

In[6]:=
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ImageAdd[reconstructor[#], meanImage] & /@ {\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQwU/x9A8CWTyfQBDrlbLCxMU7BLvbLCKTfRkQUoFzbpIBY5JhaQHAuL8hkM KU8GJiAQVQQS6FIHlED6cjYdrGdhmYYqdV8CaJxy2df//x9IsvD0/UJ3vvNr MHMSUNUdNDmzhxDmA3N0OYQL7psyMEUjyxWzsMCYGGaqweReHQC6SvIhVrl8 oE+UDv3HJuepBJTzRvWfKhPTtm3STEzgwEGV+t8HDkoIkYMmBwwNiJyk052v aHL/DxZC5LDH3/ZAlqAd2x9ilaMPAABwyokL "], {{0, 28}, {28, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{28, 28}, PlotRange->{{0, 28}, {0, 28}}]\), \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQwU/x9gcJNxEk65FcxrccpV8OGUusSdiVNuNeMBnHKmCl9wSd1nVMepbQGj DU65YsZNuKSOCRl9xyXXzBCF08gQxnW4pJ6La+DU1s6YgFMug7EQp5w0415c UodYcMsVMRr9wSH1VYOxDZe2X5b+X3E6hS4AAAjL8xI= "], {{0, 28}, {28, 0}}, { 0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{28, 28}, PlotRange->{{0, 28}, {0, 28}}]\), \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQwU/6cp6G4KYWDIXIRNKowJDFQfYpfSKvRnYmrFkDrNyqR7//P/n4ZMxRhy m1h0nwGpVnamfZhmPngLIvWYsMmBQRcHk+VX7FKbOZgkDuDQVs/ElI9Dyp+T KeEzdqlnokxid3Bos2RiKsIhtZGdyQmHiW/McWurZGIKwqHtPzsT0zMcUiC5 K6+B4Nf/X69f38rMzMz5iiwHBuEFkVBWC1wukAkB2Dg4wrq6jiEM7WxpaQFp SWlpuYbL4gEEADLRqO8= "], {{0, 28}, {28, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{28, 28}, PlotRange->{{0, 28}, {0, 28}}]\), \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQwU/x8Q8Plabu55HFJ1TExMrDFvsclVMYGB1E4scrOYmPNmThFi4qj/iiHn xRQBJA+JMDHF/EKXY2C6AqKO2jExRf9Gk3Nhug+mTwgzMa1Ek8sFys12XLFi RQ4TUwua3EKmjdfZIW5lUlj9AUXu4+LPd/iZYIB7Gbprt8T5wGX1rqC79s/7 9zduvn+fx8PE5IYagK+PwlhH9ZiYPJClNilxbICxP6kw8W9HklvKwcR8DMY5 xcLkgKyxm4npCIw9h5kpD8UfzkxKiTdBrAk6nEyocv8/K3EysbABAcgX5m/Q PLHAQxriP5vmF+ge/P//+a3SrY3Lb/3AlKEHAAAeUY84 "], {{0, 28}, {28, 0}}, { 0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{28, 28}, PlotRange->{{0, 28}, {0, 28}}]\), \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQwU/x+U4Kw8lLHzEYZcmwSUkR2OLvXbBiY3X/cLmtwu5kooq5f5FarUJWG1 z1CmPbpcOMcpKOstAxOq3GpeHRiziMnpF4pcGPNUKOu+OOteFKkPcswwZiWz DorU/5fM0QgTIlDlvhnrvYWqYmKagioHVG2xCgjqom2Y4TbDwLVQLmYgEJdg YWb+9h8dnFsNBP//xzEzY0jBQAMz8yVccvVMTPj04ZSrYObGKScuPAGnnM9e nFJUAQDVl858 "], {{0, 28}, {28, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{28, 28}, PlotRange->{{0, 28}, {0, 28}}]\)}
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Obtenez un sous-réseau qui produit le vecteur de code.

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encoder = Take[trained, {NetPort["Input"], 4}]
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Calculez les codes pour toutes les images de test.

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testImages = Keys[testSubset]; features = encoder[testImages];

Projetez les vecteurs de code en trois dimensions et visualisez-les avec les classes originales (non vues par le réseau). Les classes de chiffres ont tendance à se regrouper.

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coords = DimensionReduce[features, 3]; classes = Values[testSubset]; Table[Extract[coords, Position[classes, i]], {i, 0, 4}] ListPointPlot3D[ Table[Extract[coords, Position[classes, i]], {i, 0, 4}], PlotLegends -> PointLegend[96, Range[0, 4]], BoxRatios -> 1, Axes -> None, Boxed -> True, PlotStyle -> Map[ColorData[96], Range[1, 5]], AspectRatio -> 1]
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Effectuez la classification automatique directement sur les vecteurs de code et montrez un échantillon prélevé de chaque groupe.

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components = ClusteringComponents[features, 5, 1]; Map[Part[testImages, RandomSample[#, 10]] &, PositionIndex[components]]
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Visualisez une classification hiérarchique des représentants aléatoires de chaque classe.

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representatives = Catenate@GroupBy[testSubset, Last -> First, RandomSample[#, 6] &]; ClusteringTree[ encoder[representatives] -> Map[ImageCrop, representatives]]
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