# Wolfram Mathematica

## Unsupervised Learning with Autoencoders

Train an autoencoder network to reconstruct images of handwritten digits after projecting them to a lower-dimensional "code" vector space. Use these code vectors to perform clustering and visualization.

First obtain the training data, then select images corresponding to digits 0 through 4.

In[1]:=
```resource = ResourceObject["MNIST"]; trainingData = ResourceData[resource, "TrainingData"]; trainingSubset = Select[trainingData, Last[#] <= 4 &]; testData = ResourceData[resource, "TestData"]; testSubset = Select[testData, Last[#] <= 4 &]; RandomSample[trainingSubset, 8]```
Out[1]=

Obtain the "mean image" to subtract from the training data.

In[2]:=
```trainingImages = Keys[trainingSubset]; meanImage = Image[Mean@Map[ImageData, trainingImages]]```
Out[2]=

Create a network to train that produces both the reconstruction and the reconstruction error.

In[3]:=
```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"}] ]```
Out[3]=

Train the network to minimize the reconstruction error.

In[4]:=
```trained = If[\$VersionNumber < 11.3, NetTrain[net, <|"Input" -> trainingImages|>, "Loss"], NetTrain[net, <|"Input" -> trainingImages|>, LossFunction -> "Loss"] ];```
Out[4]=

Obtain a subnetwork that performs only reconstruction.

In[5]:=
`reconstructor = Take[trained, {NetPort["Input"], NetPort["Output"]}]`
Out[5]=

Reconstruct some sample images.

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

Obtain a subnetwork that produces the code vector.

In[7]:=
`encoder = Take[trained, {NetPort["Input"], 4}]`
Out[7]=

Compute codes for all of the test images.

In[8]:=
```testImages = Keys[testSubset]; features = encoder[testImages];```

Project the code vectors to three dimensions and visualize them along with the original classes (not seen by the network). The digit classes tend to cluster together.

In[9]:=
```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]```
Out[9]=

Perform automatic clustering directly on the code vectors and show a sample taken from each cluster.

In[10]:=
```components = ClusteringComponents[features, 5, 1]; Map[Part[testImages, RandomSample[#, 10]] &, PositionIndex[components]]```
Out[10]=

Visualize a hierarchical clustering of random representatives from each class.

In[11]:=
```representatives = Catenate@GroupBy[testSubset, Last -> First, RandomSample[#, 6] &]; ClusteringTree[ encoder[representatives] -> Map[ImageCrop, representatives]]```
In[12]:=
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