Unsupervised Learning with Autoencoders: New in Wolfram Language 11

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["
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"], {{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}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 28}, {28, 0}}, {
       0, 255},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
      "Byte", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{28, 28},
PlotRange->{{0, 28}, {0, 28}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 28}, {28, 0}}, {0, 255},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
      "Byte", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{28, 28},
PlotRange->{{0, 28}, {0, 28}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 28}, {28, 0}}, {
       0, 255},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
      "Byte", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{28, 28},
PlotRange->{{0, 28}, {0, 28}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 28}, {28, 0}}, {0, 255},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
      "Byte", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{28, 28},
PlotRange->{{0, 28}, {0, 28}}]\)}

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]:=

\!\(\*
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"], {{0, 0}, {360, 258}}, {0,
     255},
ColorFunction->RGBColor],
ImageSize->{360, 258},
PlotRange->{{0, 360}, {0, 258}}]\)

Wolfram Language™

Unsupervised Learning with Autoencoders

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