Learn to Classify Points from Different Clusters
Use a net to learn to distinguish points from three concentric clusters.
Create an artificial dataset from three concentric clusters.
In[1]:=
sampledata[sd_] :=
RandomVariate[MultinormalDistribution[{0, 0}, sd*IdentityMatrix[2]],
500];
clusters = Map[sampledata, {3, 1.5, 0.2}];
ListPlot[clusters,
PlotStyle ->
Map[Directive[#, PointSize[0.015]] &, {RGBColor[
1, 0.21, 0.35000000000000003`], RGBColor[0.3, 0.78, 0.38],
RGBColor[0.46, 0.5700000000000001, 1]}], Axes -> None,
AspectRatio -> 1]
Out[1]=
Create the training data by associating each point to a label.
In[2]:=
trainingData =
Join[Thread[clusters[[1]] -> Red], Thread[clusters[[2]] -> Green],
Thread[clusters[[3]] -> Blue]];
RandomSample[trainingData, 8]
Out[2]=
Create a net to compute the probability of a point lying in each cluster.
In[3]:=
net = NetChain[{30, Tanh, 20, Tanh, 3, SoftmaxLayer[]},
"Input" -> {2},
"Output" -> NetDecoder[{"Class", {Red, Green, Blue}}]]
Out[3]=
Train the net on the data.
In[4]:=
trained = NetTrain[net, trainingData]
In[5]:=
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"], {{0, 752}, {560, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag[
"Byte", ColorSpace -> "RGB", Interleaving -> True,
Magnification -> 0.5],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Magnification[0.5],
ImageSizeRaw->{560, 752},
PlotRange->{{0, 560}, {0, 752}}]\)
Predict the probabilities of points along the x axis.
In[6]:=
Show[Table[
Plot[trained[{x, 0}, {"Probability", col}], {x, -5, 5},
PlotStyle -> col], {col, {Blue, Green, Red}}], PlotRange -> All]
Out[6]=
Plot the probabilities of each class as the red, green, and blue channels of an image.
In[7]:=
row = Range[-4, 4, 0.05];
coords = Tuples[row, 2];
preds = Partition[trained[coords, None], Length[row]];
Image[Reverse@Transpose@preds]
Out[7]=
Plot the probability density as a function of position for each class separately.
In[8]:=
GraphicsRow@
Table[ContourPlot[
trained[{x, y}, {"Probability", col}], {x, -5, 5}, {y, -5, 5},
ColorFunction -> (Blend[{White, Darker[col]}, #] &),
PlotRange -> All, ContourStyle -> None], {col, {Red, Green, Blue}}]
Out[8]=
Plot the entropy of the posterior distribution as a function of position to visualize where the network is most uncertain.
In[9]:=
row = Range[-5, 5, 0.05];
coords = Tuples[row, 2];
entropy = Partition[trained[coords, "Entropy"], Length[row]];
Image[Reverse@Transpose@entropy]
Out[9]=