Wolfram Language

Neuronale Netze

Klassifizierung von Punkten aus verschiedenen Clustern

Verwenden Sie ein Netz, um Punkte aus drei konzentrischen Clusters zu unterscheiden.

Erstellen Sie einen künstlichen Datensatz aus drei konzentrischen Clusters.

In[1]:=
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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]=

Erzeugen Sie die Trainingssaten, indem Sie jeden Punkt mit einem Label assoziieren.

In[2]:=
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trainingData = Join[Thread[clusters[[1]] -> Red], Thread[clusters[[2]] -> Green], Thread[clusters[[3]] -> Blue]]; RandomSample[trainingData, 8]
Out[2]=

Erzeuegen Sie ein Netz, um die Wahrscheinlichkeit zu berechnen, mit der ein Punkt in den drei Clustern liegt.

In[3]:=
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net = NetChain[{30, Tanh, 20, Tanh, 3, SoftmaxLayer[]}, "Input" -> {2}, "Output" -> NetDecoder[{"Class", {Red, Green, Blue}}]]
Out[3]=

Trainieren Sie das Netz mit den Daten.

In[4]:=
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trained = NetTrain[net, trainingData]
In[5]:=
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apfQTmGytwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA QG7z/wFt4Sws "], {{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}}]\)

Sagen Sie die Wahrscheinlichkeiten vorher, mit denen Punkte entlang der x-Achse liegen.

In[6]:=
Click for copyable input
Show[Table[ Plot[trained[{x, 0}, {"Probability", col}], {x, -5, 5}, PlotStyle -> col], {col, {Blue, Green, Red}}], PlotRange -> All]
Out[6]=

Plotten Sie die Wahrscheinlichkeit jeder Klasse als den roten, grünen und blauen Farbkanal eines Bildes.

In[7]:=
Click for copyable input
row = Range[-4, 4, 0.05]; coords = Tuples[row, 2]; preds = Partition[trained[coords, None], Length[row]]; Image[Reverse@Transpose@preds]
Out[7]=

Plotten Sie die Wahrscheinlichkeitsdichte als eine Funktion der Position separat für jede Klasse.

In[8]:=
Click for copyable input
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]=

Plotten Sie die Entropie der vorherigen Verteilung als eine Funktion der Position, um zu visualisieren, wo das Netz am unsichersten bei den Vorhersagen ist.

In[9]:=
Click for copyable input
row = Range[-5, 5, 0.05]; coords = Tuples[row, 2]; entropy = Partition[trained[coords, "Entropy"], Length[row]]; Image[Reverse@Transpose@entropy]
Out[9]=

Verwandte Beispiele

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