Wolfram Language

Réseaux neuronaux

Apprenez à classer des points à partir de différents groupements

Utilisez un réseau pour apprendre à distinguer les points de trois groupes concentriques.

Créez un ensemble de données artificielles à partir de trois groupes concentriques.

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]=

Créez les données d'apprentissage en associant chaque point à une étiquette.

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]=

Créez un réseau pour calculer la probabilité d'un point se trouvant dans chaque groupe.

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

Entraînez le réseau sur les données.

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}}]\)

Prédites les probabilités de points le long de l'axe x.

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]=

Tracez les probabilités de chaque classe comme les canaux rouge, vert et bleu d'une image.

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]=

Tracez la densité de probabilité en fonction de la position pour chaque classe séparément.

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]=

Tracez l'entropie de la distribution a posteriori en fonction de la position de visualisation où le réseau est plus incertain.

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]=

Exemples connexes

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