Classify

Machine Learning
Visualization & Graphics

Visualize the Decision Boundary of a Classifier

Classify 2D data and plot the decision boundaries of the classifier function

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A decision boundary is the dividing line or hypersurface that separates different classes in the input data based on a classifier's predictions. This example shows how to create a decision boundary plot for a two-dimensional dataset.

Generate labeled 2D data:

In[1]:=

data=Association[Table[Module[{μ,σ,pts},μ=RandomReal[{-3,3},2];σ=0.6;pts=RandomVariate[MultinormalDistribution[μ,σIdentityMatrix[2]],12];classpts],{class,{"A","B","C"}}]]

Out[1]=

A{{-1.32705,2.01582},{-1.79702,2.96851},{-2.03066,3.5596},{-3.01073,2.83675},{-2.96812,2.63323},{-3.62523,3.00827},{-1.81094,2.05455},{-2.74756,1.60957},{-3.55275,3.57359},{-3.57329,2.68873},{-2.57876,3.2766},{-2.04627,4.56359}},B{{1.26937,0.93681},{2.13432,-0.464788},{0.941366,1.07688},{1.05864,1.86309},{0.69328,1.09616},{0.585798,-0.575863},{0.759311,1.86834},{1.75265,1.74845},{1.72411,0.538025},{1.20775,0.759948},{0.754546,0.903569},{1.19428,-0.749209}},C{{-3.31126,-1.00393},{-1.17445,-0.369141},{-1.01277,0.354704},{-0.623029,0.84263},{-0.121657,1.53876},{-1.60112,-0.307009},{-1.9071,0.0465109},{-4.03852,1.89305},{-3.58048,2.54104},{-1.83165,0.594093},{-2.18791,0.467588},{-0.979524,0.120325}}

Train a classifier on the data:

In[2]:=

clf=Classify[data,Method"SupportVectorMachine"]

Out[2]=

ClassifierFunction

Input type: NumericalVector (2)

Classes: A,B,C



Get all points from the training data:

In[3]:=

points=Flatten[Values[data],1];Short[points]

Out[3]//Short=

{{-1.32705,2.01582},34,{-0.979524,0.120325}}

Determine the

and

ranges of the training data, adding a small margin for visualization:

In[4]:=

{xMin,xMax}=MinMax[points〚All,1〛]+{-0.1,0.1};{yMin,yMax}=MinMax[points〚All,2〛]+{-0.1,0.1};{xRange,yRange}={Range[xMin,xMax,0.01],Range[yMin,yMax,0.01]};Short[{xRange,yRange}]

Out[4]//Short=

{{-4.13852,-4.12852,634,2.22148,2.23148},{1}}

Create a grid of points from the specified ranges:

In[5]:=

gridPoints=Flatten[Outer[List,xRange,yRange],1];Short[gridPoints]

Out[5]//Short=

{{-4.13852,-1.10393},368124,{2.23148,4.65607}}

Use the

ClassifierFunction

created to classify each point in the grid, and reshape the result:

In[6]:=

predictedClasses=Transpose[Partition[clf[gridPoints],Length[yRange]]];Short[predictedClasses]

Out[6]//Short=

{1}

Create an

ArrayPlot

of the predicted classes, specifying a color for each class:

In[7]:=

array=ArrayPlotpredictedClasses,DataRange{{xMin,xMax},{yMin,yMax}},ColorRules"A"

,"B"

,"C"

,



Out[7]=

Plot the training points for each class using their respective colors:

In[8]:=

pointsAll=ListPlotdata,



Out[8]=

Show the decision regions and the training points together:

In[9]:=

Show[array,pointsAll]

Out[9]=

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Contributed by: Felipe Amorim

Wolfram Language Example Repository

Visualize the Decision Boundary of a Classifier

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