File:Naive Bayes Classifier.gif

Summary[edit]

Mathematica 11.0 code[edit]

n = 20;
red[z_] := {Opacity[z], Red};
purple[z_] := {Opacity[z], Purple};
cyan[z_] := {Opacity[z], Cyan}
pop1 = RandomVariate[MultinormalDistribution[{3, 4}, {{1, 1}, {1, 2}}], n];
pop2 = RandomVariate[MultinormalDistribution[{6, 4}, {{0.5, 0}, {0, 1}}], n];
pop3 = RandomVariate[MultinormalDistribution[{6, 8}, {{2, 0}, {0, 0.5}}], n];

meas = RandomSample[Join[pop1, pop2, pop3]];
meascol = Table[Which[MemberQ[pop1, meas[[j]]], 1, MemberQ[pop2, meas[[j]]], 2, MemberQ[pop3, meas[[j]]], 3], {j, 1, Dimensions[meas][[1]]}]
plots = Table[
   p1 = Count[meascol[[1 ;; j]], 1]/j;
   \[Mu]x1 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 1]][[All, 1]];
   \[Mu]y1 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 1]][[All, 2]];
   \[Sigma]x1 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 1]][[All, 1]] - \[Mu]x1)^2]/(p1*j)];
   \[Sigma]y1 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 1]][[All, 2]] - \[Mu]y1)^2]/(p1*j)];
   p1x = If[\[Sigma]x1 == 0, 0, PDF[NormalDistribution[\[Mu]x1, \[Sigma]x1], x]];
   p1y = If[\[Sigma]y1 == 0, 0, PDF[NormalDistribution[\[Mu]y1, \[Sigma]y1], y]];
   p2 = Count[meascol[[1 ;; j]], 2]/j;
   \[Mu]x2 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 2]][[All, 1]];
   \[Mu]y2 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 2]][[All, 2]];
   \[Sigma]x2 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 2]][[All, 1]] - \[Mu]x2)^2]/(p2*j)];
   \[Sigma]y2 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 2]][[All, 2]] - \[Mu]y2)^2]/(p2*j)];
   p2x = If[\[Sigma]x2 == 0, 0, PDF[NormalDistribution[\[Mu]x2, \[Sigma]x2], x]];
   p2y = If[\[Sigma]y2 == 0, 0, PDF[NormalDistribution[\[Mu]y2, \[Sigma]y2], y]];
   p3 = Count[meascol[[1 ;; j]], 3]/j;
   \[Mu]x3 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 3]][[All, 1]];
   \[Mu]y3 = Mean@Extract[meas, Position[meascol[[1 ;; j]], 3]][[All, 2]];
   \[Sigma]x3 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 3]][[All, 1]] - \[Mu]x3)^2]/(p3*j)];
   \[Sigma]y3 = Sqrt[Total[(Extract[meas, Position[meascol[[1 ;; j]], 3]][[All, 2]] - \[Mu]y3)^2]/(p3*j)];
   p3x = If[\[Sigma]x3 == 0, 0, PDF[NormalDistribution[\[Mu]x3, \[Sigma]x3], x]];
   p3y = If[\[Sigma]y3 == 0, 0, PDF[NormalDistribution[\[Mu]y3, \[Sigma]y3], y]];
   Legended[Show[
   ContourPlot[p1*p1x*p1y, {x, 0, 10}, {y, 0, 10}, ColorFunction -> red, PlotRange -> All, PlotPoints -> 50] ,
     ContourPlot[p2*p2x*p2y, {x, 0, 10}, {y, 0, 10}, ColorFunction -> purple, PlotRange -> All, PlotPoints -> 50] ,
     ContourPlot[p3*p3x*p3y, {x, 0, 10}, {y, 0, 10}, ColorFunction -> cyan, PlotRange -> All, PlotPoints -> 50]
     ,
     Graphics[{PointSize[0.02], Black, Point[Join[Extract[meas, Position[meascol[[1 ;; j]], 1]], Extract[meas, Position[meascol[[1 ;; j]], 2]], Extract[meas, Position[meascol[[1 ;; j]], 3]]]], 
       PointSize[0.015], Red, Point[Extract[meas, Position[meascol[[1 ;; j]], 1]]], Purple, Point[Extract[meas, Position[meascol[[1 ;; j]], 2]]], Cyan, Point[Extract[meas, Position[meascol[[1 ;; j]], 3]]]}]
     , PlotRange -> All, FrameLabel -> {"Feature 1", "Feature 2"}, LabelStyle -> {Bold, Black}
     ], SwatchLegend[{Red, Purple, Cyan}, {"Class Lucas", "Class B", "Class C"}] ]
   , {j, 1, n*3}];

Licensing[edit]

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