Example (i)

Definitions of Gaussian #1

μ1 = {0, 0} ; Σ1 = DiagonalMatrix[{1, 1}] ;

Definition of Gaussian #2

μ2 = {0, 0} ; Σ2 = DiagonalMatrix[{2, 2}] ;

Desired plot range

prLocal = {{-3, 3}, {-3, 3}} ;

Log likelihood of first Gaussian

lp1 = logpdf[μ1, Σ1] ;  lp1 // TraditionalForm

-x^2/2 - y^2/2 - log(π) - log(2)

Log likelihood of second Gaussian

lp2 = logpdf[μ2, Σ2] ; lp2 // TraditionalForm

-x^2/4 - y^2/4 - log(π) - log(4)

Decision boundary

Simplify[lp1 - lp2  0]   // TraditionalForm

1/4 (x^2 + y^2) == log(2)

View Gaussians

ShowTwoGaussianPDFs[Exp[lp1 // N], Exp[lp2 // N], prLocal, x, y, yS, imSize] ;

[Graphics:../HTMLFiles/index_26.gif]

View decision boundary

ShowDecisionBoundary[μ1, Σ1, μ2, Σ2, prLocal, classColors, {data1Color, data2Color}, yS] ;

[Graphics:../HTMLFiles/index_28.gif]


Created by Mathematica  (September 8, 2003)