IRIS_discriminant.m

%Load the sample data.
load fisheriris

%Use petal length (third column in meas ) and petal width (fourth column in meas ) measurements. 
PL = meas(:,3);
PW = meas(:,4);

%Plot the data, showing the classification
h1 = gscatter(PL,PW,species,'krb','ov^',[],'off');
h1(1).LineWidth = 2;
h1(2).LineWidth = 2;
h1(3).LineWidth = 2;
legend('Setosa','Versicolor','Virginica','Location','best')
hold on

%Create a linear classifier.
X = [PL,PW];
MdlLinear = fitcdiscr(X,species);

%Retrieve the coefficients for the linear boundary between the second and third classes.
MdlLinear.ClassNames([2 3])
K = MdlLinear.Coeffs(2,3).Const;
L = MdlLinear.Coeffs(2,3).Linear;

%Plot the curve that separates the second and third classes
f = @(x1,x2) K + L(1)*x1 + L(2)*x2;
h2 = ezplot(f,[.9 7.1 0 2.5]);
h2.Color = 'r';
h2.LineWidth = 2;

%Retrieve the coefficients for the linear boundary between the first and second classes.
MdlLinear.ClassNames([1 2])
K = MdlLinear.Coeffs(1,2).Const;
L = MdlLinear.Coeffs(1,2).Linear;

%Plot the curve that separates the first and second classes.
f = @(x1,x2) K + L(1)*x1 + L(2)*x2;
h3 = ezplot(f,[.9 7.1 0 2.5]);
h3.Color = 'k';
h3.LineWidth = 2;
axis([.9 7.1 0 2.5])
xlabel('Petal Length')
ylabel('Petal Width')
title('{\bf Linear Classification with Fisher Training Data}')

%Create a quadratic discriminant classifier.
MdlQuadratic = fitcdiscr(X,species,'DiscrimType','quadratic');

%Remove the linear boundaries from the plot.
delete(h2);
delete(h3);

%Retrieve the coefficients for the quadratic boundary between the second and third classes.
MdlQuadratic.ClassNames([2 3])
K = MdlQuadratic.Coeffs(2,3).Const;
L = MdlQuadratic.Coeffs(2,3).Linear;
Q = MdlQuadratic.Coeffs(2,3).Quadratic;

%Plot the curve that separates the second and third classes
f = @(x1,x2) K + L(1)*x1 + L(2)*x2 + Q(1,1)*x1.^2 + ...
    (Q(1,2)+Q(2,1))*x1.*x2 + Q(2,2)*x2.^2;
h2 = ezplot(f,[.9 7.1 0 2.5]);
h2.Color = 'r';
h2.LineWidth = 2;

%Retrieve the coefficients for the quadratic boundary between the first and second classes.
MdlQuadratic.ClassNames([1 2])
K = MdlQuadratic.Coeffs(1,2).Const;
L = MdlQuadratic.Coeffs(1,2).Linear;
Q = MdlQuadratic.Coeffs(1,2).Quadratic;

%Plot the curve that separates the first and second and classes.
f = @(x1,x2) K + L(1)*x1 + L(2)*x2 + Q(1,1)*x1.^2 + ...
    (Q(1,2)+Q(2,1))*x1.*x2 + Q(2,2)*x2.^2;
h3 = ezplot(f,[.9 7.1 0 1.02]); % Plot the relevant portion of the curve. ezplot(fun2,[xmin,xmax,ymin,ymax])
h3.Color = 'k';
h3.LineWidth = 2;
axis([.9 7.1 0 2.5])
xlabel('Petal Length')
ylabel('Petal Width')
title('{\bf Quadratic Classification with Fisher Training Data}')
hold off