# Create and Visualize Discriminant Analysis Classifier

This example shows how to perform linear and quadratic classification of Fisher iris data.

Load the sample data.

```
load fisheriris
```

The column vector, `species` , consists of iris flowers of three different species, setosa, versicolor, virginica. The double matrix `meas` consists of four types of measurements on the flowers, the length and width of sepals and petals in centimeters, respectively.

Use petal length (third column in `meas` ) and petal width (fourth column in `meas` ) measurements. Save these as variables PL and PW, respectively.

PL = meas(:,3); PW = meas(:,4);

Plot the data, showing the classification, that is, create a scatter plot of the measurements, grouped by species.

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;

ans = 2x1 cell array {'versicolor'} {'virginica' }

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;

ans = 2x1 cell array {'setosa' } {'versicolor'}

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;

ans = 2x1 cell array {'versicolor'} {'virginica' }

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;

ans = 2x1 cell array {'setosa' } {'versicolor'}

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. 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