How to add LDA axis to scatter plot?

I would like to ask how can I add LDA axis to the scatter plot in the link attached below?

https://de.mathworks.com/help/stats/create-and-visualize-discriminant-analysis-classifier.html

Thanks a lot

[Ameer Hamza]

The link does show an example of how to plot the line. Which part is confusing to you? Do you have a specific dataset?

[EK]

Hi Ameer

I assume that the line in this example indicate the category boundary not LDA axis. I would like to get a plot as in example attached below

thank you

Answer 1

[Guillaume Erny]

I have used the fisheriris dataset to test.

1. Load fisheriris and do analysis

load fisheriris
Mdl = fitcdiscr(meas,species, 'DiscrimType','quadratic')

what you are looking for is the Mu, the center positions of the group obatined by the discriminant analysis

2. Visualisation

So you can see the position of the center of the groups within your data

figure, nexttile
gscatter(meas(:,1), meas(:,2), species);
hold on
scatter(Mdl.Mu(:, 1), Mdl.Mu(:, 2), 100, 'xK', 'LineWidth', 1.5)
hold off

nexttile
gscatter(meas(:,1), meas(:,3), species);
hold on
scatter(Mdl.Mu(:, 1), Mdl.Mu(:, 3), 100, 'xK', 'LineWidth', 1.5)
hold off
legend('off')

nexttile
gscatter(meas(:,1), meas(:,4), species);
hold on
scatter(Mdl.Mu(:, 1), Mdl.Mu(:, 4), 100, 'xK', 'LineWidth', 1.5)
hold off
legend('off')

nexttile
gscatter(meas(:,2), meas(:,3), species);
hold on
scatter(Mdl.Mu(:, 2), Mdl.Mu(:, 3), 100, 'xK', 'LineWidth', 1.5)
hold off
legend('off')

etc for 2/4 and 3/4

your LDA axis is the projection of your data to all possible lines crossing two centers (black crosses), in this case three possible axis. so from 4 axis to three

3. Projection

Here is the code I used to project the original data to LD axis (in this quadratic discriminant). This is not vectorized. I am sure clever peoples will find very easy to improve the code below to improve speed.

V = Mdl.Mu; % positions of the centers
Comb = [1, 2; 1, 3; 2, 3]; % all possible combinations to form the axis with 3 groups

for ii = 1:3 % for each axis
    V1 = V(Comb(ii,2), :);
    V2 = V(Comb(ii,1), :);
    v = (V2-V1)./norm(V2-V1); % normalised vector for projection 
    
    for jj =1:size(meas, 1)
        Q(jj, :) = dot(meas(jj, :)-V1,v)*v+V1;
        LD(jj, ii) = (Q(jj, 1)-V1(1))/(V2(1)-V1(1));
    end
end

4. Quick Visualisation of the results

figure
hold on
for ii = 1:3
    scatter3(LD(strcmp(species, 'setosa'), 1), LD(strcmp(species, 'setosa'), 2), LD(strcmp(species, 'setosa'), 3), 'r')
    scatter3(LD(strcmp(species, 'versicolor'), 1), LD(strcmp(species, 'versicolor'), 2), LD(strcmp(species, 'versicolor'), 3), 'g') 
    scatter3(LD(strcmp(species, 'virginica'), 1), LD(strcmp(species, 'virginica'), 2), LD(strcmp(species, 'virginica'), 3), 'b') 
end
hold off
legend({'setosa', 'versicolor', 'virginica' })
xlabel('LD1')
ylabel('LD2')
zlabel('LD3')
view(40,35)

[EK]

Thank you very much!