Plotting output of 3D discriminant analysis in MATLAB

Question

How do I visualise the output of discriminant analysis, such as linear discriminant analysis into 3D dimensions in MATLAB. The fitcdiscr function seems to be working with the 3 dimensional input, but I'm struggling to plot the "discrimination plane" with scatter3, which I'm using to plot the data.

I understand there are a few ways of plotting a plane, but what outputs of fitcdiscr do I need to pass to something like surf()?

I.e. if I have data like this:

    clear
clc
close all

%----------------------------
x1 = 1:0.01:3;
r = -1 + (1+1)*rand(1,201);
x1 = x1 + r;

y1 = 1:0.01:3;
r = -1 + (1+1)*rand(1,201);
y1 = y1 + r;

z1 = 1:0.01:3;
r = -1 + (1+1)*rand(1,201);
z1 = z1 + r;

x1 = x1';
y1 = y1';
z1 = z1';
label1 = ones(length(y1),1);

Tclust1 = [label1,x1,y1,z1];
%----------------------------
x2 = 4:0.01:6;
r = -1 + (1+1)*rand(1,201);
x2 = x2 + r;

y2 = 10:0.01:12;
r = -1 + (1+1)*rand(1,201);
y2 = y2 + r;

z2 = 10:0.01:12;
r = -1 + (1+1)*rand(1,201);
z2 = z2 + r;

x2 = x2';
y2 = y2';
z2 = z2';

label2 = 2.*ones(length(y2),1);

Tclust2 = [label2,x2,y2,z2];

%----------------------------
x3 = 5:0.01:7;
r = -1 + (1+1)*rand(1,201);
x3 = x3 + r;

y3 = 11:0.01:13;
r = -1 + (1+1)*rand(1,201);
y3 = y3 + r;

z3 = 11:0.01:13;
r = -1 + (1+1)*rand(1,201);
z3 = z3 + r;

x3 = x3';
y3 = y3';
z3 = z3';

label3 = 3.*ones(length(y3),1);

Tclust3 = [label3,x3,y3,z3];

%----------------------------
T = [Tclust1;Tclust2;Tclust3];
   
data = T(:,2:4);
labels = T(:,1);

%do the discriminant analysis
MdlLinear = fitcdiscr(data,labels);

%plot data with boundaries -----------------------------------------------
figure()

scatter3(x1,y1,z1,'g')
hold on
scatter3(x2,y2,z2,'b')
scatter3(x3,y3,z3,'r')
% hold off
title('Full data set')


surf(?,?,?)

For reference, I want to do this but in 3 dimensions: Matlab fitcdiscr

Answer 1

Having understood what I needed to plot, I found the following an extension of the example in the matlab example using "fimplicit3":

    %group 1 and group 2
figure()
scatter3(x1,y1,z1,'g')
hold on
scatter3(x2,y2,z2,'b')
scatter3(x3,y3,z3,'r')
K12 = MdlLinear.Coeffs(1,2).Const;
L12 = MdlLinear.Coeffs(1,2).Linear;
f12 = @(x1,x2,x3) K12 + L12(1)*x1 + L12(2)*x2 + L12(3)*x3;
h2 = fimplicit3(f12,[xmin xmax ymin ymax zmin zmax]);
legend('Data 1','Data 2','Data 3','Boundary 1 -> 2','location','eastoutside') 

Answer 2

To visualise the plane of LInear Discriminant Analysis (LDA) in 3D, here's some follow through steps:

1. Fit the LDA model using fitcdiscr
2. Extract coefficients from fitted model to define discrimination plane
3. Plot the data points using scatter3
4. Plot the discrimination plane using surf

Heres how you can do it:

You have already done this part so nothing to worry about

MdlLinear = fitcdiscr(data, labels);

This next part is for extracting the coefficients, you can access them by using the coeffs property of the model.

coeff = MdlLinear.Coeffs(1,2).Linear; % Coefficients between class 1 and 2

The plane above can be defined using the equation

a⋅x + b⋅y + c⋅z + d = 0

Where a. b, c are the coefficients from the coeff, and d is the bias term shown in the const property.

You can dow define a 3-dimensional grid and evaluate the plane equation as shown below:

[xGrid, yGrid] = meshgrid(min(data(:,1)):0.1:max(data(:,1)), min(data(:,2)):0.1:max(data(:,2)));
zGrid = -(coeff(1) * xGrid + coeff(2) * yGrid + MdlLinear.Coeffs(1,2).Const) / coeff(3);

After that all you need to do is just plot the data and the plane ill paste my MATLAB script to show.

figure;
hold on;

% Plot the original data points
scatter3(x1, y1, z1, 'g');
scatter3(x2, y2, z2, 'b');
scatter3(x3, y3, z3, 'r');

% Plot the discrimination plane
surf(xGrid, yGrid, zGrid, 'FaceAlpha', 0.5, 'EdgeColor', 'none');

title('LDA Discrimination Plane and Data');
xlabel('X');
ylabel('Y');
zlabel('Z');
legend({'Class 1', 'Class 2', 'Class 3', 'Discrimination Plane'});

hold off;

Notes

It should be noted that

• The surf function does plot the plane in 3D space
• FaceAlpha makes the plane semi-transparent
• coeff(1, 2) correspond to separation between class 1 and class 2. You can modify it to whatever you desire.

Let me know if I have answered your question adequetly.