fitcsvm decision boundary equation

I have trained a linear SVM on 2D data and can't seem to get the line equation describing the decision boundary.

Here is some code that fails miserably.

rng(1)
n=5;
X=rand(n,2);
Y=logical([1 0 0 0 0]);
svmStruct=fitcsvm(X,Y);
gscatter(X(:,1),X(:,2),Y); hold on;
fplot(@(x)-(svmStruct.Beta(1)*x+svmStruct.Bias)/svmStruct.Beta(2))

Would appreciate help!

[Brendan Hamm]

It seems to me the reason why this fails is you are trying to train a model with only 5 points. Stop and think, how do you make a support vector with only one data point for the True class? An infinite number of ways should be your answer.

One other issue you seem to have is in the orientation of your data. X is a 5-by-2 and Y is 1-by-5. So, you should transpose your response. No that this solves the above problem.

Y=logical([1 0 0 0 0])';

Otherwise what you have for the plotting seems fine.

Answer 1

[Brendan Hamm]

Generate some data for the classes

rng('default')
n = 100;
X = [2 + 0.5*randn(n,2);...
    3 + 0.6*randn(n,2)];
Y = [zeros(n,1);ones(n,1)];
gscatter(X(:,1),X(:,2),Y)

Fit a model

mdl = fitcsvm(X,Y);

Make a plot showing the decision boundary

Begin by making a grid of values

x = linspace(0,5);
y = linspace(0,5);
[XX,YY] = meshgrid(x,y);

Stack the values into an m-by-2 matrix

pred = [XX(:),YY(:)];
p = predict(mdl,pred);

Look at a scatter of the predictions

gscatter(pred(:,1),pred(:,2),p)

Define the boundary function, note that:

f = @(x) -(x*mdl.Beta(1) + mdl.Bias)/mdl.Beta(2);
y = f(x);
hold on
plot(x,y,'g--','LineWidth',2,'DisplayName','Boundary')
hold off

On the original data

gscatter(X(:,1),X(:,2),Y(:,1))
hold on
plot(x,y,'g--','LineWidth',2,'DisplayName','Boundary')
hold off

More generally for ECOC you might consider the code in this example:

https://www.mathworks.com/matlabcentral/answers/412365-how-to-find-the-multi-class-hyperplane-decision-boundaries-using-support-vector-machines-svm