Where did I go wrong with support vector

https://www.mathworks.com/help/stats/support-vector-machines-for-binary-classification.html

I am following the example above.

I am trying to get the two figures that look like this.

but mine ends up looking like this

Below is my code. Can you spot what I did wrong? I believe it's around where I commented %%%%%mysigmoid2

commandwindow;

rng(1); % For reproducibility
r = sqrt(rand(100,1)); % Radius
t = 2*pi*rand(100,1);  % Angle
data1 = [r.*cos(t), r.*sin(t)]; % Points

r2 = sqrt(3*rand(100,1)+1); % Radius
t2 = 2*pi*rand(100,1);      % Angle
data2 = [r2.*cos(t2), r2.*sin(t2)]; % points

data3 = [data1;data2];
theclass = ones(200,1);
theclass(1:100) = -1;

%Train the SVM Classifier
cl = fitcsvm(data3,theclass,'KernelFunction','rbf',...
    'BoxConstraint',Inf,'ClassNames',[-1,1]);

% Predict scores over the grid
d = 0.02;
[x1Grid,x2Grid] = meshgrid(min(data3(:,1)):d:max(data3(:,1)),...
    min(data3(:,2)):d:max(data3(:,2)));
xGrid = [x1Grid(:),x2Grid(:)];
[~,scores] = predict(cl,xGrid);

cl2 = fitcsvm(data3,theclass,'KernelFunction','rbf');
[~,scores2] = predict(cl2,xGrid);

figure;
h(1:2) = gscatter(data3(:,1),data3(:,2),theclass,'rb','.');
hold on
ezpolar(@(x)1);
h(3) = plot(data3(cl2.IsSupportVector,1),data3(cl2.IsSupportVector,2),'ko');
contour(x1Grid,x2Grid,reshape(scores2(:,2),size(x1Grid)),[0 0],'k');
legend(h,{'-1','+1','Support Vectors'});
axis equal
hold off

rng(1);  % For reproducibility
n = 100; % Number of points per quadrant

r1 = sqrt(rand(2*n,1));                     % Random radii
t1 = [pi/2*rand(n,1); (pi/2*rand(n,1)+pi)]; % Random angles for Q1 and Q3
X1 = [r1.*cos(t1) r1.*sin(t1)];             % Polar-to-Cartesian conversion

r2 = sqrt(rand(2*n,1));
t2 = [pi/2*rand(n,1)+pi/2; (pi/2*rand(n,1)-pi/2)]; % Random angles for Q2 and Q4
X2 = [r2.*cos(t2) r2.*sin(t2)];

X = [X1; X2];        % Predictors
Y = ones(4*n,1);
Y(2*n + 1:end) = -1; % Labels

%%%%%mysigmoid2
Mdl2 = fitcsvm(X,Y,'KernelFunction','mysigmoid2','Standardize',true);
[~,scores2] = predict(Mdl2,xGrid);



figure;
h(1:2) = gscatter(X(:,1),X(:,2),Y);
hold on
h(3) = plot(X(Mdl2.IsSupportVector,1),...
    X(Mdl2.IsSupportVector,2),'ko','MarkerSize',10);
title('Scatter Diagram with the Decision Boundary')
contour(x1Grid,x2Grid,reshape(scores2(:,2),size(x1Grid)),[0 0],'k');
legend({'-1','1','Support Vectors'},'Location','Best');
hold off

CVMdl2 = crossval(Mdl2);
misclass2 = kfoldLoss(CVMdl2);
misclass2;



%mysigmoid
% Mdl1 = fitcsvm(X,Y,'KernelFunction','mysigmoid','Standardize',true);
% 
%     % Compute the scores over a grid
% d = 0.02; % Step size of the grid
% [x1Grid,x2Grid] = meshgrid(min(X(:,1)):d:max(X(:,1)),...
%     min(X(:,2)):d:max(X(:,2)));
% xGrid = [x1Grid(:),x2Grid(:)];        % The grid
% [~,scores1] = predict(Mdl1,xGrid); % The scores
% 
% figure;
% h(1:2) = gscatter(X(:,1),X(:,2),Y);
% hold on
% h(3) = plot(X(Mdl1.IsSupportVector,1),...
%     X(Mdl1.IsSupportVector,2),'ko','MarkerSize',10);
%     % Support vectors
% contour(x1Grid,x2Grid,reshape(scores1(:,2),size(x1Grid)),[0 0],'k');
%     % Decision boundary
% title('Scatter Diagram with the Decision Boundary')
% legend({'-1','1','Support Vectors'},'Location','Best');
% hold off

mysigmoid2.m

function G = mysigmoid2(U,V)
% Sigmoid kernel function with slope gamma and intercept c
gamma = 0.5;
c = -1;
G = tanh(gamma*U*V' + c);
end

Answer 1

[Divyajyoti Nayak]

Hi @G. Nardi,

From what I understand. You are following an example and are not getting the same graphs. The graphs seem to be plotted correctly but don’t look the same. This is because the limits of the y axis are different from the example figure since you have used the same grid for the second figure as the first. Making another grid for the second figure should solve the issue.

%%%%%mysigmoid2
Mdl2 = fitcsvm(X,Y,'KernelFunction','mysigmoid2','Standardize',true);

%Making Grid for second figure
d = 0.02; % Step size of the grid
[x1Grid,x2Grid] = meshgrid(min(X(:,1)):d:max(X(:,1)),...
    min(X(:,2)):d:max(X(:,2)));
xGrid = [x1Grid(:),x2Grid(:)]; 
[~,scores2] = predict(Mdl2,xGrid);

figure;
h(1:2) = gscatter(X(:,1),X(:,2),Y);
hold on
h(3) = plot(X(Mdl2.IsSupportVector,1),...
    X(Mdl2.IsSupportVector,2),'ko','MarkerSize',10);
title('Scatter Diagram with the Decision Boundary')
contour(x1Grid,x2Grid,reshape(scores2(:,2),size(x1Grid)),[0 0],'k');
legend({'-1','1','Support Vectors'},'Location','Best');
hold off
CVMdl2 = crossval(Mdl2);
misclass2 = kfoldLoss(CVMdl2);
misclass2;

Here's the result:

Hope this helps!