TP SVM

close all
clear all
c = [1; 0.2; 0.5]; % coéfficients du canal
%c = [0.4048; 0.8164; 0.4084];
M = length(c);
sigv = 0.01; % variance bruit additif pour .001 1e-3 pour 0.01 1e-30
N = 10000; % nombre de données
d = sign(randn(1, N)); % séquence binaire générée
dbuffer = zeros(M, 1); % Buffer
y = zeros(1, N);
for n = 1 : N,
dbuffer = [d(n); dbuffer(1 : M - 1)];
y(n) = c' * dbuffer + sqrt(sigv) * randn; % entrée récepteur
end

P = 3;
ybuffer = zeros(P, 1);
y2 = zeros(P, N);
for n = 1 : N,
ybuffer = [y(n); ybuffer(1 : P - 1)];
y2(:,n) = ybuffer;
%y(n) = wopt' ? ybuffer;
if (n <= (N/2)) && (mod(n, 5) == 0),
if d(n) == 1,
plot3(ybuffer(1), ybuffer(2), ybuffer(3), 'O');
hold on;
else
plot3(ybuffer(1), ybuffer(2), ybuffer(3), 'X');
hold on;
end
pause(0.0001);
end
end
disp('ok pour affichage des motifs pour les deux classes')

trainset = transpose(y2(:,1:N/2));
trainsetclass = transpose(d(1:N/2));
testset = transpose(y2(:,N/2+1:N));
testsetclass = transpose(d(N/2+1:N));

%% CV partition
c = cvpartition(trainsetclass, 'k', 5);

%% Feature selection
opts = statset('display', 'iter');
fun = @(train_data, train_labels, test_data, test_labels) ...
sum(predict(fitcsvm(train_data, train_labels, 'KernelFunction', 'rbf'), test_data) ~= test_labels);

[fs, history] = sequentialfs(fun, trainset, trainsetclass, 'cv', c, 'options', opts, 'nfeatures', 3);

%% Best hyperparameters

BF = trainset(:, fs);

mdl = fitcsvm(BF, trainsetclass, 'KernelFunction', 'rbf');

%% Ploting

%Gather support vectors from ClassificationSVM struct
sv = mdl.SupportVectors;
%set step size for finer sampling
dd = 0.05;
%generate grid for predictions at finer sample rate
[x, y, z] = meshgrid(min(trainset(:,1)):dd:max(trainset(:,1)),...
min(trainset(:,2)):dd:max(trainset(:,2)),...
min(trainset(:,3)):dd:max(trainset(:,3)));
xGrid = [x(:),y(:),z(:)];
%get scores, f
[ ~ , f] = predict(mdl,xGrid);
%reshape to same grid size as the input
f = reshape(f(:,2), size(x));
% Assume class labels are 1 and 0 and convert to logical
t = logical(trainsetclass);
%plot data points, color by class label
figure
plot3(trainset(t, 1), trainset(t, 2), trainset(t, 3), 'b.');
hold on
plot3(trainset(~t, 1), trainset(~t, 2), trainset(~t, 3), 'r.');
hold on
% load unscaled support vectors for plotting
plot3(sv(:, 1), sv(:, 2), sv(:, 3), 'go');
%plot decision surface
[faces,verts,~] = isosurface(x, y, z, f, 0, x);
patch('Vertices', verts, 'Faces', faces, 'FaceColor','k','edgecolor', 'none', 'FaceAlpha', 0.2);
grid on
box on
view(3)
hold off