Come tracciare un iperpiano in 3D per i risultati SVM?

Question

Mi chiedo solo come tracciare un iperpiano dei risultati SVM.

Ad esempio, qui stiamo utilizzando due funzioni, possiamo tracciare il limite decisionale in 2D. Ma se come possiamo tracciare un iperpiano in 3D se usiamo 3 funzioni?

load fisheriris; 

features = meas(1:100,:); 
featureSelcted = features(1:100,1:2); % For example, featureSelcted = features(1:100,1:3) can not be plotted 
groundTruthGroup = species(1:100); 


svmStruct        = svmtrain(featureSelcted, groundTruthGroup, ... 
    'Kernel_Function', 'rbf', 'boxconstraint', Inf, 'showplot', true, 'Method', 'QP'); 
svmClassified       = svmclassify(svmStruct,featureSelcted,'showplot',true); 

Una soluzione simile in R sono disponibili all'indirizzo svm-fit-hyperplane ma un'implementazione Matlab sarebbe utile. Grazie mille.

A.

Answer 1

Ecco una funzione per tracciare i risultati 3D SVM in MATLAB.

function [] = svm_3d_matlab_vis(svmStruct,Xdata,group) 
sv = svmStruct.SupportVectors; 
alphaHat = svmStruct.Alpha; 
bias = svmStruct.Bias; 
kfun = svmStruct.KernelFunction; 
kfunargs = svmStruct.KernelFunctionArgs; 
sh = svmStruct.ScaleData.shift; % shift vector 
scalef = svmStruct.ScaleData.scaleFactor; % scale vector 

group = group(~any(isnan(Xdata),2)); 
Xdata =Xdata(~any(isnan(Xdata),2),:); % remove rows with NaN 

% scale and shift data 
Xdata1 = repmat(scalef,size(Xdata,1),1).*(Xdata+repmat(sh,size(Xdata,1),1)); 
k = 50; 
cubeXMin = min(Xdata1(:,1)); 
cubeYMin = min(Xdata1(:,2)); 
cubeZMin = min(Xdata1(:,3)); 

cubeXMax = max(Xdata1(:,1)); 
cubeYMax = max(Xdata1(:,2)); 
cubeZMax = max(Xdata1(:,3)); 
stepx = (cubeXMax-cubeXMin)/(k-1); 
stepy = (cubeYMax-cubeYMin)/(k-1); 
stepz = (cubeZMax-cubeZMin)/(k-1); 
[x, y, z] = meshgrid(cubeXMin:stepx:cubeXMax,cubeYMin:stepy:cubeYMax,cubeZMin:stepz:cubeZMax); 
mm = size(x); 
x = x(:); 
y = y(:); 
z = z(:); 
f = (feval(kfun,sv,[x y z],kfunargs{:})'*alphaHat(:)) + bias; 
t = strcmp(group, group{1}); 

% unscale and unshift data 
Xdata1 =(Xdata1./repmat(scalef,size(Xdata,1),1)) - repmat(sh,size(Xdata,1),1); 
x =(x./repmat(scalef(1),size(x,1),1)) - repmat(sh(1),size(x,1),1); 
y =(y./repmat(scalef(2),size(y,1),1)) - repmat(sh(2),size(y,1),1); 
z =(z./repmat(scalef(3),size(z,1),1)) - repmat(sh(3),size(z,1),1); 
figure 
plot3(Xdata1(t, 1), Xdata1(t, 2), Xdata1(t, 3), 'b.'); 
hold on 
plot3(Xdata1(~t, 1), Xdata1(~t, 2), Xdata1(~t, 3), 'r.'); 
hold on 
% load unscaled support vectors for plotting 
sv = svmStruct.SupportVectorIndices; 
sv = [Xdata1(sv, :)]; 
plot3(sv(:, 1), sv(:, 2), sv(:, 3), 'go'); 
legend(group{1},group{end},'support vectors') 

x0 = reshape(x, mm); 
y0 = reshape(y, mm); 
z0 = reshape(z, mm); 
v0 = reshape(f, mm); 

[faces,verts,colors] = isosurface(x0, y0, z0, v0, 0, x0); 
patch('Vertices', verts, 'Faces', faces, 'FaceColor','k','edgecolor', 'none', 'FaceAlpha', 0.5); 
grid on 
box on 
view(3) 
hold off 
end 

Esempio trama:

% load data 
    load fisheriris; 
% train svm using three features for two species 
    svmStruct = svmtrain(meas(1:100,1:3),species(1:100),'showplot','false','kernel_function','rbf',... 
     'boxconstraint',1,'kktviolationlevel',0.05,'tolkkt',5e-3); 
    % run function described above 
    svm_3d_matlab_vis(svmStruct,meas(1:100,1:3),species(1:100))