How to plot a hyper plane in 3D for the SVM results?

I just wondering how to plot a hyper plane of the SVM results.

For example, here we are using two features, we can plot the decision boundary in 2D. But if how can we plot a hyper plane in 3D if we use 3 features?

    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);

A similar solution in R can be found at

http://stackoverflow.com/questions/8017427/plotting-data-from-an-svm-fit-hyperplane

but a Matlab implementation would be handy. Thanks very much.

A.

Answer 1

[Mohamed]

http://stackoverflow.com/questions/16146212/how-to-plot-a-hyper-plane-in-3d-for-the-svm-results/19969412#19969412

Answer 2

[manan lalit]

Just putting my answer here in case someone is curious about how to find the analytical equation of the 3-D linear plane separating data belonging to two classes with the fitcsvm function in MATLAB.

You can find the coefficients ( and ) using the two equations below. Quoting from "Support-Vector Networks" by Cortes and Vapnik, 1995, "... the vector that determines the optimal hyperplane can be written as a linear combination of training vectors"

Here, l is the number of support vectors. In MATLAB version 2018b can be extracted using code such as:

SVMModel = fitcsvm(data, groups); 
% "data" contains the (N * D) matrix. 
% "groups" is a (N*1) matrix indicating the two groups (+1 and -1)

alpha = SVMModel.Alpha;

Similarly, can be determined using the equation below:

Once, and are available, then plotting such a plane can be done, in the following manner:

xgrid=[0:200];
ygrid=[0:200];
[X, Y]=meshgrid(xgrid, ygrid);
% w0 and b0 were determined through the two equations mentioned above.
Z=(-b0-w0(1)*X-w0(2)*Y)/w0(3);
surf(X, Y, Z)

[Joy]

I like this analytical solution . Could you please share your example code? I don't exactly get the deriving part.

Thanks!

[Joseph Olson]

w0 and b0 can be extracted with

w0 = SVMModel.Beta;
b0 = SVMModel.Bias;