How do I get the distance between the point and the hyperplane using libsvm?

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Stef
Stef 2018-7-18
编辑： Stef 2018-8-2
I am using libsvm. I need to know, which observations are farest away from the hyperplane. libsvm returns me the "decision_value" but how can I use it to get the distance from the hyperplane? Taking the largest positive and smallest negative values or do I have to compute it manually and if yes, how?

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Rishabh Gupta
Rishabh Gupta 2018-8-2
Hey Stef
You can find the distance of a point i from hyperplane as follows:
distance_i = |decision_value|_i / |w|-b
where,
w = (alpha * support_vectors)
|w| = sqrt(sum(w^2))
alphas, support_vectors and b is generated from SVM model
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Stef
Stef 2018-8-2
SV_indices contrains the index of the Support vectors in the original matrix. The problem is that I want to find the 5% of observations which are most likely in the -1 category. Therefore I take the x observations which are furthest away from the hyperplane in one direction and the rest (5%-x) which are closest to the hyperplane but in class 1.
Stef
Stef 2018-8-2
编辑：Stef 2018-8-2
See here an example for the fisher Iris. Is there a possibility to find the on which side of the hyperplane the observations are?
load 'fisheriris'
% create X and y
X = meas([1:100],[3:4]);
y = grp2idx(species);
% recode 2 to -1 that lables are 1 and -1
y(y==2) = -1;
%create training and testing sample
rand = randperm(100);
y_train = y(rand([1:80]),:);
X_train = X(rand([1:80]),:);
y_test = y(rand([81:100]),:);
X_test = X(rand([81:100]),:);
% SVM
options =[ '-s 0 -t 0']
[model] = svmtrain(y_train, X_train, options)
[predict_label, accuracy, decision_values] = svmpredict(y_test, X_test, model);
% find distance
w = model.sv_coef' * model.SVs;
w_abs = sqrt(sum(w.^2));
bias = model.rho;
distance = abs(decision_values) ./ (w_abs-bias);

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