function model = llsvm(x,r,y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% a simple implementation of LL-SVM 
%%% (Ladický and Torr, Locally Linear Support Vector Machines, ICML'11)
%%%
%%% inputs: 
%%% x:  input data (D1*N matrix, a vector for each data)
%%% r:  the coordinate coefficients (D2*N matrix, a vector for each data)
%%% y:  data labels (1*N vector, 1...L)
%%% outputs:
%%% model: multiclass svm model (learned by liblinear)
%%%
%%% NOTICE:
%%% (1) In the original paper, the margin is defined as H(x)=r(x)^T*W*x+r(x)^T*b, 
%%% where r(x) is a vector, W is a matrix, x is a vector, and b is a vector. 
%%% Here, I represent each data x as a matrix x=r(x)*x^T and vectorize it,
%%% and correspondingly W is represented as a long vector, and b=r(x)^T*b.
%%% (2) Here liblinear toolbox (Fan et. al., LIBLINEAR: A library for large 
%%% linear classification,JMLR'08) is used instead of stochastic gradient decent
%%% to learn W and b.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% represent the data for learning
[D1 N] = size(x);
[D2 N] = size(r);
d = zeros(D1*D2,N,'single');
for i = 1:N    
    X = x(:,i)*r(:,i)';   
    d(:,i) = X(:);
end    

%%% multiclass svm (liblinear, parameters should be tuned)
L = max(y);
h = hist(y,1:L);
h = max(h)./h;
str = [];
for i = 1:L
    str = [str,' -w',num2str(i),' ',num2str(h(i))];
end
d = sparse(double(d'));
model = train(double(y'),d,['-s 1 -B 1 -c 1e1',str]);   

%%% classification can be performed using the "predict" function in the 
%%% liblinear toolbox

return