wehub-resource-sync
58 lines
1.3 KiB
Matlab
Executable File
58 lines
1.3 KiB
Matlab
Executable File
function [model, llh] = mixLogitBin(X, t, k)
|
|
% Mixture of logistic regression model for binary classification optimized by Newton-Raphson method
|
|
% Input:
|
|
% X: d x n data matrix
|
|
% t: 1 x n label (0/1)
|
|
% k: number of mixture component
|
|
% Output:
|
|
% model: trained model structure
|
|
% llh: loglikelihood
|
|
% Written by Mo Chen (sth4nth@gmail.com).
|
|
n = size(X,2);
|
|
X = [X; ones(1,n)];
|
|
d = size(X,1);
|
|
z = ceil(k*rand(1,n));
|
|
R = full(sparse(1:n,z,1,n,k,n)); % n x k
|
|
|
|
W = zeros(d,k);
|
|
tol = 1e-4;
|
|
maxiter = 100;
|
|
llh = -inf(1,maxiter);
|
|
|
|
t = t(:);
|
|
h = ones(n,1);
|
|
h(t==0) = -1;
|
|
A = X'*W;
|
|
for iter = 2:maxiter
|
|
% maximization
|
|
nk = sum(R,1);
|
|
alpha = nk/n;
|
|
Y = sigmoid(A);
|
|
for j = 1:k
|
|
W(:,j) = newtonStep(X, t, Y(:,j), W(:,j), R(:,j));
|
|
end
|
|
% expectation
|
|
A = X'*W;
|
|
logRho = -log1pexp(-bsxfun(@times,A,h));
|
|
logRho = bsxfun(@plus,logRho,log(alpha));
|
|
T = logsumexp(logRho,2);
|
|
llh(iter) = sum(T)/n; % loglikelihood
|
|
logR = bsxfun(@minus,logRho,T);
|
|
R = exp(logR);
|
|
|
|
if abs(llh(iter)-llh(iter-1)) < tol*abs(llh(iter)); break; end
|
|
end
|
|
llh = llh(2:iter);
|
|
model.alpha = alpha; % mixing coefficient
|
|
model.W = W; % logistic model coefficent
|
|
|
|
|
|
function w = newtonStep(X, t, y, w, r)
|
|
lambda = 1e-6;
|
|
v = y.*(1-y).*r;
|
|
H = bsxfun(@times,X,v')*X'+lambda*eye(size(X,1));
|
|
s = (y-t).*r;
|
|
g = X*s;
|
|
w = w-H\g;
|
|
|