www.pudn.com > Classification_toolbox.part01.rar > Chernoff.m

function Perror = Chernoff(mu1, sigma1, mu2, sigma2, p1) 
 
% Find the Chernoff bound given means and covariances of single gaussian distributions 
% Inputs: 
%   mu1         - Mean for class 1 
%   sigma1      - Covariance matrix for class 1 
%   mu2         - Mean for class 2 
%   sigma2      - Covariance matrix for class 2 
%   p1          - Probability of class 1 
% 
% Outputs 
%	Perror  	- Error bound 
 
beta    = linspace(0,1,100); 
k       = zeros(1,length(beta)); 
 
%First, claculate k(beta) 
for i = 1:length(beta), 
    k(i) = beta(i)*(1-beta(i))/2*(mu2-mu1)*inv(beta(i)*sigma1+(1-beta(i))*sigma2)*(mu2-mu1)'+... 
              1/2*log(det(beta(i)*sigma1+(1-beta(i))*sigma2)/(det(sigma1)^beta(i)*det(sigma2)^(1-beta(i)))); 
end 
       
%Find the minimum of exp(-k) 
[m, index]  = min(exp(-k)); 
min_beta    = beta(index); 
 
Perror      = p1^min_beta*(1-p1)^(1-min_beta)*exp(-k(index));