::::::::::::::
batta_4_select.m
::::::::::::::
function b_dis = batta_4_select(x, cn, mx)

% BATTA_4_SELECT   Bhattacharyya distance given training feature matrix.
% ***************************************************************************
% Inputs:
%    X,  training feature matrix, each row is an ovservation of a feature 
%        vector.
%    CN, class number.
%    MX, training data size in each class.
% Outputs:
%    B_DIS, Distance vector, each element is the distance of a feature. 
% Usage:
%    b_dis = batta_4_select(x, cn, mx);
%    b_dis = batta_4_select(x, cn);
% Defaults:
%    If no MX as input, assume equal data size of all classes.
% Functions: 
%    Batta, Var.        

% Created:       8/30/94, Xiaoou Tang
% Last modified: 2/25/95, X. Tang 
%***************************************************************************

[mall, nall] = size(x);
if nargin == 3
   if length(mx) ~= cn | sum(mx) ~= mall,
      error('Input data matrix does not match its class size discription')
   end
   mx = mx(mx~=0);
   cn = length(mx);
   if cn<2|sum(mx)<cn*3
     cn
     mx
     disp('left over training data too sparse')
   end
   mx = cumsum(mx);
   mx = [0;mx(:)];
elseif nargin == 2
   if rem(mall,cn) ~= 0, 
      error('Invalid input') 
   end
   mx = ones(1,cn)*mall/cn;
   mx = cumsum(mx);
   mx = [0;mx(:)];
else
   error('Wrong input arguement number');
end

var_mat = zeros(cn, nall);
mean_mat = zeros(cn, nall);
for i = 1:cn
%   xclass = x(i*mx+1:i*mx+mx, :);
   xclass = x(mx(i)+1:mx(i+1), :);
   if min(size(xclass)) == 1
      var_mat(i,:) = zeros(size(xclass));
      mean_mat(i,:) = xclass;
   else   
      var_mat(i,:) = var(xclass);
      mean_mat(i,:) = mean(xclass);
   end 
end
var_mat(var_mat==0) = var_mat(var_mat==0)+eps;
b_dis = batta(var_mat, mean_mat);








::::::::::::::
batta.m
::::::::::::::
function [b_dis] = batta(c, m);
% BATTA   Bhattacharyya distance given class means and variances
% ***************************************************************************
% Inputs:
%    C,  Variance matrix, col # = feature #; row # = class #.
%    M,  Mean matrix,  col # = feature #; row # = class #. 
% Outputs:
%    B_DIS, Distance vector, each element is the distance of a feature. 
% Usage:
%    b_dis = batta(c, m);
% Defaults:
% Functions:         

%  Notes: 
%     There are two way to average multiclass distance . One is simply average
%     the Bhatta distance. The other is to average the error bound, that is to 
%     average exp(-B). We use the later one.

% Created:       8/24/94, Xiaoou Tang
% Last modified: 2/25/95, X. Tang
%***************************************************************************

[clus, dim] = size(c);
b_dis = zeros(1, dim);
for k = 1:dim                % feature dimension #
    n = 1;
    for i = 1:clus-1         % class i
        for j = i+1:clus     % class j
            b(n) = 1/4*log((c(i,k)/c(j,k)+c(j,k)/c(i,k)+2)/4)+1/4*(m(i,k)-m(j,k))^2/(c(i,k)+c(j,k));        % kth dimension's class i and j distance
            n = n+1;
        end
    end
    size(b);
%    b_dis(k) = sum(b)/(n-1); 
    b_dis(k) = sum(exp(-b));
end
b_dis = ones(size(b_dis))./(b_dis+eps);   % inverse of the error bound