function [alpha,theta,solution,t,lambda,gamma,maxerr]=...   oanders(MI,SIGMA,J,tmax,delta,t,lambda)% OANDERS solves the original Anderson's task, two Gaussians.% [alpha,theta,solution,t,lambda,gamma,maxerr]=...%    oanders(MI,SIGMA,J,tmax,delta,t,lambda)%% OANDERS solves Anderson-Bahadur's task. The goal is to separate two %   classes in order to minimize probability of bad classification. %   Each class is described by conditional probability density function p(x|k) %   (where x is observation and k is class 1 or 2) which has normal %   distribution. %% Input:% (notation: N is dimension of feature space)% OANDERS(MI,SIGMA,J,tmax,delta)%   MI [Nx2] matrix containing two column vectors of mean values %      MI = [mi_1,mi_2].%   SIGMA [Nx(2*N)] matrix containing two square covariance matrices N-by-N,%      SIGMA = [Sigma1,Sigma2].%   J [1x2] vector containing class labels (1 and 2) for pairs of arguments %      {mi_i,sigma_i}. (Note: the vector J can contain one of following %      combinatins J=[1,2] or J=[2,1]).%   tmax [1x1] is maximal number of steps of the algorithm. Acceptable%      value is positive integer or inf (which means infinity).%   delta [1x1] is positive real number which determines accuracy of finding%      solution (note: setting delta=0 means that the most accurate solution %      will be finding). The algorithm works until desired accuracy is%      achieved or maximal step number is exceeded.%% OANDERS(MI,SIGMA,J,tmax,delta,t,lambda) begins from state given by%   t [1x1] is initial step number.%   lambda [1x1] real number which is state variable of the algorithm %% Output:%   alpha [Nx1] is normal vector of found separation hyperplane.%   theta [1x1] is threshold of found separation hyperplane.%   solution [1x1] contains 0 if solution is not found (step number exceeded)%                  contains 1 is solution is found%   t [1x1] is step number in which the algorithm halted.%   lambda [1x1], gamma [1x1] are status variables of the algorithm.%   maxerr [1x1] is upper bound of probability of bad classification.%% See also GANDERS, GANDERS2, EANDERS, GGANDERS.%% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz% Written Vojtech Franc (diploma thesis) 04.11.1999, 6.5.2000% Modifications% 24. 6.00 V. Hlavac, comments polished.% 1. 8. 00 V. Franc, comments changed% default settingif nargin < 6,   t=0;end% determines precision of result (0 the most precise)if nargin < 5,   delta=0;endif nargin < 4,  tmax=inf;endif nargin < 3,  error('Not enought input arguments.');end% if the function is called for first if t==0,   lambda=0.5;   t=1;end% get dimension and number of the distributionsN=size(MI,1);K=size(MI,2);% get mi and sigma for the first and second class class1=0;class2=0;for i=1:K,   if J(i)==1 & class1==0,      class1=1;      mi1=MI(:,i);      sg1=SIGMA(:,(i-1)*N+1:i*N);   elseif J(i)==2 & class2==0,      class2=1;      mi2=MI(:,i);      sg2=SIGMA(:,(i-1)*N+1:i*N);   endend% start iterationssolution=0;while tmax > 0 & solution==0,   tmax=tmax-1;   % perform one iteration   alpha=inv((1-lambda)*sg1+lambda*sg2)*(mi1-mi2);   gamma=sqrt((alpha'*sg2*alpha)/(alpha'*sg1*alpha));   % if the last change of gamma is smaller then delta then   if abs( gamma - (1-lambda)/lambda ) < delta,      solution=1;      t=t;   else      % updtate lambda      t=t+1;      lambda=1/(1+gamma);   endend% compute thetatheta=lambda*(alpha'*sg2*alpha)+(alpha'*mi2);% upper bound of probability of bad classificationmaxerr=andrerr(MI,SIGMA,J,alpha,theta);