function [alphas,solution,t]=fisherp(X,J,K,tmax,t,alphas)% FISHERP learns the Fisher classifier using Perceptron rule.%  [alphas,solution,t]=fisherk(X,J,K,tmax,t,alphas)%% FISHERP This algorithm finds the Fisher`s classifier%   by the use of the modified Perceptron algorithm.%   This task is equivalent to finding solution of%   the array of linear nonequalities. The goal is to%   find such alphas(:,i), i=1,2,...K that hold%       alphas(:,i)'*X(:,k) > alphas(:,j)'*X(:,k)  for J(k)=i, i ~= j%%   This algorithm works iteratively and find solution in finite%   number of steps if the solution exists. %% Input:%  X [NxM] matrix containing M training points in N-dimensional%     feture space. X=[x1,x2,...xM].%  J [1xM] vector containing M integer class labels for%     each point from X. Possible are integer values from 1 to K.%  K [1x1] is number of classes.%  tmax [1x1] is upper limit of number of algorithm steps.%%  t [1x1], alphas [NxK] if these arguments enter function then%     the algorithm starts up from the state they define.%     The argument t is an initial step number and matrix 'alphas' %     contains an initial solution.%% Output:%  alphas [NxK] contains found solution. Vector alphas(:,i) coresponds %     the to i-th class.%  solution [1x1] is equal to 1 if solution was found.%                 is equal to 0 if was not found.%  t [1x1] number of iterations.%% See also FISHERK, FISHDEMO, PERCEPTR, KOZINEC.%% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz% Written Vojtech Franc (diploma thesis) 02.01.2000% Modifications% 26-June-2001, V.Franc, comments improved.% 24. 6.00 V. Hlavac, comments polished.% get dim. and # of pointsN=size(X,1);NX=size(X,2);% default settingif nargin < 5,   t=0;endif nargin < 4,   tmax=inf;end% STEP (1)if t==0,   alphas=zeros(N,K);end% iterate until solution is not foundsolution = 0;while solution == 0 & tmax > 0,   tmax = tmax-1;   solution=1;   for i=1:NX,       b=alphas'*X(:,i);      [b,k]=max(b);      j=J(i);      if k ~= j,         % adjust alpha       alphas(:,j)=alphas(:,j)+X(:,i);         alphas(:,k)=alphas(:,k)-X(:,i);         t=t+1;         solution=0;         break;      end   endend