ekozinec.m

svm在matlab中的应用的一些程序以及说明

function [alpha,theta,solution,t]=ekozinec(X,J,epsilon,tmax,t,alpha,theta)
% EKOZINEC finds epsilon-optimal decision hyperplane, dichotomy.
% [alpha,theta,solution,t]=ekozinec(X,J,epsilon,tmax,t,alpha,theta)
%
% EKOZINEC find epsilon-optimal solution by the help of modified Kozinec's
%  algorithm. This algorithm finds a vector alpha and a threshold theta
%  which hold 
%  1)   alpha' * x >= theta    for x=X(:,i), J(i)=1 (1st class)
%       alpha' * x < theta     for x=X(:,i), J(i)=2 (2nd class)
%
%  2) quality( alpha_o, theta_o ) - quality ( alpha, theta ) <= epsilon
%  Where the quality is, informaly speaking, a boundary width between 
%  the classes (see html-documentaion for more details).
%
% This algorithm works iteratively and if input classes are linearly 
% separable then it stops in finite number of steps. This 
% implementation allows to limit maximal number of steps and allows to 
% start the algorithm from defined state which is determined with alpha 
% and theta.
%
%  Input:
%   X [DxM] contains M training points in D-dimensional the feature 
%      space. X=[x1,x2,..XM] where xi is i-th column vectors.
%   J [1xM] contains class labels of the points in X. A class label 
%      has  to be 1 for the first class and 2 for the second class.
%   epsilon [1x1] desired quality of the solution.
%   tmax [1x1] 1. if is integer tmax > 0 then it determines a maximal 
%      number of algorithm steps, i.e. if the solution is not found 
%      until tmax-th step the algorithm will exit and set solution = 0.
%      2. if tmax==-1, then the algorithm only returns, in the variable
%      alpha, badly classified point which would have been used in
%      the adaptation step but the adaptation is not performed.
%   t [1x1], alpha [Dx1], theta [1x1] if this arguments enter function
%      the algorithm starts from the state which they determine.
%
%  Output:
%   alpha [Dx1] found normal vector of the hyperplane or, if tmax==-1,
%      badly classified point.
%   theta [1x1] found threshold of the hyperplane.
%   solution [1x1], 1 ... solution is found,
%                   0 ... solution is not found.
%   t [1x1] is number of steps the algorithm performed.
%
% See also KOZINEC, PERCEPTR, LINSVM.
%

% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac
% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz
% Written Vojtech Franc (diploma thesis) 02.11.1999, 13.4.2000
% Modifications
% 18-apr-2001, V.Franc, stop condition repared.
% 15-dec-2000, V. Franc, returns bad point.
% 24. 6.00 V. Hlavac, comments polished.

% Process input arguments
if nargin < 5,
   t=0;
   alpha=0;
   theta=0;
end
if nargin < 4,
   tmax=inf;
end

% Transform original feature space into the homogenous (theta=0)
% coordinates.
[alpha,X]=ctransf(alpha,theta,X,J);

N=size(X,1);    % dimension
K=size(X,2);    % number of thraing poins

% It returns only the first wrong classified point which 
% will be used for updating solution.
% ----------------------------------------------------
if tmax == -1,

   % find minimum of ((alpha/|alpha|)*x)
   anormal=sqrt(alpha'*alpha);
   [minr,mini]=min((alpha/anormal)'*X);

   if (anormal-minr) > epsilon,

      x=X(:,mini);
      if J(mini)==1,
        alpha = x(1:(end-1));
      else
        alpha = -x(1:(end-1));
      end
      solution=0;
      return;
   end % if

   solution=1;
   return;
else

  % Perform the step t=0.
  % alpha = any vector from X, for example the first.
  if t==0,
     alpha=X(:,1);
     t=1;
     tmax=tmax-1;
  end

% Iterate until solution is found or
% number of steps exceeds given limit tmax.
% ------------------------------------------------- 
  solution=0;
  while solution == 0 & tmax > 0,
    tmax = tmax-1;
    solution=1;

    % Find minimum of ((alpha/|alpha|)*x).
    anormal=sqrt(alpha'*alpha);
    [minr,mini]=min((alpha/anormal)'*X);

    % Check, if the solution of required quality is already found.
    if ((anormal-minr) > epsilon) | ((anormal-minr) < epsilon & minr < 0),

       % Update  alpha
       x=X(:,mini);
       k=min(1,abs((alpha-x)'*alpha/((alpha-x)'*(alpha-x))));
       alpha=(1-k)*alpha+k*x;
       t=t+1;
       solution=0;
    end % if
  end % while
end  % if, else

% Transform the found solution from the homogenous coordinates
% into original space.
[alpha,theta]=ictransf(alpha);