function [ ws ] = prob_4_5(Niter)
% PROB_4_5 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Note: I am using the update formula on page 68 equation (4.30) to
% perform the optimization.
% 
%-----

data = [ 0 1 -1 2;
         1 1 1 1;
         2 1 1 1;
         -1 1 0 -1; ];
class = [ 1 2 2 3 ];

d = 0.5;
% Weights that sparate the three classes:
%ws = rand( 3, size(data,2)+1 ); % Row one is for class #1; row two is for class #2, etc.
ws = zeros( 3, size(data,2)+1 ); % Row one is for class #1; row two is for class #2, etc.

%
% Code begins:
%---

% Append +1 to all data: 
data = [ data, ones(size(data,1),1) ]; 

w_history = zeros( Niter, size(ws,2) ); 
for ni=0:Niter+1,
  % Select a sample:
  si = mod( ni, size(data,1) ) + 1;
  
  % Get feature vector and the true classification:
  y_mi = data(si,:).';
  tc   = class(si); 
  
  % Find the predicted classification:
  [mTmp,pc] = max( ws * y_mi + d ); 
  
  % Adjust linear weights if there is a misclassification:
  % 
  e_i = 1;                % Using fixed increment update...
  if( pc ~= tc )
    wstp = ws(tc,:) + e_i * y_mi.';
    wspp = ws(pc,:) - e_i * y_mi.'; 
  else
    wstp = ws(tc,:);
    wspp = ws(pc,:); 
  end
  
  % Prepare for next iteration:
  ws(tc,:) = wstp; 
  ws(pc,:) = wspp; 
end