function D = C4_5(train_features, train_targets, inc_node, region)

% Classify using Quinlan's C4.5 algorithm
% Inputs:
% 	features	- Train features
%	targets	    - Train targets
%	inc_node    - Percentage of incorrectly assigned samples at a node
%	region	    - Decision region vector: [-x x -y y number_of_points]
%
% Outputs
%	D			- Decision sufrace

%NOTE: In this implementation it is assumed that a feature vector with fewer than 10 unique values (the parameter Nu)
%is discrete, and will be treated as such. Other vectors will be treated as continuous

[Ni, M]		= size(train_features);
inc_node    = inc_node*M/100;
Nu          = 10;

%For the decision region
N           = region(5);
mx          = ones(N,1) * linspace (region(1),region(2),N);
my          = linspace (region(3),region(4),N)' * ones(1,N);
flatxy      = [mx(:), my(:)]';

%Preprocessing
%[f, t, UW, m]      = PCA(train_features, train_targets, Ni, region);
%train_features  = UW * (train_features - m*ones(1,M));;
%flatxy          = UW * (flatxy - m*ones(1,N^2));;

%Find which of the input features are discrete, and discretisize the corresponding
%dimension on the decision region
discrete_dim = zeros(1,Ni);
for i = 1:Ni,
   Nb = length(unique(train_features(i,:)));
   if (Nb <= Nu),
      %This is a discrete feature
      discrete_dim(i)	= Nb;
      [H, flatxy(i,:)]	= high_histogram(flatxy(i,:), Nb);
   end
end

%Build the tree recursively
disp('Building tree')
tree        = make_tree(train_features, train_targets, inc_node, discrete_dim, max(discrete_dim), 0);

%Make the decision region according to the tree
disp('Building decision surface using the tree')
targets		= use_tree(flatxy, 1:N^2, tree, discrete_dim, unique(train_targets));

D   		= reshape(targets,N,N);
%END

function targets = use_tree(features, indices, tree, discrete_dim, Uc)
%Classify recursively using a tree

targets = zeros(1, size(features,2));

if (tree.dim == 0)
   %Reached the end of the tree
   targets(indices) = tree.child;
   break
end
        
%This is not the last level of the tree, so:
%First, find the dimension we are to work on
dim = tree.dim;
dims= 1:size(features,1);

%And classify according to it
if (discrete_dim(dim) == 0),
   %Continuous feature
   in				= indices(find(features(dim, indices) <= tree.split_loc));
   targets		= targets + use_tree(features(dims, :), in, tree.child(1), discrete_dim(dims), Uc);
   in				= indices(find(features(dim, indices) >  tree.split_loc));
   targets		= targets + use_tree(features(dims, :), in, tree.child(2), discrete_dim(dims), Uc);
else
   %Discrete feature
   Uf				= unique(features(dim,:));
	for i = 1:length(Uf),
	   in   	   = indices(find(features(dim, indices) == Uf(i)));
      targets	= targets + use_tree(features(dims, :), in, tree.child(i), discrete_dim(dims), Uc);
   end
end
    
%END use_tree 

function tree = make_tree(features, targets, inc_node, discrete_dim, maxNbin, base)
%Build a tree recursively

[Ni, L]    					= size(features);
Uc         					= unique(targets);
tree.dim						= 0;
%tree.child(1:maxNbin)	= zeros(1,maxNbin);
tree.split_loc				= inf;

if isempty(features),
   break
end

%When to stop: If the dimension is one or the number of examples is small
if ((inc_node > L) | (L == 1) | (length(Uc) == 1)),
   H					= hist(targets, length(Uc));
   [m, largest] 	= max(H);
   tree.child	 	= Uc(largest);
   break
end

%Compute the node's I
for i = 1:length(Uc),
    Pnode(i) = length(find(targets == Uc(i))) / L;
end
Inode = -sum(Pnode.*log(Pnode)/log(2));

%For each dimension, compute the gain ratio impurity
%This is done separately for discrete and continuous features
delta_Ib    = zeros(1, Ni);
split_loc	= ones(1, Ni)*inf;

for i = 1:Ni,
   data	= features(i,:);
   Nbins	= length(unique(data));
   if (discrete_dim(i)),
      %This is a discrete feature
		P	= zeros(length(Uc), Nbins);
      for j = 1:length(Uc),
         for k = 1:Nbins,
            indices 	= find((targets == Uc(j)) & (features(i,:) == k));
            P(j,k) 	= length(indices);
         end
      end
      Pk          = sum(P);
      P           = P/L;
      Pk          = Pk/sum(Pk);
      info        = sum(-P.*log(eps+P)/log(2));
      delta_Ib(i) = (Inode-sum(Pk.*info))/-sum(Pk.*log(eps+Pk)/log(2));
   else
      %This is a continuous feature
      P	= zeros(length(Uc), 2);
      
      %Sort the features
      [sorted_data, indices] = sort(data);
      sorted_targets = targets(indices);
      
      %Calculate the information for each possible split
      I	= zeros(1, L-1);
      for j = 1:L-1,
         for k =1:length(Uc),
            P(k,1) = length(find(sorted_targets(1:j) 		== Uc(k)));
            P(k,2) = length(find(sorted_targets(j+1:end) == Uc(k)));
         end
         Ps		= sum(P)/L;
         P		= P/L;
         info	= sum(-P.*log(eps+P)/log(2));
         I(j)	= Inode - sum(info.*Ps);   
      end
      [delta_Ib(i), s] = max(I);
		split_loc(i) = sorted_data(s);      
   end
end

%Find the dimension minimizing delta_Ib 
[m, dim] = max(delta_Ib);
dims		= 1:Ni;
tree.dim = dim;

%Split along the 'dim' dimension
Nf		= unique(features(dim,:));
Nbins	= length(Nf);
if (discrete_dim(dim)),
   %Discrete feature
   for i = 1:Nbins,
      indices    		= find(features(dim, :) == Nf(i));
      tree.child(i)	= make_tree(features(dims, indices), targets(indices), inc_node, discrete_dim(dims), maxNbin, base);
   end
else
   %Continuous feature
   tree.split_loc		= split_loc(dim);
   indices1		   	= find(features(dim,:) <= split_loc(dim));
   indices2	   		= find(features(dim,:) > split_loc(dim));
   tree.child(1)		= make_tree(features(dims, indices1), targets(indices1), inc_node, discrete_dim(dims), maxNbin);
   tree.child(2)		= make_tree(features(dims, indices2), targets(indices2), inc_node, discrete_dim(dims), maxNbin);
end