function test_targets = C4_5(train_patterns, train_targets, test_patterns, inc_node)

% Classify using Quinlan's C4.5 algorithm
% Inputs:
% 	training_patterns   - Train patterns
%	training_targets	- Train targets
%   test_patterns       - Test  patterns
%	inc_node            - Fraction of incorrectly assigned samples at a node
%
% Outputs
%	test_targets        - Predicted targets

%NOTE: In this implementation it is assumed that a pattern 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_patterns);
inc_node    = inc_node*M/100;
Nu          = 10;

%Find which of the input patterns are discrete, and discretisize the corresponding
%dimension on the test patterns
discrete_dim = zeros(1,Ni);
for i = 1:Ni,
    Ub = unique(train_patterns(i,:));
    Nb = length(Ub);
    if (Nb <= Nu),
        %This is a discrete pattern
        discrete_dim(i)	= Nb;
        dist            = abs(ones(Nb ,1)*test_patterns(i,:) - Ub'*ones(1, size(test_patterns,2)));
        [m, in]         = min(dist);
        test_patterns(i,:)  = Ub(in);
    end
end

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

%Classify test samples
disp('Classify test samples using the tree')
test_targets    = use_tree(test_patterns, 1:size(test_patterns,2), tree, discrete_dim, unique(train_targets));

%END

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

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

if (tree.dim == 0)
    %Reached the end of the tree
    targets(indices) = tree.child;
    return
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(patterns,1);

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

%END use_tree

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

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

if isempty(patterns),
    return
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);
    return
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 patterns
delta_Ib    = zeros(1, Ni);
split_loc	= ones(1, Ni)*inf;

for i = 1:Ni,
    data	= patterns(i,:);
    Ud      = unique(data);
    Nbins	= length(Ud);
    if (discrete_dim(i)),
        %This is a discrete pattern
        P	= zeros(length(Uc), Nbins);
        for j = 1:length(Uc),
            for k = 1:Nbins,
                indices 	= find((targets == Uc(j)) & (patterns(i,:) == Ud(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 pattern
        P	= zeros(length(Uc), 2);

        %Sort the patterns
        [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;
            
            Pk      = sum(P);            
            P1      = repmat(Pk, length(Uc), 1);
            P1(find(P1==0)) = eps;
            
            info	= sum(-P.*log(eps+P./P1)/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(patterns(dim,:));
Nbins	= length(Nf);
if (discrete_dim(dim)),
    %Discrete pattern
    for i = 1:Nbins,
        indices    	= find(patterns(dim, :) == Nf(i));
        tree.child(i)	= make_tree(patterns(dims, indices), targets(indices), inc_node, discrete_dim(dims), maxNbin, base);
    end
else
    %Continuous pattern
    tree.split_loc	= split_loc(dim);
    indices1		   	= find(patterns(dim,:) <= split_loc(dim));
    indices2	   		= find(patterns(dim,:) > split_loc(dim));
    if ~(isempty(indices1) | isempty(indices2))
        tree.child(1)	= make_tree(patterns(dims, indices1), targets(indices1), inc_node, discrete_dim(dims), maxNbin, base+1);
        tree.child(2)	= make_tree(patterns(dims, indices2), targets(indices2), inc_node, discrete_dim(dims), maxNbin, base+1);
    else
        H				= hist(targets, length(Uc));
        [m, largest] 	= max(H);
        tree.child	 	= Uc(largest);
        tree.dim                = 0;
    end
end