function D = ID3(train_features, train_targets, params, region)

% Classify using Quinlan?s ID3 algorithm
% Inputs:
% features - Train features
% targets     - Train targets
% params - [Number of bins for the data, Percentage of incorrectly assigned samples at a node]
% region     - Decision region vector: [-x x -y y number_of_points]
%
% Outputs
% D - Decision sufrace

[Ni, M]    = size(train_features);

%Get parameters
[Nbins, inc_node] = process_params(params);
inc_node    = inc_node*M/100;

%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));;

%First, bin the data and the decision region data
[H, binned_features]= high_histogram(train_features, Nbins, region);
[H, binned_xy]      = high_histogram(flatxy, Nbins, region);

%Build the tree recursively
disp(?Building tree?)
tree        = make_tree(binned_features, train_targets, inc_node, Nbins);

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

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

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

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

if (size(features,1) == 1),
    %Only one dimension left, so work on it
    for i = 1:Nbins,
        in = indices(find(features(indices) == i));
        if ~isempty(in),
            if isfinite(tree.child(i)),
                targets(in) = tree.child(i);
            else
                %No data was found in the training set for this bin, so choose it randomally
                n           = 1 + floor(rand(1)*length(Uc));
                targets(in) = Uc(n);
            end
        end
    end
    break
end
        
%This is not the last level of the tree, so:
%First, find the dimension we are to work on
dim = tree.split_dim;
dims= find(~ismember(1:size(features,1), dim));

%And classify according to it
for i = 1:Nbins,
    in      = indices(find(features(dim, indices) == i));
    targets = targets + use_tree(features(dims, :), in, tree.child(i), Nbins, Uc);
end
    
%END use_tree

function tree = make_tree(features, targets, inc_node, Nbins)
%Build a tree recursively

[Ni, L]     = size(features);
Uc          = unique(targets);

%When to stop: If the dimension is one or the number of examples is small
if ((Ni == 1) | (inc_node > L)),
    %Compute the children non-recursively
    for i = 1:Nbins,
        tree.split_dim  = 0;
        indices         = find(features == i);
        if ~isempty(indices),
            if (length(unique(targets(indices))) == 1),
                tree.child(i) = targets(indices(1));
            else
                H               = hist(targets(indices), Uc);
                [m, T]          = max(H);
                tree.child(i)   = Uc(T);
            end
        else
            tree.child(i)   = inf;
        end
    end
    break
end

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

%For each dimension, compute the gain ratio impurity
delta_Ib    = zeros(1, Ni);
P           = zeros(length(Uc), Nbins);
for i = 1:Ni,
    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));
end

%Find the dimension minimizing delta_Ib
[m, dim] = max(delta_Ib);

%Split along the ?dim? dimension
tree.split_dim = dim;
dims           = find(~ismember(1:Ni, dim));
for i = 1:Nbins,
    indices       = find(features(dim, :) == i);
    tree.child(i) = make_tree(features(dims, indices), targets(indices), inc_node, Nbins);
end