function D = CART(train_features, train_targets, params, region)
% Classify using classification and regression trees
% Inputs:
% features - Train features
% targets - Train targets
% params - [Impurity type, Percentage of incorrectly assigned samples at a node]
% Impurity can be: Entropy, Variance (or Gini), or Missclassification
% region - Decision region vector: [-x x -y y number_of_points]
%
% Outputs
% D - Decision sufrace
[Ni, M] = size(train_features);
%Get parameters
[split_type, inc_node] = process_params(params);
%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));;
%Build the tree recursively
disp('Building tree')
tree = make_tree(train_features, train_targets, M, split_type, inc_node, region);
%Make the decision region according to the tree
disp('Building decision surface using the tree')
targets = use_tree(flatxy, 1:N^2, tree);
D = reshape(targets,N,N);
%END
function targets = use_tree(features, indices, tree)
%Classify recursively using a tree
if isnumeric(tree.Raction)
%Reached an end node
targets = zeros(1,size(features,2));
targets(indices) = tree.Raction(1);
else
%Reached a branching, so:
%Find who goes where
in_right = indices(find(eval(tree.Raction)));
in_left = indices(find(eval(https://www.doczj.com/doc/1811420298.html,ction)));
Ltargets = use_tree(features, in_left, tree.left);
Rtargets = use_tree(features, in_right, tree.right);
targets = Ltargets + Rtargets;
end
%END use_tree
function tree = make_tree(features, targets, Dlength, split_type, inc_node, region)
%Build a tree recursively
if (length(unique(targets)) == 1),
%There is only one type of targets, and this generates a warning, so deal with it separately
tree.right = [];
tree.left = [];
tree.Raction = targets(1);
https://www.doczj.com/doc/1811420298.html,ction = targets(1);
break
end
[Ni, M] = size(features);
Nt = unique(targets);
N = hist(targets, Nt);
if ((sum(N < Dlength*inc_node) == length(Nt) - 1) | (M == 1)),
%No further splitting is neccessary
tree.right = [];
tree.left = [];
if (length(Nt) ~= 1),
MLlabel = find(N == max(N));
else
MLlabel = 1;
end
tree.Raction = Nt(MLlabel);
https://www.doczj.com/doc/1811420298.html,ction = Nt(MLlabel);
else
%Split the node according to the splitting criterion
deltaI = zeros(1,Ni);
split_point = zeros(1,Ni);
op = optimset('Display', 'off');
for i = 1:Ni,
split_point(i) = fminbnd('CARTfunctions', region(i*2-1), region(i*2), op, features, targets, i, split_type);
I(i) = feval('CARTfunctions', split_point(i), features, targets, i, split_type);
end
[m, dim] = min(I);
loc = split_point(dim);
%So, the split is to be on dimention 'dim' at location 'loc'
indices = 1:M;
tree.Raction= ['features(' num2str(dim) ',indices) > ' num2str(loc)];
https://www.doczj.com/doc/1811420298.html,ction= ['features(' num2str(dim) ',indices) <= ' num2str(loc)];
in_right = find(eval(tree.Raction));
in_left = find(eval(https://www.doczj.com/doc/1811420298.html,ction));
if isempty(in_right) | isempty(in_left)
%No possible split found
tree.right = [];
tree.left = [];
if (length(Nt) ~= 1),
MLlabel = find(N == max(N));
else
MLlabel = 1;
end
tree.Raction = Nt(MLlabel);
https://www.doczj.com/doc/1811420298.html,ction = Nt(MLlabel);
else
%...It's possible to build new nodes
tree.right = make_tree(features(:,in_right), targets(in_right), Dlength, split_type, inc_node, region);
tree.left = make_tree(features(:,in_left), targets(in_left), Dlength, split_type, inc_node, region);
end
end