# Example of CART on the Banknote dataset from random import seed from random import randrange from csv import reader # Load a CSV file def load_csv(filename): dataset = list() with open(filename, 'r') as file: csv_reader = reader(file) for row in csv_reader: if not row: continue dataset.append(row) return dataset # Convert string column to float def str_column_to_float(dataset, column): for row in dataset: row[column] = float(row[column].strip()) # Split a dataset into k folds def cross_validation_split(dataset, n_folds): dataset_split = list() dataset_copy = list(dataset) fold_size = len(dataset) / n_folds for i in range(n_folds): fold = list() while len(fold) < fold_size: index = randrange(len(dataset_copy)) fold.append(dataset_copy.pop(index)) dataset_split.append(fold) return dataset_split # Calculate accuracy percentage def accuracy_metric(actual, predicted): correct = 0 for i in range(len(actual)): if actual[i] == predicted[i]: correct += 1 return correct / float(len(actual)) * 100.0 # Evaluate an algorithm using a cross validation split def evaluate_algorithm(dataset, algorithm, n_folds, *args): folds = cross_validation_split(dataset, n_folds) scores = list() for fold in folds: train_set = list(folds) train_set.remove(fold) train_set = sum(train_set, []) test_set = list() for row in fold: row_copy = list(row) test_set.append(row_copy) row_copy[-1] = None predicted = algorithm(train_set, test_set, *args) actual = [row[-1] for row in fold] accuracy = accuracy_metric(actual, predicted) scores.append(accuracy) return scores # Split a dataset based on an attribute and an attribute value def test_split(index, value, dataset): left, right = list(), list() for row in dataset: if row[index] < value: left.append(row) else: right.append(row) return left, right # Calculate the Gini index for a split dataset def gini_index(groups, class_values): gini = 0.0 for class_value in class_values: for group in groups: size = len(group) if size == 0: continue proportion = [row[-1] for row in group].count(class_value) / float(size) gini += (proportion * (1.0 - proportion)) return gini # Select the best split point for a dataset def get_split(dataset): class_values = list(set(row[-1] for row in dataset)) b_index, b_value, b_score, b_groups = 999, 999, 999, None for index in range(len(dataset[0])-1): for row in dataset: groups = test_split(index, row[index], dataset) gini = gini_index(groups, class_values) if gini < b_score: b_index, b_value, b_score, b_groups = index, row[index], gini, groups return {'index':b_index, 'value':b_value, 'groups':b_groups} # Create a terminal node value def to_terminal(group): outcomes = [row[-1] for row in group] return max(set(outcomes), key=outcomes.count) # Create child splits for a node or make terminal def split(node, max_depth, min_size, depth): left, right = node['groups'] del(node['groups']) # check for a no split if not left or not right: node['left'] = node['right'] = to_terminal(left + right) return # check for max depth if depth >= max_depth: node['left'], node['right'] = to_terminal(left), to_terminal(right) return # process left child if len(left) <= min_size: node['left'] = to_terminal(left) else: node['left'] = get_split(left) split(node['left'], max_depth, min_size, depth+1) # process right child if len(right) <= min_size: node['right'] = to_terminal(right) else: node['right'] = get_split(right) split(node['right'], max_depth, min_size, depth+1) # Build a decision tree def build_tree(train, max_depth, min_size): root = get_split(dataset) split(root, max_depth, min_size, 1) return root # Make a prediction with a decision tree def predict(node, row): if row[node['index']] < node['value']: if isinstance(node['left'], dict): return predict(node['left'], row) else: return node['left'] else: if isinstance(node['right'], dict): return predict(node['right'], row) else: return node['right'] # Classification and Regression Tree Algorithm def decision_tree(train, test, max_depth, min_size): tree = build_tree(train, max_depth, min_size) predictions = list() for row in test: prediction = predict(tree, row) predictions.append(prediction) return(predictions) # Test CART on Bank Note dataset seed(1) # load and prepare data filename = 'data_banknote_authentication.csv' dataset = load_csv(filename) # convert string attributes to integers for i in range(len(dataset[0])): str_column_to_float(dataset, i) # evaluate algorithm n_folds = 5 max_depth = 5 min_size = 10 scores = evaluate_algorithm(dataset, decision_tree, n_folds, max_depth, min_size) print('Scores: %s' % scores) print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))