- 决策树的构建是一个递归的过程，理想情况下所有的记录都能被精确分类，即生成决策树叶节点都有确定的类型，但现实这种条件往往很难满足，这使得决策树在构建时可能很难停止。即使构建完成，也常常会使得最终的节点数过多，从而导致过度拟合（overfitting），因此在实际应用中需要设定停止条件，当达到停止条件时，直接停止决策树的构建。但这仍然不能完全解决过度拟合问题，过度拟合的典型表现是决策树对训练数据错误率很低，而对测试数据其错误率却非常高。过度拟合常见原因有：（1）训练数据中存在噪声；（2）数据不具有代表性。过度拟合的典型表现是决策树的节点过多，因此实际中常常需要对构建好的决策树进行枝叶裁剪（Prune Tree），但它不能解决根本问题，随机森林算法的出现能够较好地解决过度拟合问题。
下面是随机森林的完整代码，以及数据集，其中有一些部分还不是很懂，感觉需要将随机森林算法的一般步骤给出来，先从整体上来看，然后再去看具体细节！！！
# Random Forest Algorithm on Sonar Dataset
from random import seed
from random import randrange
from csv import reader
from math import sqrt
# 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())
# Convert string column to integer
def str_column_to_int(dataset, column):
class_values = [row[column] for row in dataset]
unique = set(class_values)
lookup = dict()
for i, value in enumerate(unique):
lookup[value] = i
for row in dataset:
row[column] = lookup[row[column]]
return lookup
# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
dataset_split = list()
dataset_copy = list(dataset)
fold_size = int(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, classes):
# count all samples at split point
n_instances = float(sum([len(group) for group in groups]))
# sum weighted Gini index for each group
gini = 0.0
for group in groups:
size = float(len(group))
# avoid divide by zero
if size == 0:
continue
score = 0.0
# score the group based on the score for each class
for class_val in classes:
p = [row[-1] for row in group].count(class_val) / size
score += p * p
# weight the group score by its relative size
gini += (1.0 - score) * (size / n_instances)
return gini
# Select the best split point for a dataset
def get_split(dataset, n_features):
class_values = list(set(row[-1] for row in dataset))
b_index, b_value, b_score, b_groups = 999, 999, 999, None
features = list()
while len(features) < n_features:
index = randrange(len(dataset[0])-1)
if index not in features:
features.append(index)
for index in features:
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, n_features, 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, n_features)
split(node['left'], max_depth, min_size, n_features, depth+1)
# process right child
if len(right) <= min_size:
node['right'] = to_terminal(right)
else:
node['right'] = get_split(right, n_features)
split(node['right'], max_depth, min_size, n_features, depth+1)
# Build a decision tree
def build_tree(train, max_depth, min_size, n_features):
root = get_split(train, n_features)
split(root, max_depth, min_size, n_features, 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']
# Create a random subsample from the dataset with replacement
def subsample(dataset, ratio):
sample = list()
n_sample = round(len(dataset) * ratio)
while len(sample) < n_sample:
index = randrange(len(dataset))
sample.append(dataset[index])
return sample
# Make a prediction with a list of bagged trees
def bagging_predict(trees, row):
predictions = [predict(tree, row) for tree in trees]
return max(set(predictions), key=predictions.count)
# Random Forest Algorithm
def random_forest(train, test, max_depth, min_size, sample_size, n_trees, n_features):
trees = list()
for i in range(n_trees):
sample = subsample(train, sample_size)
tree = build_tree(sample, max_depth, min_size, n_features)
trees.append(tree)
predictions = [bagging_predict(trees, row) for row in test]
return(predictions)
'''数据集：https://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+(Sonar,+Mines+vs.+Rocks)'''
# Test the random forest algorithm
seed(2)
# load and prepare data
filename = '/Users/liuchaoqun01/Desktop/sonar.all-data.csv'
dataset = load_csv(filename)
# convert string attributes to integers
for i in range(0, len(dataset[0])-1):
str_column_to_float(dataset, i)
# convert class column to integers
str_column_to_int(dataset, len(dataset[0])-1)
# evaluate algorithm
n_folds = 5
max_depth = 10
min_size = 1
sample_size = 1.0
n_features = int(sqrt(len(dataset[0])-1))
for n_trees in [1, 5, 10]:
scores = evaluate_algorithm(dataset, random_forest, n_folds, max_depth, min_size, sample_size, n_trees, n_features)
print('Trees: %d' % n_trees)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))
