python中决策树分类方法原理,Python实现决策树(Decision Tree)分类

在  https://machinelearningmastery.com/implement-decision-tree-algorithm-scratch-python/ 中给出了CART(Classification and Regression Trees,分类回归树算法,简称CART)算法的Python实现，采用的数据集为Banknote Dataset，关于此数据集的介绍可以参考：http://www.javashuo.com/article/p-npykuehc-bqz.html ，这里在原作者的基础上，进行了略微改动，使其可以直接执行，code如下：

# reference: https://machinelearningmastery.com/implement-decision-tree-algorithm-scratch-python/

# http://zhuanlan.51cto.com/art/201702/531945.htm

# using CART(Classification and Regression Trees,分类回归树算法,简称CART算法)) for classification

# CART on the Bank Note dataset

from random import seed

from random import randrange

from csv import reader

# Load a CSV file

def load_csv(filename):

file = open(filename, "r")

lines = reader(file)

dataset = list(lines)

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 = 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])) # 计算总的样本数

# 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 # row[-1]指每个样本(一行)中最后一列即类别

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):

class_values = list(set(row[-1] for row in dataset)) # class_values的值为: [0, 1]

b_index, b_value, b_score, b_groups = 999, 999, 999, None

for index in range(len(dataset[0])-1): # index的值为: [0, 1, 2, 3]

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} # 返回字典数据类型

# 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(train)

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/database/BacknoteDataset/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) # dataset为嵌套列表的列表，类型为float

# 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))))

执行结果如下：