统计学习方法第二章：感知机(perceptron)算法及python实现
统计学习方法第三章：k近邻法(k-NN),kd树及python实现
统计学习方法第四章：朴素贝叶斯法(naive Bayes)，贝叶斯估计及python实现
统计学习方法第五章：决策树(decision tree),CART算法，剪枝及python实现
统计学习方法第五章：决策树(decision tree),ID3算法，C4.5算法及python实现
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决策树(decision tree)是一种基本的分类与回归方法。决策树模型呈树状结构，在分类问题中，表示基于特征对实例进行分类的过程。
它可以认为是if-then规则的集合，也可以认为是定义在特征空间与类空间上的条件概率分布。
其主要优点是模型具有可读性，分类速度快。
学习时，利用训练数据，根据损失函数最小化的原则建立决策树模型。预测时，对新的数据，利用决策树模型进行分类。
决策树学习通常包括3个步骤：特征选择，决策树的生成和决策树的修剪
主要的决策树算法包括ID3,C4.5,CART。
ID3算法的核心是在决策树各个结点上应用信息增益准则选择特征，递归的构建决策树。具体方法是：从根结点开始，对结点计算所有特征的信息增益，选择信息增益最大的特征作为结点的特征，由该特征的不同取值建立子结点；再对子结点递归的调用以上方法，构建决策树直到所有特征的信息增益很小或没有特征可以选择为止。最后得到一个决策树。ID3相当于用极大似然法进行概率模型的选择。
ID3算法
ID3算法
代码如下：
import cv2
import time
import logging
import numpy as np
import pandas as pd
import random
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
total_class = 10
def log(func):
def wrapper(*args, **kwargs):
start_time = time.time()
logging.debug('start %s()' % func.__name__)
ret = func(*args, **kwargs)
end_time = time.time()
logging.debug('end %s(), cost %s seconds' % (func.__name__, end_time - start_time))
return ret
return wrapper
# 二值化
def binaryzation(img):
cv_img = img.astype(np.uint8)
cv2.threshold(cv_img, 50, 1, cv2.THRESH_BINARY, cv_img)
return cv_img
@log
def binaryzation_features(trainset):
features = []
for img in trainset:
img = np.reshape(img, (10, 10))
cv_img = img.astype(np.uint8)
img_b = binaryzation(cv_img)
# hog_feature = np.transpose(hog_feature)
features.append(img_b)
features = np.array(features)
features = np.reshape(features, (-1, 100))
return features
class Tree(object):
def __init__(self, node_type, Class=None, feature=None):
self.node_type = node_type
self.dict = {}
self.Class = Class
self.feature = feature
def add_tree(self, val, tree):
self.dict[val] = tree
def predict(self, features):
if self.node_type == 'leaf':
return self.Class
if (features[self.feature] in self.dict.keys()):
tree = self.dict[features[self.feature]]
else:
if (self.Class is None):
return random.randint(0, 1)
else:
return self.Class
return tree.predict(features)
def calc_ent(x):
"""
calculate empirical entropy of x
"""
x_value_list = set([x[i] for i in range(x.shape[0])])
ent = 0.0
for x_value in x_value_list:
p = float(x[x == x_value].shape[0]) / x.shape[0]
logp = np.log2(p)
ent -= p * logp
return ent
def calc_condition_ent(train_feature, train_label):
"""
calculate empirical entropy H(y|x)
"""
# calc ent(y|x)
ent = 0
train_feature_set = set(train_feature)
# print("train_feature_set", train_feature_set)
for train_feature_value in train_feature_set:
Di = train_feature[train_feature == train_feature_value]
label_i = train_label[train_feature == train_feature_value]
# print("Di", Di)
train_label_set = set(train_label)
temp = 0
# print("train_label_set", train_label_set)
for train_label_value in train_label_set:
Dik = Di[label_i == train_label_value]
# print(Dik)
if (len(Dik) != 0):
p = float(len(Dik)) / len(Di)
logp = np.log2(p)
temp -= p * logp
ent += float(len(Di)) / len(train_feature) * temp
return ent
def recurse_train(train_set, train_label, features, epsilon):
global total_class
LEAF = 'leaf'
INTERNAL = 'internal'
# 步骤1——如果train_set中的所有实例都属于同一类Ck
label_set = set(train_label)
# print(label_set)
if len(label_set) == 1:
return Tree(LEAF, Class=label_set.pop())
# 步骤2——如果features为空
class_count0 = 0
class_count1 = 0
for i in range(len(train_label)):
if (train_label[i] == 1):
class_count1 += 1
else:
class_count0 += 1
if (class_count0 >= class_count1):
max_class = 0
else:
max_class = 0
if features is None:
return Tree(LEAF, Class=max_class)
if len(features) == 0:
return Tree(LEAF, Class=max_class)
# 步骤3——计算信息增益
max_feature = 0
max_gda = 0
D = train_label
HD = calc_ent(D)
for feature in features:
A = np.array(train_set[:, feature].flat)
gda = HD - calc_condition_ent(A, D)
if gda > max_gda:
max_gda, max_feature = gda, feature
# 步骤4——小于阈值
if max_gda < epsilon:
return Tree(LEAF, Class=max_class)
# 步骤5——构建非空子集
sub_features = features.remove(max_feature)
tree = Tree(INTERNAL, feature=max_feature)
feature_col = np.array(train_set[:, max_feature].flat)
feature_value_list = set([feature_col[i] for i in range(feature_col.shape[0])])
for feature_value in feature_value_list:
index = []
for i in range(len(train_label)):
if train_set[i][max_feature] == feature_value:
index.append(i)
sub_train_set = train_set[index]
sub_train_label = train_label[index]
sub_tree = recurse_train(sub_train_set, sub_train_label, sub_features, epsilon)
tree.add_tree(feature_value, sub_tree)
return tree
@log
def train(train_set, train_label, features, epsilon):
# print(features)
return recurse_train(train_set, train_label, features, epsilon)
@log
def predict(test_set, tree):
result = []
for features in test_set:
tmp_predict = tree.predict(features)
result.append(tmp_predict)
return np.array(result)
if __name__ == '__main__':
logger = logging.getLogger()
logger.setLevel(logging.DEBUG)
raw_data = pd.read_csv('../data/train_binary2.csv', header=0)
data = raw_data.values
images = data[0:, 1:]
labels = data[:, 0]
# 图片二值化
features = binaryzation_features(images)
# 选取 2/3 数据作为训练集， 1/3 数据作为测试集
train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33,randomstate=1)
# print(train_features.shape)
tree = train(train_features, train_labels, [i for i in range(99)], 0.1)
test_predict = predict(test_features, tree)
# print(test_predict)
score = accuracy_score(test_labels, test_predict)
print("The accuracy score is ", score)
实现中最主要的还是对信息增益的计算，特征选择后结点的分类以及递归调用
但我这个正确率其实挺低的，自己也百思不得其解，我觉得关键算法应该是没有问题，如果有大神看出问题了希望指正！
C4.5算法
C4.5算法其实与ID3类似，主要的不同就是C4.5使用信息增益比来选择特征
C4.5算法
代码如下：
def recurse_train(train_set, train_label, features, epsilon):
LEAF = 'leaf'
INTERNAL = 'internal'
# 步骤1——如果train_set中的所有实例都属于同一类Ck
label_set = set(train_label)
# print(label_set)
if len(label_set) == 1:
return Tree(LEAF, Class=label_set.pop())
# 步骤2——如果features为空
class_count0 = 0
class_count1 = 0
for i in range(len(train_label)):
if (train_label[i] == 1):
class_count1 += 1
else:
class_count0 += 1
if (class_count0 >= class_count1):
max_class = 0
else:
max_class = 0
if features is None:
return Tree(LEAF, Class=max_class)
if len(features) == 0:
return Tree(LEAF, Class=max_class)
# 步骤3——计算信息增益
max_feature = 0
max_grda = 0
D = train_label
HD = calc_ent(D)
for feature in features:
A = np.array(train_set[:, feature].flat)
gda = HD - calc_condition_ent(A, D)
had = calc_ent(A)
grda = gda / had
if grda > max_grda:
max_grda, max_feature = grda, feature
# 步骤4——小于阈值
if max_grda < epsilon:
return Tree(LEAF, Class=max_class)
# 步骤5——构建非空子集
sub_features = features.remove(max_feature)
tree = Tree(INTERNAL, feature=max_feature)
feature_col = np.array(train_set[:, max_feature].flat)
feature_value_list = set([feature_col[i] for i in range(feature_col.shape[0])])
for feature_value in feature_value_list:
index = []
for i in range(len(train_label)):
if train_set[i][max_feature] == feature_value:
index.append(i)
sub_train_set = train_set[index]
sub_train_label = train_label[index]
sub_tree = recurse_train(sub_train_set, sub_train_label, sub_features, epsilon)
tree.add_tree(feature_value, sub_tree)
return tree
与ID3代码的不同只有在特征选择时的标准不同
在写代码的过程中参考了别人的实现，水平有限，如有错误，希望指出
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