李航《统计学习方法》第五章——用Python实现决策树（MNIST数据集）

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看了决策树啊，就有那么几个疑问：

1. 决策树是否只能处理特征值可数的情况
2. 决策树是否无法处理不在训练集中出现的特征值

这几个疑问等以后有空的时候在慢慢探索吧！

决策树

按照传统不详述该算法，具体内容可以看《统计学习方法》第五章。

我实现的是ID3算法

这里只将书中算法贴出来

数据集

数据集没什么可以说的，和KNN那个博文用的是同样的数据集。

数据地址：https://github.com/WenDesi/lihang_book_algorithm/blob/master/data/train.csv

特征

将整个图作为特征，但需要二值化处理。

代码

计算信息增益的代码参考的是Avalon的博客

代码已放到Github上，代码注释中标识了书中伪代码的各步骤，因此还算易懂（吐槽一下，这代码相较之前的代码还真不太好写）

#encoding=utf-8

import cv2
import time
import logging
import numpy as np
import pandas as pd


from sklearn.cross_validation 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.cv.CV_THRESH_BINARY_INV,cv_img)
    return cv_img

@log
def binaryzation_features(trainset):
    features = []

    for img in trainset:
        img = np.reshape(img,(28,28))
        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,(-1,784))

    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

        tree = self.dict[features[self.feature]]
        return tree.predict(features)

def calc_ent(x):
    """
        calculate shanno ent 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(x, y):
    """
        calculate ent H(y|x)
    """

    # calc ent(y|x)
    x_value_list = set([x[i] for i in range(x.shape[0])])
    ent = 0.0
    for x_value in x_value_list:
        sub_y = y[x == x_value]
        temp_ent = calc_ent(sub_y)
        ent += (float(sub_y.shape[0]) / y.shape[0]) * temp_ent

    return ent

def calc_ent_grap(x,y):
    """
        calculate ent grap
    """

    base_ent = calc_ent(y)
    condition_ent = calc_condition_ent(x, y)
    ent_grap = base_ent - condition_ent

    return ent_grap

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)
    if len(label_set) == 1:
        return Tree(LEAF,Class = label_set.pop())

    # 步骤2——如果features为空
    (max_class,max_len) = max([(i,len(filter(lambda x:x==i,train_label))) for i in xrange(total_class)],key = lambda x:x[1])

    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 = filter(lambda x:x!=max_feature,features)
    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 xrange(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):
    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.csv',header=0)
    data = raw_data.values

    imgs = data[0::,1::]
    labels = data[::,0]

    # 图片二值化
    features = binaryzation_features(imgs)

    # 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, random_state=23323)

    tree = train(train_features,train_labels,[i for i in range(784)],0.1)
    test_predict = predict(test_features,tree)
    score = accuracy_score(test_labels,test_predict)

    print "The accruacy socre is ", score

运行结果

准确率一般，预测速度到挺快的。