决策树算法(DecisionTree)

手动实现决策树算法

1. 算法使用如下数据集（来自统计学习方法）：

   https://github.com/xu1995yong/ml/tree/master/python%E5%AE%9E%E7%8E%B0

2. 代码：

   from pandas import Seriesimport numpy as npclass DecisionTree:    def __init__(self):        self.tree = None    def entropy(self,data,y):    '''        求经验熵    '''        m = data.shape[0]        yType = Series(y).unique()        count = []        for v in yType:            sub_data = data[np.where(y == v)]            count.append(sub_data.shape[0])        p = np.array(count) / m         s = np.dot(-1 * p,np.log2(p))        return s    def conditionalEntropy(self,xi,y):          '''            计算特征A对数据集D的经验条件熵        '''        m = xi.shape[0]        s = 0        for i in Series(xi).value_counts().index:            sub_xi = xi[np.where(xi == i)]            sub_y = y[np.where(xi == i)]            p = self.entropy(sub_xi,sub_y) #计算特征A的某个取值的经验熵            s += 1.0 * sub_xi.shape[0] / m * p        return s    def infoGain(self,x,y):        n = x.shape[1]        index = None        g = None        for i in range(n):            t = self.entropy(y,y) - self.conditionalEntropy(x[:,i],y)  #计算每个特征的信息增益            if i == 0:                g = t                index = 0            if t > g:                g = t                index = i        return index,g    def train(self,x,y,theta):        if np.sum(y == y[0]) == y.shape[0]:  #y中只有同一类样本            return y[0]        [i,g] = self.infoGain(x,y)  #返回信息增益最大的特征的索引、信息增益值        tree = {str(i):{}}        if g < theta:               #特征x的信息增益小于阈值theta,则返回y中数量最多的类             returnVal = Series(y).value_counts().index[0]             return returnVal        else :                          #根据（信息增益最大的）特征的取值，划分数据集，并递归求每一部分数据集的信息增益            uniqueVal = Series(x[:,i]).unique()            for val in uniqueVal:                xi = x[np.where(x[:,i] == val)]                yi = y[np.where(x[:,i] == val)]                xi = np.hstack((xi[:,0:i],xi[:,i+1:xi.shape[1]+1]))                returnVal = self.train(xi,yi,theta)                tree[str(i)][val] = returnVal        self.tree = tree        return treeif __name__ == '__main__':    x = np.loadtxt('x.txt')    y = np.loadtxt('y.txt')    dt = DecisionTree()    dt.train(x,y,0)    print(dt.tree)

3. 输出结果：
   {‘2’: {0.0: {‘1’: {0.0: 0.0, 1.0: 1.0}}, 1.0: 1.0}}

4. 树的可视化：