id3算法python实现

ID3算法是一种分类算法，它基于信息增益选择最优特征来构建决策树。下面是一个简单的Python实现：

import math

def calc_entropy(data):
    """
    计算数据集的熵
    """
    size = len(data)
    classes = {}
    for item in data:
        label = item[-1]
        if label not in classes:
            classes[label] = 0
        classes[label] += 1
    entropy = 0.0
    for key in classes:
        prob = float(classes[key]) / size
        entropy -= prob * math.log(prob, 2)
    return entropy

def split_data(data, axis, value):
    """
    划分数据集
    """
    ret_data = []
    for item in data:
        if item[axis] == value:
            reduced_item = item[:axis]
            reduced_item.extend(item[axis+1:])
            ret_data.append(reduced_item)
    return ret_data

def choose_feature(data):
    """
    选择最优特征
    """
    num_features = len(data[0]) - 1
    base_entropy = calc_entropy(data)
    best_info_gain = 0.0
    best_feature = -1
    for i in range(num_features):
        feat_list = [example[i] for example in data]
        unique_vals = set(feat_list)
        new_entropy = 0.0
        for value in unique_vals:
            sub_data = split_data(data, i, value)
            prob = len(sub_data) / float(len(data))
            new_entropy += prob * calc_entropy(sub_data)
        info_gain = base_entropy - new_entropy
        if info_gain > best_info_gain:
            best_info_gain = info_gain
            best_feature = i
    return best_feature

def create_tree(data, labels):
    """
    构建决策树
    """
    class_list = [example[-1] for example in data]
    if class_list.count(class_list[0]) == len(class_list):
        return class_list[0]
    if len(data[0]) == 1:
        return max(set(class_list), key=class_list.count)
    best_feat = choose_feature(data)
    best_feat_label = labels[best_feat]
    my_tree = {best_feat_label: {}}
    del(labels[best_feat])
    feat_values = [example[best_feat] for example in data]
    unique_vals = set(feat_values)
    for value in unique_vals:
        sub_labels = labels[:]
        my_tree[best_feat_label][value] = create_tree(split_data(data, best_feat, value), sub_labels)
    return my_tree

以上是一个简单的ID3算法的Python实现，其中calc_entropy函数计算数据集的熵，split_data函数用于划分数据集，choose_feature函数选择最优特征，create_tree函数递归地构建决策树。