ID3算法的自然语言伪代码

ID3 (Iterative Dichotomiser 3) 算法是一种基于信息增益的决策树生成算法。以下是它的基本自然语言伪代码描述：

function ID3(dataSet, attributes):
    if dataSet is empty or all elements have the same class:
        return a leaf node with the most common class in dataSet
    
    if no more attributes left to choose from:
        return a leaf node representing the majority class of dataSet
    
    best_attribute = select_best_attribute(dataSet, attributes)
    
    sub_trees = {}
    for attribute_value in best_attribute.values:
        subset = filter_data(dataSet, attribute_value)
        sub_trees[attribute_value] = ID3(subset, remove_attribute(attributes, best_attribute))
    
    return a decision node with best_attribute and sub_trees

function select_best_attribute(dataSet, attributes):
    max_info_gain = -1
    best_attribute = None
    for attribute in attributes:
        info_gain = calculate_info_gain(dataSet, attribute)
        if info_gain > max_info_gain:
            max_info_gain = info_gain
            best_attribute = attribute
            
    return best_attribute

function calculate_info_gain(dataSet, attribute):
    entropy_before = calculate_entropy(dataSet)
    subsets = split_data_set_by_attribute(dataSet, attribute)
    entropy_after = sum([calculate_entropy(subset) / len(subsets) for subset in subsets])
    return entropy_before - entropy_after

function calculate_entropy(dataSet):
    # 计算数据集中各类别的概率乘以其对应的熵
    probabilities = count_classes(dataSet)
    entropy = sum([-p * log2(p) for p in probabilities])
    return entropy

在这个伪代码中，`dataSet` 是训练数据集，`attributes` 是当前可供选择的属性列表。算法首先检查是否达到终止条件，然后找到信息增益最高的属性作为节点划分依据，递归地创建子树。`select_best_attribute` 和 `calculate_info_gain` 负责信息增益的计算，`calculate_entropy` 则负责计算熵。