TF-IDF 算法原理以及源码实现

TF-IDF（Term Frequency-Inverse Document Frequency），是用来衡量一个词在文档中的重要性，下面看一下TDF-IDF的公式：

首先是TF，也就是词频，用来衡量一个词在文档中出现频率的指标。假设某词在文档中出现了( n )次，而文档总共包含( N )个词，则该词的TF定义为：

注意：（t，d）中的t表示的是文档中的词汇，d表示的是文档的词汇集合，通过计算TF也就是进行词频率的统计，好的，那么看一下代码的实现。

def compute_tf(word_dict, doc_words):
    """

    :param word_dict: 字符的统计个数
    :param doc_words: 文档中的字符集合
    :return:
    """
    tf_dict = {}
    words_len = len(doc_words)
    for word_i, count_i in word_dict.items():
        tf_dict[word_i] = count_i / words_len
    return tf_dict

# 示例文档
doc1 = "this is a sample"
doc2 = "this is another example example example"
doc3 = "this is a different example example"

# 分割单词
doc1_words = doc1.split()
doc2_words = doc2.split()
doc3_words = doc3.split()

# 计算每个文档的词频
word_dict1 = Counter(doc1_words)
word_dict2 = Counter(doc2_words)
word_dict3 = Counter(doc3_words)

# 计算TF
tf1 = compute_tf(word_dict1, doc1_words)
tf2 = compute_tf(word_dict2, doc2_words)
tf3 = compute_tf(word_dict3, doc3_words)

print(f'tf1:{tf1}')
print(f'tf2:{tf2}')
print(f'tf3:{tf3}')

# tf1:{'this': 0.25, 'is': 0.25, 'a': 0.25, 'sample': 0.25}
# tf2:{'this': 0.16666666666666666, 'is': 0.16666666666666666, 'another': 0.16666666666666666, 'example': 0.5}
# tf3:{'this': 0.16666666666666666, 'is': 0.16666666666666666, 'a': 0.16666666666666666, 'different': 0.16666666666666666, 'example': 0.3333333333333333}

看完TF的计算之后，我们看一下IDF的定义，公式和对应的实现吧，IDF的定义是：即逆文档频率，反映了词的稀有程度，IDF越高，说明词越稀有。这个逆文档频率也就是说一个词的文档集合中出现的次数越少，他就越具有表征型，因为在文中有很多“的”，“了”这种词，这些词重要性不大，反而出现少的词重要性大一点，来看一下IDF的公式：

其中，( D )是文档总数，( df_t )是包含词( t )的文档数量。通过取对数，可以避免数值过大的问题，同时保证了IDF的单调递减特性，下面看一下代码的现实：

def compute_idf(doc_list):
    """

    :param doc_list: 文档的集合
    :return:
    """

    sum_list = list(set([word_i for doc_i in doc_list for word_i in doc_i]))

    idf_dict = {word_i: 0 for word_i in sum_list}

    for word_j in sum_list:
        for doc_j in doc_list:
            if word_j in doc_j:
                idf_dict[word_j] += 1
    return {k: math.log(len(doc_list) / (v + 1)) for k, v in idf_dict.items()}

# 示例文档
doc1 = "this is a sample"
doc2 = "this is another example example example"
doc3 = "this is a different example example"

# 分割单词
doc1_words = doc1.split()
doc2_words = doc2.split()
doc3_words = doc3.split()

# 计算每个文档的词频
word_dict1 = Counter(doc1_words)
word_dict2 = Counter(doc2_words)
word_dict3 = Counter(doc3_words)

# 计算整个文档集合的IDF
idf = compute_idf([doc1_words, doc2_words, doc3_words])
# idf:{'different': 0.4054651081081644, 'another': 0.4054651081081644, 'a': 0.0, 'example': 0.0, 'this': -0.2876820724517809, 'sample': 0.4054651081081644, 'is': -0.2876820724517809}

通过结果可以发现，different、another和sample都比is、a等词汇的IDF值要高，代表越重要。

好的，最后看一下TF-IDF的公式吧，

$$TF-IDF=TF*IDF  $$

TF-IDF 就是TF*IDF，来综合的评价一个词在文档中的重要性。

最后看一下完整的代码，

import math
from collections import Counter
import math

def compute_tfidf(tf_dict, idf_dict):
    tfidf = {}
    for word, tf_value in tf_dict.items():
        tfidf[word] = tf_value * idf_dict[word]
    return tfidf

def compute_tf(word_dict, doc_words):
    """

    :param word_dict: 字符的统计个数
    :param doc_words: 文档中的字符集合
    :return:
    """
    tf_dict = {}
    words_len = len(doc_words)
    for word_i, count_i in word_dict.items():
        tf_dict[word_i] = count_i / words_len
    return tf_dict

def compute_idf(doc_list):
    """

    :param doc_list: 文档的集合
    :return:
    """

    sum_list = list(set([word_i for doc_i in doc_list for word_i in doc_i]))

    idf_dict = {word_i: 0 for word_i in sum_list}

    for word_j in sum_list:
        for doc_j in doc_list:
            if word_j in doc_j:
                idf_dict[word_j] += 1
    return {k: math.log(len(doc_list) / (v + 1)) for k, v in idf_dict.items()}

# 示例文档
doc1 = "this is a sample"
doc2 = "this is another example example example"
doc3 = "this is a different example example"

# 分割单词
doc1_words = doc1.split()
doc2_words = doc2.split()
doc3_words = doc3.split()

# 计算每个文档的词频
word_dict1 = Counter(doc1_words)
word_dict2 = Counter(doc2_words)
word_dict3 = Counter(doc3_words)

# 计算TF
tf1 = compute_tf(word_dict1, doc1_words)
tf2 = compute_tf(word_dict2, doc2_words)
tf3 = compute_tf(word_dict3, doc3_words)

print(f'tf1:{tf1}')
print(f'tf2:{tf2}')
print(f'tf3:{tf3}')

# 计算整个文档集合的IDF
idf = compute_idf([doc1_words, doc2_words, doc3_words])

print(f'idf:{idf}')
# 计算每个文档的TF-IDF
tfidf1 = compute_tfidf(tf1, idf)
tfidf2 = compute_tfidf(tf2, idf)
tfidf3 = compute_tfidf(tf3, idf)

print("TF-IDF for Document 1:", tfidf1)
print("TF-IDF for Document 2:", tfidf2)
print("TF-IDF for Document 3:", tfidf3)

"""
tf1:{'this': 0.25, 'is': 0.25, 'a': 0.25, 'sample': 0.25}
tf2:{'this': 0.16666666666666666, 'is': 0.16666666666666666, 'another': 0.16666666666666666, 'example': 0.5}
tf3:{'this': 0.16666666666666666, 'is': 0.16666666666666666, 'a': 0.16666666666666666, 'different': 0.16666666666666666, 'example': 0.3333333333333333}
idf:{'example': 0.0, 'different': 0.4054651081081644, 'this': -0.2876820724517809, 'another': 0.4054651081081644, 'is': -0.2876820724517809, 'a': 0.0, 'sample': 0.4054651081081644}
TF-IDF for Document 1: {'this': -0.07192051811294523, 'is': -0.07192051811294523, 'a': 0.0, 'sample': 0.1013662770270411}
TF-IDF for Document 2: {'this': -0.047947012075296815, 'is': -0.047947012075296815, 'another': 0.06757751801802739, 'example': 0.0}
TF-IDF for Document 3: {'this': -0.047947012075296815, 'is': -0.047947012075296815, 'a': 0.0, 'different': 0.06757751801802739, 'example': 0.0}

"""