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词袋模型与句子相似度计算

本文将会介绍NLP中常见的词袋模型（Bag of Words）以及如何利用词袋模型来计算句子间的相似度（余弦相似度，cosine similarity）。
 首先，让我们来看一下，什么是词袋模型。

将所有词语装进一个袋子里，不考虑其词法和语序的问题，即每个词语都是独立的。例如下面个例句，就可以构成一个词袋，袋子里包括所有词语。假设建立一个数组（或词典）用于映射匹配

我们以下面两个简单句子为例：

sent1 = "Word bag model,Put all the words in a bag, regardless of their morphology and word order, that is, each word is independent. For example, the above two examples can form a word bag, which includes Jane, wants, to, go, Shenzhen, Bob and Shanghai. Suppose you build an array (or dictionary) for mapping matches." sent2 = "Words bags model,Put all the words in a bag, regardless of their morphology and word order, this is, each word is independent. For example, the above two examples can form a word bag, which includes Jane, wants, to, go, Shenzhen, Bob and Shanghai. Suppose you build an array (or dictionary) for mapping matches." 

通常，NLP无法一下子处理完整的段落或句子，因此，第一步往往是分句和分词。这里只有句子，因此我们只需要分词即可。对于英语句子，可以使用NLTK中的word_tokenize函数，对于中文句子，则可使用jieba模块。故第一步为分词，代码如下：

from nltk import word_tokenize sents = [sent1, sent2] texts = [[word for word in word_tokenize(sent)] for sent in sents] 

输出的结果如下：

[['Word', 'bag', 'model', ',', 'Put', 'all', 'the', 'words', 'in', 'a', 'bag', ',', 'regardless', 'of', 'their', 'morphology', 'and', 'word', 'order', ',', 'that', 'is', ',', 'each', 'word', 'is', 'independent', '.', 'For', 'example', ',', 'the', 'above', 'two', 'examples', 'can', 'form', 'a', 'word', 'bag', ',', 'which', 'includes', 'Jane', ',', 'wants', ',', 'to', ',', 'go', ',', 'Shenzhen', ',', 'Bob', 'and', 'Shanghai', '.', 'Suppose', 'you', 'build', 'an', 'array', '(', 'or', 'dictionary', ')', 'for', 'mapping', 'matches', '.'], ['Words', 'bags', 'model', ',', 'Put', 'all', 'the', 'words', 'in', 'a', 'bag', ',', 'regardless', 'of', 'their', 'morphology', 'and', 'word', 'order', ',', 'this', 'is', ',', 'each', 'word', 'is', 'independent', '.', 'For', 'example', ',', 'the', 'above', 'two', 'examples', 'can', 'form', 'a', 'word', 'bag', ',', 'which', 'includes', 'Jane', ',', 'wants', ',', 'to', ',', 'go', ',', 'Shenzhen', ',', 'Bob', 'and', 'Shanghai', '.', 'Suppose', 'you', 'build', 'an', 'array', '(', 'or', 'dictionary', ')', 'for', 'mapping', 'matches', '.']]  

分词完毕。下一步是构建语料库，即所有句子中出现的单词及标点。代码如下：

all_list = [] for text in texts:     all_list += text corpus = set(all_list) print(corpus) 

输出如下：

{'wants', 'to', 'each', 'mapping', 'Words', 'morphology', 'array', '.', 'for', 'you', 'and', 'is', 'matches', 'Word', 'word', ',', 'Bob', 'can', 'which', 'a', 'that', 'an', 'Put', 'includes', 'bag', 'this', 'the', 'bags', 'words', 'two', 'in', 'Suppose', 'build', 'dictionary', 'examples', 'Shanghai', 'all', 'For', 'Jane', 'of', 'or', 'form', 'go', 'their', 'model', 'regardless', 'order', 'independent', 'example', 'above', 'Shenzhen', '(', ')'}  

可以看到，语料库中一共是8个单词及标点。接下来，对语料库中的单词及标点建立数字映射，便于后续的句子的向量表示。代码如下：

corpus_dict = dict(zip(corpus, range(len(corpus)))) print(corpus_dict) 

输出如下：

{'wants': 0, 'to': 1, 'each': 2, 'mapping': 3, 'Words': 4, 'morphology': 5, 'array': 6, '.': 7, 'for': 8, 'you': 9, 'and': 10, 'is': 11, 'matches': 12, 'Word': 13, 'word': 14, ',': 15, 'Bob': 16, 'can': 17, 'which': 18, 'a': 19, 'that': 20, 'an': 21, 'Put': 22, 'includes': 23, 'bag': 24, 'this': 25, 'the': 26, 'bags': 27, 'words': 28, 'two': 29, 'in': 30, 'Suppose': 31, 'build': 32, 'dictionary': 33, 'examples': 34, 'Shanghai': 35, 'all': 36, 'For': 37, 'Jane': 38, 'of': 39, 'or': 40, 'form': 41, 'go': 42, 'their': 43, 'model': 44, 'regardless': 45, 'order': 46, 'independent': 47, 'example': 48, 'above': 49, 'Shenzhen': 50, '(': 51, ')': 52}  

虽然单词及标点并没有按照它们出现的顺序来建立数字映射，不过这并不会影响句子的向量表示及后续的句子间的相似度。
 下一步，也就是词袋模型的关键一步，就是建立句子的向量表示。这个表示向量并不是简单地以单词或标点出现与否来选择0，1数字，而是把单词或标点的出现频数作为其对应的数字表示，结合刚才的语料库字典，句子的向量表示的代码如下：

# 建立句子的向量表示 def vector_rep(text, corpus_dict):     vec = [] for key in corpus_dict.keys(): if key in text:             vec.append((corpus_dict[key], text.count(key))) else:             vec.append((corpus_dict[key], 0))      vec = sorted(vec, key= lambda x: x[0]) return vec  vec1 = vector_rep(texts[0], corpus_dict) vec2 = vector_rep(texts[1], corpus_dict) print(vec1) print(vec2) 

输出如下：

[(0, 1), (1, 1), (2, 1), (3, 1), (4, 0), (5, 1), (6, 1), (7, 3), (8, 1), (9, 1), (10, 2), (11, 2), (12, 1), (13, 1), (14, 3), (15, 11), (16, 1), (17, 1), (18, 1), (19, 2), (20, 1), (21, 1), (22, 1), (23, 1), (24, 3), (25, 0), (26, 2), (27, 0), (28, 1), (29, 1), (30, 1), (31, 1), (32, 1), (33, 1), (34, 1), (35, 1), (36, 1), (37, 1), (38, 1), (39, 1), (40, 1), (41, 1), (42, 1), (43, 1), (44, 1), (45, 1), (46, 1), (47, 1), (48, 1), (49, 1), (50, 1), (51, 1), (52, 1)] [(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 3), (8, 1), (9, 1), (10, 2), (11, 2), (12, 1), (13, 0), (14, 3), (15, 11), (16, 1), (17, 1), (18, 1), (19, 2), (20, 0), (21, 1), (22, 1), (23, 1), (24, 2), (25, 1), (26, 2), (27, 1), (28, 1), (29, 1), (30, 1), (31, 1), (32, 1), (33, 1), (34, 1), (35, 1), (36, 1), (37, 1), (38, 1), (39, 1), (40, 1), (41, 1), (42, 1), (43, 1), (44, 1), (45, 1), (46, 1), (47, 1), (48, 1), (49, 1), (50, 1), (51, 1), (52, 1)]  

让我们稍微逗留一会儿，来看看这个向量。在第一句中I出现了两次，在预料库字典中，I对应的数字为5，因此在第一句中5出现2次，在列表中的元组即为(5,2)，代表单词I在第一句中出现了2次。以上的输出可能并不那么直观

OK，词袋模型到此结束。接下来，我们会利用刚才得到的词袋模型，即两个句子的向量表示，来计算相似度。
 在NLP中，如果得到了两个句子的向量表示，那么，一般会选择用余弦相似度作为它们的相似度，而向量的余弦相似度即为两个向量的夹角的余弦值。其计算的Python代码如下：

from math import sqrt def similarity_with_2_sents(vec1, vec2):     inner_product = 0     square_length_vec1 = 0     square_length_vec2 = 0 for tup1, tup2 in zip(vec1, vec2):         inner_product += tup1[1]*tup2[1]         square_length_vec1 += tup1[1]**2         square_length_vec2 += tup2[1]**2 return (inner_product/sqrt(square_length_vec1*square_length_vec2))   cosine_sim = similarity_with_2_sents(vec1, vec2) print('两个句子的余弦相似度为： %.4f。'%cosine_sim) 

输出结果如下：

两个句子的余弦相似度为： 0.9853。 

这样，我们就通过句子的词袋模型，得到了它们间的句子相似度。
 当然，在实际的NLP项目中，如果需要计算两个句子的相似度，我们只需调用gensim模块即可，它是NLP的利器，能够帮助我们处理很多NLP任务。下面为用gensim计算两个句子的相似度的代码：

sent1 = "I love sky, I love sea." sent2 = "I like running, I love reading." from nltk import word_tokenize sents = [sent1, sent2] texts = [[word for word in word_tokenize(sent)] for sent in sents] print(texts) from gensim import corpora from gensim.similarities import Similarity  #  语料库 dictionary = corpora.Dictionary(texts) # 利用doc2bow作为词袋模型 corpus = [dictionary.doc2bow(text) for text in texts] similarity = Similarity('-Similarity-index', corpus, num_features=len(dictionary)) print(similarity) # 获取句子的相似度 new_sensence = sent1 test_corpus_1 = dictionary.doc2bow(word_tokenize(new_sensence))  cosine_sim = similarity[test_corpus_1][1] print("利用gensim计算得到两个句子的相似度： %.4f。"%cosine_sim) 

输出结果如下：

[['I', 'love', 'sky', ',', 'I', 'love', 'sea', '.'], ['I', 'like', 'running', ',', 'I', 'love', 'reading', '.']] Similarity index with 2 documents in 0 shards (stored under -Similarity-index) 利用gensim计算得到两个句子的相似度： 0.7303。 

注意，如果在运行代码时出现以下warning:

gensimutils.py:1209: UserWarning: detected Windows; aliasing chunkize to chunkize_serial   warnings.warn("detected Windows; aliasing chunkize to chunkize_serial")  gensimmatutils.py:737: FutureWarning: Conversion of the second argument of issubdtype from `int` to `np.signedinteger` is deprecated. In future, it will be treated as `np.int32 == np.dtype(int).type`.   if np.issubdtype(vec.dtype, np.int): 

如果想要去掉这些warning，则在导入gensim模块的代码前添加以下代码即可：

import warnings warnings.filterwarnings(action='ignore',category=UserWarning,module='gensim') warnings.filterwarnings(action='ignore',category=FutureWarning,module='gensim') 

附上源码

from nltk import word_tokenize  sent1 = "Word bag model,Put all the words in a bag, regardless of their morphology and word order, that is, each word is independent. For example, the above two examples can form a word bag, which includes Jane, wants, to, go, Shenzhen, Bob and Shanghai. Suppose you build an array (or dictionary) for mapping matches." sent2 = "Words bags model,Put all the words in a bag, regardless of their morphology and word order, this is, each word is independent. For example, the above two examples can form a word bag, which includes Jane, wants, to, go, Shenzhen, Bob and Shanghai. Suppose you build an array (or dictionary) for mapping matches." sents = [sent1, sent2] texts = [[word for word in word_tokenize(sent)] for sent in sents] print(texts) all_list = [] for text in texts:     all_list += text corpus = set(all_list) print(corpus) corpus_dict = dict(zip(corpus, range(len(corpus)))) print(corpus_dict) def create_vector(text, corpus_dict):     vec = [] for key in corpus_dict.keys(): if key in text:             vec.append((corpus_dict[key], text.count(key))) else:             vec.append((corpus_dict[key], 0)) print(vec)     vec = sorted(vec, key=lambda x: x[0]) return vec  vec1 = create_vector(texts[0], corpus_dict) vec2 = create_vector(texts[1], corpus_dict) print(vec1, vec2) from math import sqrt def similarity_with_2_sents(vec1, vec2):     inner_product = 0     square_length_vec1 = 0     square_length_vec2 = 0 for tup1, tup2 in zip(vec1, vec2):         inner_product += tup1[1]*tup2[1]         square_length_vec1 += tup1[1]**2         square_length_vec2 += tup2[1]**2 return (inner_product/sqrt(square_length_vec1*square_length_vec2))   cosine_sim = similarity_with_2_sents(vec1, vec2) print('两个句子的余弦相似度为： %.4f。'%cosine_sim)    sent1 = "I love sky, I love sea." sent2 = "I like running, I love reading." from nltk import word_tokenize sents = [sent1, sent2] texts = [[word for word in word_tokenize(sent)] for sent in sents] print(texts) from gensim import corpora from gensim.similarities import Similarity  #  语料库 dictionary = corpora.Dictionary(texts) # 利用doc2bow作为词袋模型 corpus = [dictionary.doc2bow(text) for text in texts] similarity = Similarity('-Similarity-index', corpus, num_features=len(dictionary)) print(similarity) # 获取句子的相似度 new_sensence = sent1 test_corpus_1 = dictionary.doc2bow(word_tokenize(new_sensence))  cosine_sim = similarity[test_corpus_1][1] print("利用gensim计算得到两个句子的相似度： %.4f。"%cosine_sim) 

本文到此结束，感谢阅读！如果不当之处，请速联系笔者，欢迎大家交流！祝您好运~