用权重标准化排名得分

Question

我正在处理一个文档搜索问题，给定一组文档和一个搜索查询，我希望找到最接近查询的文档。我使用的模型基于scikit中的TfidfVectorizer。我使用4种不同类型的标记器为所有文档创建了4个不同的tf_idf向量。每个标记器将字符串拆分为n个gram，其中n在范围1中。。。4。在

例如：

doc_1 = "Singularity is still a confusing phenomenon in physics"
doc_2 = "Quantum theory still wins over String theory"

所以型号1将使用1克的标记器，型号2将使用2克的标记器。在

接下来，对于给定的搜索查询，我使用这4个模型计算搜索项和所有其他文档之间的余弦相似度。在

例如，搜索查询：量子物理学中的奇点。 将搜索查询分解为n个gram，并根据相应的n-gram模型计算tf_-idf值。在

因此，对于每个查询文档对，我有4个基于使用的n-gram模型的相似性值。 例如：

^{pr2}$

所有这些相似性得分在0到1之间进行标准化。现在我想计算一个聚合的标准化分数，这样对于任何查询文档对，更高的n-gram相似度将获得非常高的权重。基本上，ngram相似度越高，对总分的影响就越大。在

有人能提出解决办法吗？在

Answer 1

有很多种方法可以玩弄数字：

>>> onegram_sim = 0.43
>>> twogram_sim = 0.36
>>> threegram_sim = 0.29
>>> fourgram_sim = 0.29
# Sum(x) / len(list)
>>> all_sim = sum([onegram_sim, twogram_sim, threegram_sim, fourgram_sim]) / 4
>>> all_sim
0.3425
# Sum(x*x) / len(list)
>>> all_sim = sum(map(lambda x: x**2, [onegram_sim, twogram_sim, threegram_sim, fourgram_sim])) / 4
>>> all_sim
0.120675
# Product(x)
>>> from operator import mul
>>> onetofour_sim = [onegram_sim, twogram_sim, threegram_sim, fourgram_sim]
>>> reduce(mul, onetofour_sim, 1)
0.013018679999999998

最终，无论什么能让你在最终的任务中获得更高的准确度分数，都是最好的解决方案。在

---

毫无疑问：

为了计算文档相似性，有一个长期运行的SemEval任务调用语义文本相似度https://groups.google.com/forum/#!forum/sts-semeval

共同的策略包括（并非详尽）：

1. 使用带有相似性分数的标注语料库，提取一些特征，训练回归器并输出相似性分数

2. 使用某种向量空间语义（强烈推荐阅读：http://www.jair.org/media/2934/live-2934-4846-jair.pdf），然后做一些向量相似度评分（看看How to calculate cosine similarity given 2 sentence strings? - Python）

   向量空间语义学术语的子集将派上用场（有时称为单词嵌入），有时人们用主题模型/神经网络/深度学习（其他相关的流行语）训练向量空间，参见http://u.cs.biu.ac.il/~yogo/cvsc2015.pdf

   二。你也可以使用一个更传统的词包向量，用TF-IDF或任何其他“潜在”维度缩减来压缩空间，然后使用一些向量相似度函数来获得相似度

   iii.创建一个奇特的向量相似性函数（例如cosmul，参见https://radimrehurek.com/gensim/models/word2vec.html），然后调整该函数并在不同的空间上对其求值。

3. 使用一些包含概念本体的词汇资源（例如WordNet、Cyc等），然后通过遍历概念图来比较相似度（参见http://www.nltk.org/howto/wordnet.html）。例如https://github.com/alvations/pywsd/blob/master/pywsd/similarity.py

---

以上述为背景，在没有注释的情况下，让我们试着找出一些向量空间的例子：

首先，让我们用简单的二进制向量来尝试普通ngram：

^{pr2}$

[出来]：

Vector Dict: [('still', 'a', 'confusing'), ('confusing', 'phenomenon', 'in'), ('theory', 'still', 'wins'), ('is', 'still', 'a'), ('over', 'String', 'theory'), ('a', 'confusing', 'phenomenon'), ('wins', 'over', 'String'), ('Singularity', 'is', 'still'), ('still', 'wins', 'over'), ('phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still')] 

Vectorzied: [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0] [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1] 

Similarity: 0 

现在让我们尝试从1gram到ngram的include（其中n = len(sent)），并将所有内容与二进制ngram一起放入向量字典：

import numpy as np
from nltk import ngrams

def everygrams(sequence):
    """
    This function returns all possible ngrams for n 
    ranging from 1 to len(sequence).
    >>> list(everygrams('a b c'.split()))
    [('a',), ('b',), ('c',), ('a', 'b'), ('b', 'c'), ('a', 'b', 'c')]
    """
    for n in range(1, len(sequence)+1):
        for ng in ngrams(sequence, n):
            yield ng

doc1 = "Singularity is still a confusing phenomenon in physics".split()
doc2 = "Quantum theory still wins over String theory".split()
_vec1 = list(everygrams(doc1))
_vec2 = list(everygrams(doc2))
# Create a full dictionary of all possible ngrams.
vec_dict = list(set(_vec1).union(_vec2))
print 'Vector Dict:', vec_dict, '\n'
# Now vectorize the documents
vec1 = [1 if ng in _vec1 else 0 for ng in vec_dict]
vec2 = [1 if ng in _vec2 else 0 for ng in vec_dict]
print 'Vectorzied:', vec1, vec2, '\n'
print 'Similarity:', np.dot(vec1, vec2), '\n'

[出来]：

Vector Dict: [('still', 'a'), ('over', 'String'), ('theory', 'still', 'wins', 'over', 'String', 'theory'), ('String', 'theory'), ('physics',), ('in',), ('wins', 'over', 'String', 'theory'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('theory', 'still', 'wins'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon'), ('a',), ('wins',), ('is', 'still', 'a'), ('Singularity', 'is'), ('phenomenon', 'in'), ('still', 'wins', 'over', 'String'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over'), ('a', 'confusing', 'phenomenon'), ('Singularity', 'is', 'still', 'a'), ('confusing', 'phenomenon'), ('confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('wins', 'over'), ('theory', 'still', 'wins', 'over'), ('phenomenon',), ('Quantum', 'theory', 'still', 'wins', 'over', 'String'), ('is', 'still'), ('still', 'wins', 'over'), ('is', 'still', 'a', 'confusing', 'phenomenon'), ('phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins'), ('Quantum', 'theory', 'still'), ('a', 'confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still', 'a', 'confusing'), ('still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'a', 'confusing'), ('is', 'still', 'a', 'confusing'), ('in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over', 'String', 'theory'), ('confusing', 'phenomenon', 'in'), ('theory', 'still'), ('Quantum', 'theory'), ('is',), ('String',), ('over', 'String', 'theory'), ('still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('a', 'confusing'), ('still', 'wins'), ('still',), ('over',), ('still', 'a', 'confusing', 'phenomenon'), ('wins', 'over', 'String'), ('Singularity',), ('confusing',), ('theory',), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'wins', 'over', 'String', 'theory'), ('a', 'confusing', 'phenomenon', 'in'), ('Quantum',), ('theory', 'still', 'wins', 'over', 'String')] 

Vectorzied: [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0] [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1] 

Similarity: 1 

现在，让我们尝试通过可能的ngram数量来规范化：

import numpy as np
from nltk import ngrams

def everygrams(sequence):
    """
    This function returns all possible ngrams for n 
    ranging from 1 to len(sequence).
    >>> list(everygrams('a b c'.split()))
    [('a',), ('b',), ('c',), ('a', 'b'), ('b', 'c'), ('a', 'b', 'c')]
    """
    for n in range(1, len(sequence)+1):
        for ng in ngrams(sequence, n):
            yield ng

doc1 = "Singularity is still a confusing phenomenon in physics".split()
doc2 = "Quantum theory still wins over String theory".split()
_vec1 = list(everygrams(doc1))
_vec2 = list(everygrams(doc2))
# Create a full dictionary of all possible ngrams.
vec_dict = list(set(_vec1).union(_vec2))
print 'Vector Dict:', vec_dict, '\n'
# Now vectorize the documents
vec1 = [1/float(len(_vec1)) if ng in _vec1 else 0 for ng in vec_dict]
vec2 = [1/float(len(_vec2)) if ng in _vec2 else 0 for ng in vec_dict]
print 'Vectorzied:', vec1, vec2, '\n'
print 'Similarity:', np.dot(vec1, vec2), '\n'

看起来好多了，出去：

Vector Dict: [('still', 'a'), ('over', 'String'), ('theory', 'still', 'wins', 'over', 'String', 'theory'), ('String', 'theory'), ('physics',), ('in',), ('wins', 'over', 'String', 'theory'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('theory', 'still', 'wins'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon'), ('a',), ('wins',), ('is', 'still', 'a'), ('Singularity', 'is'), ('phenomenon', 'in'), ('still', 'wins', 'over', 'String'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over'), ('a', 'confusing', 'phenomenon'), ('Singularity', 'is', 'still', 'a'), ('confusing', 'phenomenon'), ('confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('wins', 'over'), ('theory', 'still', 'wins', 'over'), ('phenomenon',), ('Quantum', 'theory', 'still', 'wins', 'over', 'String'), ('is', 'still'), ('still', 'wins', 'over'), ('is', 'still', 'a', 'confusing', 'phenomenon'), ('phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins'), ('Quantum', 'theory', 'still'), ('a', 'confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still', 'a', 'confusing'), ('still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'a', 'confusing'), ('is', 'still', 'a', 'confusing'), ('in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over', 'String', 'theory'), ('confusing', 'phenomenon', 'in'), ('theory', 'still'), ('Quantum', 'theory'), ('is',), ('String',), ('over', 'String', 'theory'), ('still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('a', 'confusing'), ('still', 'wins'), ('still',), ('over',), ('still', 'a', 'confusing', 'phenomenon'), ('wins', 'over', 'String'), ('Singularity',), ('confusing',), ('theory',), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'wins', 'over', 'String', 'theory'), ('a', 'confusing', 'phenomenon', 'in'), ('Quantum',), ('theory', 'still', 'wins', 'over', 'String')] 

Vectorzied: [0.027777777777777776, 0, 0, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0, 0.027777777777777776, 0, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0] [0, 0.03571428571428571, 0.03571428571428571, 0.03571428571428571, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.03571428571428571, 0, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.03571428571428571, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571, 0, 0, 0.03571428571428571, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571] 

Similarity: 0.000992063492063 

现在让我们尝试计数ngram，而不是使用1/len(_vec)，即_vec.count(ng) / len(_vec)：

import numpy as np
from nltk import ngrams

def everygrams(sequence):
    """
    This function returns all possible ngrams for n 
    ranging from 1 to len(sequence).
    >>> list(everygrams('a b c'.split()))
    [('a',), ('b',), ('c',), ('a', 'b'), ('b', 'c'), ('a', 'b', 'c')]
    """
    for n in range(1, len(sequence)+1):
        for ng in ngrams(sequence, n):
            yield ng

doc1 = "Singularity is still a confusing phenomenon in physics".split()
doc2 = "Quantum theory still wins over String theory".split()
_vec1 = list(everygrams(doc1))
_vec2 = list(everygrams(doc2))
# Create a full dictionary of all possible ngrams.
vec_dict = list(set(_vec1).union(_vec2))
print 'Vector Dict:', vec_dict, '\n'
# Now vectorize the documents
vec1 = [_vec1.count(ng)/float(len(_vec1)) if ng in _vec1 else 0 for ng in vec_dict]
vec2 = [_vec2.count(ng)/float(len(_vec2)) if ng in _vec2 else 0 for ng in vec_dict]
print 'Vectorzied:', vec1, vec2, '\n'
print 'Similarity:', np.dot(vec1, vec2), '\n'

不出意外的是，所有的相似度都是一样的：

Vector Dict: [('still', 'a'), ('over', 'String'), ('theory', 'still', 'wins', 'over', 'String', 'theory'), ('String', 'theory'), ('physics',), ('in',), ('wins', 'over', 'String', 'theory'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('theory', 'still', 'wins'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon'), ('a',), ('wins',), ('is', 'still', 'a'), ('Singularity', 'is'), ('phenomenon', 'in'), ('still', 'wins', 'over', 'String'), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over'), ('a', 'confusing', 'phenomenon'), ('Singularity', 'is', 'still', 'a'), ('confusing', 'phenomenon'), ('confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still'), ('is', 'still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('wins', 'over'), ('theory', 'still', 'wins', 'over'), ('phenomenon',), ('Quantum', 'theory', 'still', 'wins', 'over', 'String'), ('is', 'still'), ('still', 'wins', 'over'), ('is', 'still', 'a', 'confusing', 'phenomenon'), ('phenomenon', 'in', 'physics'), ('Quantum', 'theory', 'still', 'wins'), ('Quantum', 'theory', 'still'), ('a', 'confusing', 'phenomenon', 'in', 'physics'), ('Singularity', 'is', 'still', 'a', 'confusing'), ('still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'a', 'confusing'), ('is', 'still', 'a', 'confusing'), ('in', 'physics'), ('Quantum', 'theory', 'still', 'wins', 'over', 'String', 'theory'), ('confusing', 'phenomenon', 'in'), ('theory', 'still'), ('Quantum', 'theory'), ('is',), ('String',), ('over', 'String', 'theory'), ('still', 'a', 'confusing', 'phenomenon', 'in', 'physics'), ('a', 'confusing'), ('still', 'wins'), ('still',), ('over',), ('still', 'a', 'confusing', 'phenomenon'), ('wins', 'over', 'String'), ('Singularity',), ('confusing',), ('theory',), ('Singularity', 'is', 'still', 'a', 'confusing', 'phenomenon', 'in'), ('still', 'wins', 'over', 'String', 'theory'), ('a', 'confusing', 'phenomenon', 'in'), ('Quantum',), ('theory', 'still', 'wins', 'over', 'String')] 

Vectorzied: [0.027777777777777776, 0, 0, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0, 0.027777777777777776, 0, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0.027777777777777776, 0, 0.027777777777777776, 0, 0.027777777777777776, 0, 0] [0, 0.03571428571428571, 0.03571428571428571, 0.03571428571428571, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.03571428571428571, 0, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.03571428571428571, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571, 0, 0, 0.03571428571428571, 0.03571428571428571, 0.03571428571428571, 0, 0.03571428571428571, 0, 0, 0.07142857142857142, 0, 0.03571428571428571, 0, 0.03571428571428571, 0.03571428571428571] 

Similarity: 0.000992063492063 

除了ngrams你也可以试试skipgrams:How to compute skipgrams in python?