余弦相似性 – word2vec,总和或平均字嵌入？

从我做过的实验中,我总是得到相同的余弦相似度.我怀疑它与训练后word2vec生成的单词长度(单位长度(Euclidean norm))有关吗？或者我在代码中有BUG,或者我遗漏了一些东西.

这是代码：

import numpy as np
from nltk import PunktWordTokenizer
from gensim.models import Word2Vec
from numpy.linalg import norm
from scipy.spatial.distance import cosine

def pattern2vector(tokens,word2vec,AVG=False):
    pattern_vector = np.zeros(word2vec.layer1_size)
    n_words = 0
    if len(tokens) > 1:
        for t in tokens:
            try:
                vector = word2vec[t.strip()]
                pattern_vector = np.add(pattern_vector,vector)
                n_words += 1
            except KeyError,e:
                continue
        if AVG is True:
            pattern_vector = np.divide(pattern_vector,n_words)
    elif len(tokens) == 1:
        try:
            pattern_vector = word2vec[tokens[0].strip()]
        except KeyError:
            pass
    return pattern_vector


def main():
    print "Loading word2vec model ...n"
    word2vecmodelpath = "/data/word2vec/vectors_200.bin"
    word2vec = Word2Vec.load_word2vec_format(word2vecmodelpath,binary=True)
    pattern_1 = 'founder and ceo'
    pattern_2 = 'co-founder and former chairman'

    tokens_1 = PunktWordTokenizer().tokenize(pattern_1)
    tokens_2 = PunktWordTokenizer().tokenize(pattern_2)
    print "vec1",tokens_1
    print "vec2",tokens_2

    p1 = pattern2vector(tokens_1,False)
    p2 = pattern2vector(tokens_2,False)
    print "nSUM"
    print "dot(vec1,vec2)",np.dot(p1,p2)
    print "norm(p1)",norm(p1)
    print "norm(p2)",norm(p2)
    print "dot((norm)vec1,norm(vec2))",np.dot(norm(p1),norm(p2))
    print "cosine(vec1,np.divide(np.dot(p1,p2),norm(p2)))
    print "n"
    print "AVG"
    p1 = pattern2vector(tokens_1,True)
    p2 = pattern2vector(tokens_2,True)
    print "dot(vec1,norm(p2)
    print "dot(norm(vec1),norm(p2)))


if __name__ == "__main__":
    main()

这是输出：

Loading word2vec model ...

Dimensions 200
vec1 ['founder','and','ceo']
vec2 ['co-founder','former','chairman']

SUM
dot(vec1,vec2) 5.4008677771
norm(p1) 2.19382594282
norm(p2) 2.87226958166
dot((norm)vec1,norm(vec2)) 6.30125952303
cosine(vec1,vec2) 0.857109242583


AVG
dot(vec1,vec2) 0.450072314758
norm(p1) 0.731275314273
norm(p2) 0.718067395416
dot(norm(vec1),norm(vec2)) 0.525104960252
cosine(vec1,vec2) 0.857109242583

我使用的是Cosine Similarity (Wikipedia)中定义的余弦相似度.规范和点积的值确实不同.

谁能解释为什么余弦是一样的？

谢谢,
大卫