如何在Python中快速计算大量向量的余弦相似度？

Question

我有一套100万载体，我需要检索基于余弦相似性的前25名最接近的向量。

Scipy和Sklearn有用于计算余弦距离/相似度2矢量的实现，但我需要计算100k X 100k大小的余弦模拟，然后取出前25。 Python计算中有没有快速的实现？

按@Silmathoron建议，这是我在做什么 - 第一

#vectors is a list of vectors of size : 100K x 400 i.e. 100K vectors each of dimenions 400 
vectors = numpy.array(vectors) 
similarity = numpy.dot(vectors, vectors.T) 


# squared magnitude of preference vectors (number of occurrences) 
square_mag = numpy.diag(similarity) 

# inverse squared magnitude 
inv_square_mag = 1/square_mag 

# if it doesn't occur, set it's inverse magnitude to zero (instead of inf) 
inv_square_mag[numpy.isinf(inv_square_mag)] = 0 

# inverse of the magnitude 
inv_mag = numpy.sqrt(inv_square_mag) 

# cosine similarity (elementwise multiply by inverse magnitudes) 
cosine = similarity * inv_mag 
cosine = cosine.T * inv_mag 

k = 26 

box_plot_file = file("box_data.csv","w+") 

for sim,query in itertools.izip(cosine,queries): 
    k_largest = heapq.nlargest(k, sim) 
    k_largest = map(str,k_largest) 
    result = query + "," + ",".join(k_largest) + "\n" 
    box_plot_file.write(result) 
box_plot_file.close() 

Answer 1

我会尝试更智能的算法，而不是加快蛮力（计算所有的向量对）。如果您的向量维度较低，KDTrees可能会工作，scipy.spatial.KDTree（）。如果它们是高维的，那么你可能首先需要一个随机投影： http://scikit-learn.org/stable/modules/random_projection.html