两个数组之间的余弦距离计算-Python [英] Cosine distance computation between two arrays - Python
问题描述
我想应用一个函数fn
,该函数本质上是对按行分别为(10000,100)和(5000,100)的两个大型numpy数组进行cosine distance
计算,即我为每个组合计算一个值这些数组中的行数.
I want to apply a function fn
, which is essentially cosine distance
computation on two large numpy arrays of shapes (10000, 100) and (5000, 100) row-wise, i.e. i calculate a value for each combination of rows in these arrays.
我的实现:
import math
def fn(v1,v2):
sumxx, sumxy, sumyy = 0, 0, 0
for i in range(len(v1)):
x = v1[i]; y = v2[i]
sumxx += x*x
sumyy += y*y
sumxy += x*y
return sumxy/math.sqrt(sumxx*sumyy)
val = []
for i in range(array1.shape[0]):
for j in range(array2.shape[0]):
val.append(fn(array1[i, :], array2[j, :]))
该功能非常快速,只需几毫秒:
The function is very fast and takes only few ms:
CPU times: user 4 ms, sys: 0 ns, total: 4 ms
Wall time: 1.24 ms
有什么有效的方法吗?
推荐答案
Approach #1 : We could simply use Scipy's cdist
with its cosine
distance functionality -
from scipy.spatial.distance import cdist
val_out = 1 - cdist(array1, array2, 'cosine')
方法2::使用 方法3::使用 np.einsum
来计算另一项的自平方和-
Approach #3 : Using np.einsum
to compute the self squared summations for another one -
def cosine_vectorized_v2(array1, array2):
sumyy = np.einsum('ij,ij->i',array2,array2)
sumxx = np.einsum('ij,ij->i',array1,array1)[:,None]
sumxy = array1.dot(array2.T)
return (sumxy/np.sqrt(sumxx))/np.sqrt(sumyy)
方法#4:引入 square-root
计算的另一种方法-
Approach #4 : Bringing in numexpr
module to offload the square-root
computations for another method -
import numexpr as ne
def cosine_vectorized_v3(array1, array2):
sumyy = np.einsum('ij,ij->i',array2,array2)
sumxx = np.einsum('ij,ij->i',array1,array1)[:,None]
sumxy = array1.dot(array2.T)
sqrt_sumxx = ne.evaluate('sqrt(sumxx)')
sqrt_sumyy = ne.evaluate('sqrt(sumyy)')
return ne.evaluate('(sumxy/sqrt_sumxx)/sqrt_sumyy')
运行时测试
# Using same sizes as stated in the question
In [185]: array1 = np.random.rand(10000,100)
...: array2 = np.random.rand(5000,100)
...:
In [194]: %timeit 1 - cdist(array1, array2, 'cosine')
1 loops, best of 3: 366 ms per loop
In [195]: %timeit cosine_vectorized(array1, array2)
1 loops, best of 3: 287 ms per loop
In [196]: %timeit cosine_vectorized_v2(array1, array2)
1 loops, best of 3: 283 ms per loop
In [197]: %timeit cosine_vectorized_v3(array1, array2)
1 loops, best of 3: 217 ms per loop
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