计算 TensorFlow 中两个输入集合中每对之间的成对距离 [英] Compute the pairwise distance between each pair of the two collections of inputs in TensorFlow

问题描述

我有两个系列.一个包含 m₁ 个 k 维的点，另一个包含 m₂k 维中的点.我需要计算两个集合中每对之间的成对距离.

I have two collections. One consists of m₁ points in k dimensions and another one of m₂ points in k dimensions. I need to calculate pairwise distance between each pair of the two collections.

基本上有两个矩阵 A_{m1, k} 和 B_{m2, k} 我需要得到一个矩阵 C_{m1, m2}.

Basically having two matrices A_{m1, k} and B_{m2, k} I need to get a matrix C_{m1, m2}.

我可以在 scipy 中使用 distance.sdist 并选择许多距离度量之一，我也可以在循环中在 TF 中执行此操作，但我无法弄清楚如何使用矩阵操作来执行此操作，即使对于欧几里德距离也是如此.

I can easily do this in scipy by using distance.sdist and select one of many distance metrics, and I also can do this in TF in a loop, but I can't figure out how to do this with matrix manipulations even for Eucledian distance.

推荐答案

几个小时后，我终于找到了如何在 Tensorflow 中做到这一点.我的解决方案仅适用于欧几里得距离并且非常冗长.我也没有数学证明(只是大量挥手，希望能更严谨一点):

After a few hours I finally found how to do this in Tensorflow. My solution works only for Eucledian distance and is pretty verbose. I also do not have a mathematical proof (just a lot of handwaving, which I hope to make more rigorous):

import tensorflow as tf
import numpy as np
from scipy.spatial.distance import cdist

M1, M2, K = 3, 4, 2

# Scipy calculation
a = np.random.rand(M1, K).astype(np.float32)
b = np.random.rand(M2, K).astype(np.float32)
print cdist(a, b, 'euclidean'), '\n'

# TF calculation
A = tf.Variable(a)
B = tf.Variable(b)

p1 = tf.matmul(
    tf.expand_dims(tf.reduce_sum(tf.square(A), 1), 1),
    tf.ones(shape=(1, M2))
)
p2 = tf.transpose(tf.matmul(
    tf.reshape(tf.reduce_sum(tf.square(B), 1), shape=[-1, 1]),
    tf.ones(shape=(M1, 1)),
    transpose_b=True
))

res = tf.sqrt(tf.add(p1, p2) - 2 * tf.matmul(A, B, transpose_b=True))

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    print sess.run(res)

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