在numpy中矢量化(平方)mahalanobis距离

时间:2017-01-26 02:20:31

标签: python numpy matrix mahalanobis

我有X(n×d),Y(m×d)和正定L(d×d)。我想计算D,其中D_ij是(X_i - Y_i)* L *(X_i - Y_i).T。 n和m大约是250; d大约是10 ^ 4。

我可以使用scipy.spatial.distance.cdist,但这非常慢。

scipy.spatial.distance.cdist(X, Y, metric='mahalanobis', VI=L)

看看Dougal对this question的回答,我试过了

    diff = X[np.newaxis, :, :] - Y[:, np.newaxis, :]
    D = np.einsum('jik,kl,jil->ij', diff, L, diff)

这也很慢。

有没有更有效的方法来矢量化这个计算?

1 个答案:

答案 0 :(得分:1)

使用np.tensordotnp.einsum的组合有助于这些情况 -

np.einsum('jil,jil->ij',np.tensordot(diff, L, axes=(2,0)), diff)

运行时测试 -

In [26]: n,m,d = 30,40,50
    ...: X = np.random.rand(n,d)
    ...: L = np.random.rand(d,d)
    ...: Y = np.random.rand(m,d)
    ...: 

In [27]: diff = X[np.newaxis, :, :] - Y[:, np.newaxis, :]

In [28]: %timeit np.einsum('jik,kl,jil->ij', diff, L, diff)
100 loops, best of 3: 7.81 ms per loop

In [29]: %timeit np.einsum('jil,jil->ij',np.tensordot(diff, L, axes=(2,0)), diff)
1000 loops, best of 3: 472 µs per loop