How to use mahalanobis distance in sklearn DistanceMetrics?

Question

Perhaps this is elementary, but I cannot find a good example of using mahalanobis distance in sklearn.

I can't even get the metric like this:

from sklearn.neighbors import DistanceMetric
DistanceMetric.get_metric('mahalanobis')

This throws an error: TypeError: 0-dimensional array given. Array must be at least two-dimensional.

But, I can't even seem to get it to take an array:

DistanceMetric.get_metric('mahalanobis', [[0.5],[0.7]])

throws:

TypeError: get_metric() takes exactly 1 positional argument (2 given)

I checked out the docs here and here. But, I don't see what types of arguments it is expecting.
Is there an example of using the Mahalanobis distance that I can see?

Answer 1

MahalanobisDistance is expecting a parameter V which is the covariance matrix, and optionally another parameter VI which is the inverse of the covariance matrix. Furthermore, both of these parameters are named and not positional.

Also check the docstring for the class MahalanobisDistance in the file scikit-learn/sklearn/neighbors/dist_metrics.pyx in the sklearn repo.

Example:

In [18]: import numpy as np
In [19]: from sklearn.datasets import make_classification
In [20]: from sklearn.neighbors import DistanceMetric
In [21]: X, y = make_classification()
In [22]: DistanceMetric.get_metric('mahalanobis', V=np.cov(X))
Out[22]: <sklearn.neighbors.dist_metrics.MahalanobisDistance at 0x107aefa58>

Edit:

For some reasons (bug?), you can't pass the distance object to the NearestNeighbor constructor, but need to use the name of the distance metric. Also, setting algorithm='auto' (which defaults to 'ball_tree') doesn't seem to work; so given X from the code above you can do:

In [23]: nn = NearestNeighbors(algorithm='brute', 
                               metric='mahalanobis', 
                               metric_params={'V': np.cov(X)})
# returns the 5 nearest neighbors of that sample
In [24]: nn.fit(X).kneighbors(X[0, :])     
Out[24]: (array([[ 0., 3.21120892, 3.81840748, 4.18195987, 4.21977517]]), 
          array([[ 0, 36, 46,  5, 17]])) 

Answer 2

in creating cov matrix using matrix M (X x Y), you need to transpose your matrix M. mahalanobis formula is (x-x1)^t * inverse covmatrix * (x-x1). and as you see first argument is transposed, which means matrix XY changed to YX. in order to product first argument and cov matrix, cov matrix should be in form of YY.

If you just use np.cov(M), it will be XX, using np.cov(M.T), it will be YY.