Question about covariance matrix used when using Mahalanobis distance

[rchan26]

Hi, I was just wondering what is the default covariance matrix that is used when metric="mahalanobis". I see in the documentation that you could pass in any metric keywords via metric_kwds (I assume I would pass in the inverse by setting metric_kwds={"vinv": cov_inv}), but I can't seem to find in the documentation what is the default that is used if none is passed?

I see in pynndescent/distances.py, that the function to compute the malahonbis has default identity matrix, but I assume that isn't actually what is used if you don't specify vinv in pynndescent.NNDescent.

For a bit of context, for some points $y_{1}, y_{2}, ...$ I would like to approximate the minimum distances between them and some data $X_{1}, X_{2}, ...$ (i.e. for each $i$, compute the distance between $y_{i}$ and each point $X_{1}, X_{2}, ...$ and find the minimum). I want to use the malahonbis distance where I use the covariance matrix for the data $X$, and I have been doing this with:

nnd = pynndescent.NNDescent(X, metric="mahalanobis")
_, nn_d = nnd.query(inlier_signatures)
minimum_distances = inlier_nn_d[:,0]

I was just wondering if I should really be passing in the inverse covariance matrix I want to use like:

nnd = pynndescent.NNDescent(X, metric="mahalanobis", metric_kwds={"vinv": cov_inv})

Any clarification on what the default vinv that is used would be greatly appreciated :)