submet

See my post with a brief algorithmic introduction for computing distances between pairs of subspaces.

submet is a Python package for computing pairwise distances between equidimensional subspaces. All of these subspace metrics are dependent on the principle angles between the two subspaces. submet implements an sklearn-styled interface with a fitting method via a class called SubspaceDistance, along with a variety of metrics in a class called Metric.

import numpy as np
import submet

# generate random subspaces
s1 = np.random.rand((10, 2))
s2 = np.random.rand((10, 2))

# instantiate SubspaceDistance object, using the Grassmann distance metric
S = submet.subspaces.SubspaceDistance(metric='Grassmann')

# compute the distance between two subspaces
S.fit(s1, s2)

# print computed distance
print(S.distance_)

Metric implements the following distance metrics:

• Asimov
• Binet-Cauchy
• Chordal
• Fubini-Study
• Martin
• Procrustes
• Projection
• Spectral

SubspaceDistance does not currently support pairwise distance computations between more than a single pair of subspaces, in an analogous way to Scipy’s pdist or cdist methods. I am working on allowing pairwise computations using numba.

Update as of 6/30/2020: the above issue has been fixed and submet now allows for pairwise distance matrix computations, rather than only single subspace pair comparisons. See this pull request