def tangent_pca(self, points, base_point=None, point_type='vector'):
"""Perform tPCA of points on the tangent space at a base point.
Tangent Principal Component Analysis (tPCA) of points
on the tangent space at a base point.
Parameters
----------
points
base_point
point_type
Returns
-------
eigenvalues
tangent_eigenvecs
"""
if point_type == 'matrix':
raise NotImplementedError(
'This is currently only implemented for vectors.')
if base_point is None:
base_point = self.mean(points)
tangent_vecs = self.log(points, base_point=base_point)
covariance_mat = gs.cov(tangent_vecs.transpose())
eigenvalues, tangent_eigenvecs = gs.linalg.eig(covariance_mat)
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
tangent_eigenvecs = tangent_eigenvecs[idx]
return eigenvalues, tangent_eigenvecs
def tangent_pca(self, points, base_point=None):
"""
Tangent Principal Component Analysis (tPCA) of points
on the tangent space at a base point.
"""
# TODO(nina): It only works for points of ndim=2, adapt to other ndims.
if base_point is None:
base_point = self.mean(points)
tangent_vecs = self.log(points, base_point=base_point)
covariance_mat = gs.cov(tangent_vecs.transpose())
eigenvalues, tangent_eigenvecs = gs.linalg.eig(covariance_mat)
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
tangent_eigenvecs = tangent_eigenvecs[idx]
return eigenvalues, tangent_eigenvecs
def tangent_pca(self, points, base_point=None):
"""
Tangent Principal Component Analysis (tPCA) at base_point.
This is standard PCA on the Riemannian Logarithms of the points
at the base point.
"""
# TODO(xxx): It only works for points of ndim=2, adapt to other ndims.
if base_point is None:
base_point = self.mean(points)
tangent_vecs = self.log(points, base_point=base_point)
covariance_mat = gs.cov(tangent_vecs.transpose())
eigenvalues, tangent_eigenvecs = gs.linalg.eig(covariance_mat)
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
tangent_eigenvecs = tangent_eigenvecs[idx]
return eigenvalues, tangent_eigenvecs
