def dist(self, point_a, point_b):
"""
Geodesic distance between two points.
Parameters
----------
point_a : array-like, shape=[n_samples, dimension + 1]
or shape=[1, dimension + 1]
point_b : array-like, shape=[n_samples, dimension + 1]
or shape=[1, dimension + 1]
Returns
-------
dist : array-like, shape=[n_samples, 1]
or shape=[1, 1]
"""
sq_norm_a = self.embedding_metric.squared_norm(point_a)
sq_norm_b = self.embedding_metric.squared_norm(point_b)
inner_prod = self.embedding_metric.inner_product(point_a, point_b)
cosh_angle = - inner_prod / gs.sqrt(sq_norm_a * sq_norm_b)
cosh_angle = gs.clip(cosh_angle, 1.0, 1e24)
dist = gs.arccosh(cosh_angle)
return dist
def dist(self, point_a, point_b):
"""Compute the geodesic distance between two points.
Parameters
----------
point_a : array-like, shape=[..., dim + 1]
First point in hyperbolic space.
point_b : array-like, shape=[..., dim + 1]
Second point in hyperbolic space.
Returns
-------
dist : array-like, shape=[...,]
Geodesic distance between the two points.
"""
sq_norm_a = self.embedding_metric.squared_norm(point_a)
sq_norm_b = self.embedding_metric.squared_norm(point_b)
inner_prod = self.embedding_metric.inner_product(point_a, point_b)
cosh_angle = -inner_prod / gs.sqrt(sq_norm_a * sq_norm_b)
cosh_angle = gs.clip(cosh_angle, 1.0, 1e24)
dist = gs.arccosh(cosh_angle)
dist *= self.scale
return dist
def dist(self, point_a, point_b):
"""
Geodesic distance between two points.
"""
sq_norm_a = self.embedding_metric.squared_norm(point_a)
sq_norm_b = self.embedding_metric.squared_norm(point_b)
inner_prod = self.embedding_metric.inner_product(point_a, point_b)
cosh_angle = -inner_prod / gs.sqrt(sq_norm_a * sq_norm_b)
cosh_angle = gs.clip(cosh_angle, 1.0, 1e24)
dist = gs.arccosh(cosh_angle)
return dist
def dist(self, point_a, point_b):
"""Compute the geodesic distance between two points.
Parameters
----------
point_a : array-like, shape=[n_samples, dimension + 1]
First point in hyperbolic space.
point_b : array-like, shape=[n_samples, dimension + 1]
Second point in hyperbolic space.
Returns
-------
dist : array-like, shape=[n_samples, 1]
Geodesic distance between the two points.
"""
if self.point_type == 'extrinsic':
sq_norm_a = self.embedding_metric.squared_norm(point_a)
sq_norm_b = self.embedding_metric.squared_norm(point_b)
inner_prod = self.embedding_metric.inner_product(point_a, point_b)
cosh_angle = -inner_prod / gs.sqrt(sq_norm_a * sq_norm_b)
cosh_angle = gs.clip(cosh_angle, 1.0, 1e24)
dist = gs.arccosh(cosh_angle)
return self.scale * dist
elif self.point_type == 'ball':
point_a_norm = gs.clip(gs.sum(point_a**2, -1), 0., 1 - EPSILON)
point_b_norm = gs.clip(gs.sum(point_b**2, -1), 0., 1 - EPSILON)
diff_norm = gs.sum((point_a - point_b)**2, -1)
norm_function = 1 + 2 * \
diff_norm / ((1 - point_a_norm) * (1 - point_b_norm))
dist = gs.log(norm_function + gs.sqrt(norm_function**2 - 1))
dist = gs.to_ndarray(dist, to_ndim=1)
dist = gs.to_ndarray(dist, to_ndim=2, axis=1)
return self.scale * dist
else:
raise NotImplementedError(
'dist is only implemented for ball and extrinsic')
def dist(self, point_a, point_b):
"""
Compute the distance induced on the hyperbolic
space, from its embedding in the Minkowski space.
"""
if gs.all(gs.equal(point_a, point_b)):
return 0.
sq_norm_a = self.embedding_metric.squared_norm(point_a)
sq_norm_b = self.embedding_metric.squared_norm(point_b)
inner_prod = self.embedding_metric.inner_product(point_a, point_b)
cosh_angle = -inner_prod / gs.sqrt(sq_norm_a * sq_norm_b)
cosh_angle = gs.clip(cosh_angle, 1, None)
dist = gs.arccosh(cosh_angle)
return dist
