Add euclidean_distance_v2
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Jensun Ravichandran
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7d9dfc27ee
commit
e2918dffed
@ -43,9 +43,21 @@ def euclidean_distance(x, y):
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return distances
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def euclidean_distance_v2(x, y):
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diff = y - x.unsqueeze(1)
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pairwise_distances = (diff @ diff.permute((0, 2, 1))).sqrt()
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# Passing `dim1=-2` and `dim2=-1` to `diagonal()` takes the
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# batch diagonal. See:
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# https://pytorch.org/docs/stable/generated/torch.diagonal.html
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distances = torch.diagonal(pairwise_distances, dim1=-2, dim2=-1)
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# print(f"{diff.shape=}") # (nx, ny, ndim)
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# print(f"{pairwise_distances.shape=}") # (nx, ny, ny)
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# print(f"{distances.shape=}") # (nx, ny)
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return distances
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def lpnorm_distance(x, y, p):
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r"""
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Calculates the lp-norm between :math:`\bm x` and :math:`\bm y`.
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r"""Calculate the lp-norm between :math:`\bm x` and :math:`\bm y`.
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Also known as Minkowski distance.
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Compute :math:`{\| \bm x - \bm y \|}_p`.
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@ -107,26 +119,18 @@ def euclidean_distance_matrix(x, y, squared=False, epsilon=1e-10):
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for tensor in [x, y]:
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if tensor.ndim != 2:
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raise ValueError(
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"The tensor dimension must be two. You provide: tensor.ndim="
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+ str(tensor.ndim)
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+ "."
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)
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"The tensor dimension must be two. You provide: tensor.ndim=" +
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str(tensor.ndim) + ".")
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if not equal_int_shape([tuple(x.shape)[1]], [tuple(y.shape)[1]]):
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raise ValueError(
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"The vector shape must be equivalent in both tensors. You provide: tuple(y.shape)[1]="
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+ str(tuple(x.shape)[1])
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+ " and tuple(y.shape)(y)[1]="
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+ str(tuple(y.shape)[1])
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+ "."
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)
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+ str(tuple(x.shape)[1]) + " and tuple(y.shape)(y)[1]=" +
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str(tuple(y.shape)[1]) + ".")
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y = torch.transpose(y)
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diss = (
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torch.sum(x ** 2, axis=1, keepdims=True)
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- 2 * torch.dot(x, y)
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+ torch.sum(y ** 2, axis=0, keepdims=True)
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)
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diss = (torch.sum(x**2, axis=1, keepdims=True) - 2 * torch.dot(x, y) +
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torch.sum(y**2, axis=0, keepdims=True))
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if not squared:
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if epsilon == 0:
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@ -173,19 +177,18 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
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if subspaces.ndim == 2:
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# clean solution without map if the matrix_scope is global
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projectors = torch.eye(subspace_int_shape[-2]) - torch.dot(
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subspaces, torch.transpose(subspaces)
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)
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subspaces, torch.transpose(subspaces))
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projected_signals = torch.dot(signals, projectors)
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projected_protos = torch.dot(protos, projectors)
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diss = euclidean_distance_matrix(
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projected_signals, projected_protos, squared=squared, epsilon=epsilon
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)
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diss = euclidean_distance_matrix(projected_signals,
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projected_protos,
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squared=squared,
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epsilon=epsilon)
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diss = torch.reshape(
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diss, [signal_shape[0], signal_shape[2], proto_shape[0]]
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)
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diss, [signal_shape[0], signal_shape[2], proto_shape[0]])
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return torch.permute(diss, [0, 2, 1])
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@ -193,21 +196,18 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
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# no solution without map possible --> memory efficient but slow!
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projectors = torch.eye(subspace_int_shape[-2]) - torch.bmm(
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subspaces, subspaces
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) # K.batch_dot(subspaces, subspaces, [2, 2])
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subspaces,
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subspaces) # K.batch_dot(subspaces, subspaces, [2, 2])
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projected_protos = (
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protos @ subspaces
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projected_protos = (protos @ subspaces
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).T # K.batch_dot(projectors, protos, [1, 1]))
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def projected_norm(projector):
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return torch.sum(torch.dot(signals, projector)**2, axis=1)
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diss = (
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torch.transpose(map(projected_norm, projectors))
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- 2 * torch.dot(signals, projected_protos)
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+ torch.sum(projected_protos ** 2, axis=0, keepdims=True)
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)
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diss = (torch.transpose(map(projected_norm, projectors)) -
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2 * torch.dot(signals, projected_protos) +
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torch.sum(projected_protos**2, axis=0, keepdims=True))
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if not squared:
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if epsilon == 0:
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@ -216,8 +216,7 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
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diss = torch.sqrt(torch.max(diss, epsilon))
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diss = torch.reshape(
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diss, [signal_shape[0], signal_shape[2], proto_shape[0]]
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)
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diss, [signal_shape[0], signal_shape[2], proto_shape[0]])
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return torch.permute(diss, [0, 2, 1])
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@ -233,12 +232,12 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
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# Scope: Tangentspace Projections
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diff = torch.reshape(
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diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1)
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)
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diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1))
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projected_diff = diff @ projectors
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projected_diff = torch.reshape(
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projected_diff,
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(signal_shape[0], signal_shape[2], signal_shape[1]) + signal_shape[3:],
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(signal_shape[0], signal_shape[2], signal_shape[1]) +
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signal_shape[3:],
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)
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diss = torch.norm(projected_diff, 2, dim=-1)
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@ -251,13 +250,13 @@ def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
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# Scope: Tangentspace Projections
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diff = torch.reshape(
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diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1)
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)
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diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1))
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diff = diff.permute([1, 0, 2])
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projected_diff = torch.bmm(diff, projectors)
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projected_diff = torch.reshape(
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projected_diff,
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(signal_shape[1], signal_shape[0], signal_shape[2]) + signal_shape[3:],
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(signal_shape[1], signal_shape[0], signal_shape[2]) +
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signal_shape[3:],
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)
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diss = torch.norm(projected_diff, 2, dim=-1)
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