spd_learn.functional.bimap_increase_dim#

spd_learn.functional.bimap_increase_dim(X: Tensor, projection_matrix: Tensor, padding_matrix: Tensor) → Tensor[source]#

Increase the dimension of SPD matrices via embedding.

Computes the dimension expansion:

\[Y = P + W X W^\top\]

where \(X\) is the input SPD matrix, \(W\) is a semi-orthogonal projection matrix, and \(P\) is an identity padding matrix that ensures the output is SPD.

Parameters:

  • X (Tensor) – Input SPD matrices with shape (…, n_in, n_in).

  • projection_matrix (Tensor) – Semi-orthogonal projection matrix with shape (n_out, n_in).

  • padding_matrix (Tensor) – Identity padding matrix with shape (n_out, n_out). Should be a diagonal matrix with ones for indices >= n_in.

Returns:

Expanded SPD matrices with shape (…, n_out, n_out).

Return type:

Tensor

Notes

The padding matrix ensures that the output remains SPD by adding identity elements in the expanded dimensions.

See also

bimap_transform()

For dimension reduction.

BiMapIncreaseDim

Module wrapper for this function.

Examples

>>> import torch
>>> from spd_learn.functional import bimap_increase_dim
>>> X = torch.eye(4)  # 4x4 identity
>>> proj = torch.eye(8, 4)  # Projection from 4 to 8
>>> pad = torch.diag(torch.tensor([0,0,0,0,1,1,1,1], dtype=torch.float))
>>> Y = bimap_increase_dim(X, proj, pad)
>>> Y.shape
torch.Size([8, 8])