wsingular.utils

wsingular.utils.check_uniqueness(A: torch.Tensor, B: torch.Tensor, C: torch.Tensor, D: torch.Tensor) → bool

Check uniqueness of singular vectors using the graph connectivity criterion described in the paper.

Parameters:

  • A (torch.Tensor) – The samples.

  • B (torch.Tensor) – The features.

  • C (torch.Tensor) – The ground cost.

  • D (torch.Tensor) – The pairwise distance.

Returns:

Whether the criterion is verified.

Return type:

bool

wsingular.utils.hilbert_distance(D_1: torch.Tensor, D_2: torch.Tensor) → float

Compute the Hilbert distance between two distance-like matrices.

Parameters:

  • D_1 (torch.Tensor) – The first matrix

  • D_2 (torch.Tensor) – The second matrix

Returns:

The distance

Return type:

float

wsingular.utils.normalize_dataset(dataset: torch.Tensor, dtype: str, device: str, normalization_steps: int = 1, small_value: float = 1e-06) → Tuple[torch.Tensor, torch.Tensor]

Normalize the dataset and return the normalized dataset A and the transposed dataset B.

Parameters:

  • dataset (torch.Tensor) – The input dataset, samples as rows.

  • normalization_steps (int, optional) – The number of Sinkhorn normalization steps. For large numbers, we get bistochastic matrices. Defaults to 1 and should be larger or equal to 1.

  • small_value (float) – Small addition to the dataset to avoid numerical errors while computing OT distances. Defaults to 1e-6.

Returns:

The normalized matrices A and B.

Return type:

Tuple[torch.Tensor, torch.Tensor]

wsingular.utils.random_distance(size: int, dtype: str, device: str) → torch.Tensor

Return a random distance-like matrix, i.e. symmetric with zero diagonal. The matrix is also divided by its maximum, so as to have infty norm 1.

Parameters:

  • size (int) – Will return a matrix of dimensions size*size

  • dtype (str) – The dtype to be returned

  • device (str) – The device to be returned

Returns:

The random distance-like matrix

Return type:

torch.Tensor

wsingular.utils.regularization_matrix(A: torch.Tensor, p: int, dtype: str, device: str) → torch.Tensor

Return the regularization matrix

Parameters:

  • A (torch.Tensor) – The dataset, with samples as rows

  • p (int) – order of the norm

  • dtype (str) – The dtype to be returned

  • device (str) – The device to be returned

Returns:

The regularization matrix

Return type:

torch.Tensor

wsingular.utils.silhouette(D: torch.Tensor, labels: Iterable) → float

Return the average silhouette score, given a distance matrix and labels.

Parameters:

  • D (torch.Tensor) – Distance matrix n*n

  • labels (Iterable) – n labels

Returns:

The average silhouette score

Return type:

float

wsingular.utils.viz_TSNE(D: torch.Tensor, labels: Optional[Iterable] = None) → None

Visualize a distance matrix using a precomputed distance matrix.

Parameters:

  • D (torch.Tensor) – Distance matrix

  • labels (Iterable, optional) – The labels, if any. Defaults to None.