Note

This page is a reference documentation. It only explains the function signature, and not how to use it. Please refer to the user guide for the big picture.

nidl.metrics.kruskal_similarity¶

nidl.metrics.kruskal_similarity(X, Y, spherical=False)[source]¶

Kruskal similarity between two point clouds / embeddings.

Computes the pairwise Euclidean distances or cosine similarities of both point clouds. Returns the R^2 score of the upper triangular portion of both matrices.

This is essentially a scaled version of Kruskal’s stress, generalized to account for either Euclidean distance or cosine similarity.

Parameters:

Xtorch.Tensor or array-like, shape (n_samples, d1)
Ytorch.Tensor or array-like, shape (n_samples, d2)
sphericalbool, default=False: If False, compare Euclidean distances If True, compare cosine similarities

Returns:

sim0-dim torch.Tensor or np.ndarray: R^2 score in (-∞, 1]. 1 means X and Y are identical (after normalization if spherical == True) up to Euclidean isometry.

Notes

This metric is not symmetric, kruskal_similarity(X, Y) != kruskal_similarity(Y, X) in general.

References

https://en.wikipedia.org/wiki/Multidimensional_scaling#Non-metric_multidimensional_scaling_(NMDS)