topo.eval.global_scores

Functions

global_loss_(X, Y)

global_score_pca(X, Y[, Y_pca])

Compute the global score comparing an embedding to PCA.

global_score_laplacian(X, Y[, k, data_is_graph, ...])

Compute the global score comparing an embedding to a Laplacian Eigenmap baseline.

Module Contents

topo.eval.global_scores.global_loss_(X, Y)
topo.eval.global_scores.global_score_pca(X, Y, Y_pca=None)

Compute the global score comparing an embedding to PCA.

The score is defined as exp(-(L_emb - L_pca) / L_pca) where L denotes the mean reconstruction error (global loss) of a linear projection. A score of 1 means the embedding preserves as much global structure as PCA; scores below 1 indicate worse global preservation. The result is clipped to [0, 1].

Parameters:

  • X (array-like of shape (n_samples, n_features) or sparse matrix) – Input feature matrix.

  • Y (array-like of shape (n_samples, n_components)) – Low-dimensional embedding to evaluate.

  • Y_pca (array-like of shape (n_samples, n_components), optional) – Pre-computed PCA embedding. If None, computed from X.

Returns:

score (float in (0, 1]) – Global structure preservation score relative to PCA.

topo.eval.global_scores.global_score_laplacian(X, Y, k=10, data_is_graph=False, n_jobs=12, random_state=None)

Compute the global score comparing an embedding to a Laplacian Eigenmap baseline.

The score is defined as exp(-(L_emb - L_lap) / L_lap) where L denotes the mean reconstruction error (global loss) of a linear projection. A score of 1 means the embedding preserves as much global structure as a Laplacian Eigenmap of the same dimension; scores below 1 indicate worse global preservation. The result is clipped to [0, 1].

Parameters:

  • X (array-like of shape (n_samples, n_features) or sparse (n_samples, n_samples)) – Input feature matrix, or precomputed affinity graph if data_is_graph=True.

  • Y (array-like of shape (n_samples, n_components)) – Low-dimensional embedding to evaluate.

  • k (int, default 10) – Number of neighbors used by SpectralEmbedding when data_is_graph=False.

  • data_is_graph (bool, default False) – If True, X is treated as a precomputed affinity graph.

  • n_jobs (int, default 12) – Number of parallel jobs for SpectralEmbedding.

  • random_state (numpy.random.RandomState or int, optional) – Random state for SpectralEmbedding.

Returns:

score (float in (0, 1]) – Global structure preservation score relative to Laplacian Eigenmaps.