`laplacian_eigenmaps`#

hypercoil.functional.connectopy.laplacian_eigenmaps(W: Array | ndarray, k: int = 10, normalise: bool = True) → Tuple[Array | ndarray, Array | ndarray][source]#

Manifold coordinates estimated using Laplacian eigenmaps.

Warning

Sparse inputs are currently unsupported because an implementation of a sparse extremal eigenvalue solver does not yet exist in JAX. For sparse inputs, use the generalised connectopic functional instead – once we implement VJP rules for elementary operations on sparse matrices, anyway.

Dimension:

W : \((*, N, N)\): * denotes any number of preceding dimensions, N denotes number of vertices, and E denotes number of edges.
Q : \((*, N, k)\): k denotes the number of eigenmaps.
L : \((*, k)\): As above.

Parameters:

Wtensor: Edge weight tensor. If edge_index is not provided, then this should be the graph adjacency (or affinity) matrix; otherwise, it should be a list of weights corresponding to the edges in edge_index.
kint (default 10): Number of eigenmaps to compute.
normalisebool (default True): Indicates that the Laplacian should be normalised using the degree matrix.

Returns:

Qtensor: Eigenmaps.
Ltensor: Eigenvalues corresponding to eigenmaps.

laplacian_eigenmaps#

`laplacian_eigenmaps`#