covariance_order

tangles.util.matrix_order.covariance_order(adjacency_matrix: ndarray | spmatrix, feats: ndarray, shift: float = 0)

Order function defined by the matrix \(A^T A\), where \(A\) is the adjacency matrix of a graph.

For a feature indicator vector \(f\) this function computes \(|f| = f^T A^T Af = (Af)^T Af\).

Parameters

adjacency_matrixnp.ndarray or sparse.spmatrix

A matrix with seps.shape[0] columns.

featsnp.ndarray

Matrix containing indicator vectors of features as columns.

shiftfloat

This parameter changes the order function’s preference for balanced features (note: it might also have an effect on its sub- or supermodularity). Let \(c\) denote the value of shift. The order function computes the order by \(|f| = f^T (M + cJ) f\).

Returns

ordersnp.ndarray

1-dimensional np.ndarray of length seps.shape[1] containing the orders.