matrix_order

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

A general order function defined by a quadratic matrix.

For a feature indicator vector \(f\) and a matrix \(M\) this function computes \(|f| = f^T M f\).

If all entries outside the main diagonal in \(M\) are smaller or equal to 0 and shift is 0, then the submodularity of the order function is guaranteed.

Parameters

matrixnp.ndarray or sparse.spmatrix

A quadratic matrix of shape (seps.shape[0], seps.shape[0]).

featsnp.ndarray or sparse.spmatrix

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.