linear_similarity_from_distances

tangles.util.matrix_order.linear_similarity_from_distances(m: ndarray, margin: float, eps: float = 1e-08, sparse_mat: bool = True, distance_p: float = 2)

Turns a matrix of positions into a matrix of similarities (simply based on distances).

A matrix order function (quadratic form) based on the returned matrix behaves like a “margin order function”, i.e. only pairs of separated points close to a (fictitious optimal) boundary between the separation’s sides are taken into account.

Similarities range from 1, if they are equal, to 0, if they have a distance greater than margin.

Parameters

mnp.ndarray

Matrix of positions.

marginfloat

Size of the margin. In the distance matrix, all distances greater than this margin will be set to the margin.

epsfloat

A threshold. Similarities below this value are set to 0.

sparse_matbool

Whether to return a sparse.csr_matrix.

distance_pfloat

Which Minkowski p-norm to use. Must take a value in \([1, \infty)\).

Returns

sparse.csr_matrix or np.ndarray

A matrix of similarities.