transform_relations: Transform indirect relations

In schochastics/netrankr: Analyzing Partial Rankings in Networks

Transform indirect relations

Description

Mostly wrapper functions that can be used in conjunction with indirect_relations to fine tune indirect relations.

Usage

dist_2pow(x)

dist_inv(x)

dist_dpow(x, alpha = 1)

dist_powd(x, alpha = 0.5)

walks_limit_prop(x)

walks_exp(x, alpha = 1)

walks_exp_even(x, alpha = 1)

walks_exp_odd(x, alpha = 1)

walks_attenuated(x, alpha = 1/max(x) * 0.99)

walks_uptok(x, alpha = 1, k = 3)

Arguments

x	Matrix of relations.
alpha	Potential weighting factor.
k	For walk counts up to a certain length.

Details

The predefined functions follow the naming scheme relation_transformation. Predefined functions ⁠walks_*⁠ are thus best used with type="walks" in indirect_relations. Theoretically, however, any transformation can be used with any relation. The results might, however, not be interpretable.

The following functions are implemented so far:

dist_2pow returns 2^{-x}

dist_inv returns 1/x

dist_dpow returns x^{-\alpha} where \alpha should be chosen greater than 0.

dist_powd returns \alpha^x where \alpha should be chosen between 0 and 1.

walks_limit_prop returns the limit proportion of walks between pairs of nodes. Calculating rowSums of this relation will result in the principle eigenvector of the network.

walks_exp returns \sum_{k=0}^\infty \frac{A^k}{k!}

walks_exp_even returns \sum_{k=0}^\infty \frac{A^{2k}}{(2k)!}

walks_exp_odd returns \sum_{k=0}^\infty \frac{A^{2k+1}}{(2k+1)!}

walks_attenuated returns \sum_{k=0}^\infty \alpha^k A^k

walks_uptok returns \sum_{j=0}^k \alpha^j A^j

Walk based transformation are defined on the eigen decomposition of the adjacency matrix using the fact that

f(A)=Xf(\Lambda)X^T.

Care has to be taken when using user defined functions.

Value

Transformed relations as matrix

Author(s)

David Schoch

schochastics/netrankr documentation built on Jan. 10, 2024, 2 p.m.