# transform_relations: Transform indirect relations In netrankr: Analyzing Partial Rankings in Networks

## Description

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

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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^{-α} where α should be chosen greater than 0.

dist_powd returns α^x where α 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 ∑_{k=0}^∞ \frac{A^k}{k!}

walks_exp_even returns ∑_{k=0}^∞ \frac{A^{2k}}{(2k)!}

walks_exp_odd returns ∑_{k=0}^∞ \frac{A^{2k+1}}{(2k+1)!}

walks_attenuated returns ∑_{k=0}^∞ α^k A^k

walks_uptok returns ∑_{j=0}^k α^j A^j

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

f(A)=Xf(Λ)X^T.

Care has to be taken when using user defined functions.

## Value

Transformed relations as matrix

## Author(s)

David Schoch

netrankr documentation built on Sept. 5, 2021, 5:19 p.m.