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

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.

Value

Transformed relations as matrix

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.