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.

David Schoch