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)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.