Transform indirect relations
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)
x |
Matrix of relations. |
alpha |
Potential weighting factor. |
k |
For walk counts up to a certain length. |
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.
Transformed relations as matrix
David Schoch
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.