transform_relations function

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)

Arguments

• x: Matrix of relations.
• alpha: Potential weighting factor.
• k: For walk counts up to a certain length.

Returns

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

Care has to be taken when using user defined functions.

Author(s)

David Schoch