netdiffuseR (version 1.22.6)

vertex_covariate_dist: Computes covariate distance between connected vertices

Description

Computes covariate distance between connected vertices

Usage

vertex_covariate_dist(graph, X, p = 2)
vertex_mahalanobis_dist(graph, X, S)

Value

A matrix of size \(n\times n\) of class dgCMatrix. Will be symmetric only if graph is symmetric.

Arguments

graph

A square matrix of size \(n\) of class dgCMatrix.

X

A numeric matrix of size \(n \times K\). Vertices attributes

p

Numeric scalar. Norm to compute

S

Square matrix of size ncol(x). Usually the var-covar matrix.

Author

George G. Vega Yon

Details

Faster than dist, these functions compute distance metrics between pairs of vertices that are connected (otherwise skip).

The function vertex_covariate_dist is the simil of dist and returns p-norms (Minkowski distance). It is implemented as follows (for each pair of vertices):

$$% D_{ij} = \left(\sum_{k=1}^K \left|X_{ik} - X_{jk}\right|^{p} \right)^{1/p}\mbox{ if }graph_{i,j}\neq 0 $$

In the case of mahalanobis distance, for each pair of vertex \((i,j)\), the distance is computed as follows:

$$% D_{ij} = \left( (X_i - X_j)\times S \times (X_i - X_j)' \right)^{1/2}\mbox{ if }graph_{i,j}\neq 0 $$

References

Mahalanobis distance. (2016, September 27). In Wikipedia, The Free Encyclopedia. Retrieved 20:31, September 27, 2016, from https://en.wikipedia.org/w/index.php?title=Mahalanobis_distance&oldid=741488252

See Also

mahalanobis in the stats package.

Other statistics: bass, classify_adopters(), cumulative_adopt_count(), dgr(), ego_variance(), exposure(), hazard_rate(), infection(), moran(), struct_equiv(), threshold()

Other dyadic-level comparison functions: matrix_compare(), vertex_covariate_compare()

Examples

# Distance (aka p norm) -----------------------------------------------------
set.seed(123)
G <- rgraph_ws(20, 4, .1)
X <- matrix(runif(40), ncol=2)

vertex_covariate_dist(G, X)[1:5, 1:5]

# Mahalanobis distance ------------------------------------------------------
S <- var(X)

M <- vertex_mahalanobis_dist(G, X, S)

# Example with diffnet objects ----------------------------------------------

data(medInnovationsDiffNet)
X <- cbind(
  medInnovationsDiffNet[["proage"]],
  medInnovationsDiffNet[["attend"]]
)

S <- var(X, na.rm=TRUE)
ans <- vertex_mahalanobis_dist(medInnovationsDiffNet, X, S)