RANKS (version 1.1)

rw.kernel-methods: Random walk kernel

Description

Methods to compute the random walk kernel (Smola and Kondor, 2003)

Usage

# S4 method for matrix
rw.kernel(W, a = 2)
# S4 method for graph
rw.kernel(W, a = 2)
# S4 method for graph
p.step.rw.kernel(RW, p = 2)
# S4 method for matrix
p.step.rw.kernel(RW, p = 2)

Value

rw.kernel: A numeric square matrix representing a one-step random walk kernel matrix

p.step.rw.kernel: A numeric square matrix representing a p-step random walk kernel matrix

Arguments

W

a square symmetric matrix with positive values or an object of the class graphAM or graphNEL of the package graph

RW

matrix. It must be a random walk kernel matrix

a

numeric. It is correlated to the probability of remaining at the same vertex. Larger a, larger the probability (def. 2)

p

integer. Number of steps (def: p=2)

Methods

signature(W = "graph")

rw.kernel computes the random walk kernel starting from a graph of class graph (hence including objects of class graphAM and graphNEL from the package graph)

signature(W = "matrix")

rw.kernel computes the random walk kernel starting from a weighted adjacency matrix representing the graph

signature(RW = "graph")

p.step.rw.kernel computes the a p-step random walk kernel starting from a graph of class graph (hence including objects of class graphAM and graphNEL from the package graph)

signature(RW = "matrix")

p.step.rw.kernel computes the p-step random walk kernel starting from a one-step random walk kernel matrix

Details

rw.kernel methods computes the one step random walk kernel RW, i.e.: $$ RW = (a-1)I + D^{-\frac{1}{2}} * W * D^{-\frac{1}{2}} $$

where \(I\) is the identity matrix, \(W\) is the weighted adjacency matrix of an undirected graph, and \(D\) is a diagonal matrix with \(D_{ii} = \sum_j W_{ij}\)

p.step.rw.kernel methods compute the p-step random walk kernel pRW, i.e.: $$ pRW = RW^p $$

Examples

# Random walk kernel computation using Functional Interaction network data
library(bionetdata);
data(FIN.data);
W <- as.matrix(FIN.data);
K <- rw.kernel(W);
# this a 2-step random walk kernel
# \donttest{
K2 <- p.step.rw.kernel(K, p=2);# }