# rw.kernel-methods: Random walk kernel

Description Usage Arguments Details Value Methods Examples

### Description

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

### Usage

 1 2 3 4 5 6 7 8 ## S4 method for signature 'matrix' rw.kernel(W, a = 2) ## S4 method for signature 'graph' rw.kernel(W, a = 2) ## S4 method for signature 'graph' p.step.rw.kernel(RW, p = 2) ## S4 method for signature 'matrix' p.step.rw.kernel(RW, p = 2) 

### 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)

### 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} = ∑_j W_{ij}

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

pRW = RW^p

### 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

### 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

### Examples

 1 2 3 4 5 6 7 # 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 K2 <- p.step.rw.kernel(K, p=2); 

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