# GARI: Graph Adjusted Rand Index In loe: Local Ordinal Embedding

## Description

Computes the graph adjusted Rand index measuring a recovery rate of ordinal information in an unweighted graph.

## Usage

 1 GARI(ADM, EADM) 

## Arguments

 ADM The given unweighted adjacency matrix EADM An recovered unweighted adjacency matrix from an embedding. The size of EADM should be same as that of ADM.

## Details

GARI is bounded from above by 1, and GARI(A_n,\hat{A}_n) iff A_n=\hat{A}_{n}. A high GARI score implies that many of the ordinal constraints have been satisfied by the solution.

## Value

The graph adjusted rand index measuring a recovery rate of ordinal information (a scalar).

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 library(igraph) ########### #Based on the distance matrix of an embedding, #this function provides the recovered adjacency matrix for given number of nearest neighbors. ########### rec.graph <- function(DM, k, symm =FALSE, weight=FALSE ) { N <- nrow(DM) ADM <- matrix(0, N, N) #Search kNN point if(weight==TRUE){ for (i in 1:N) { nid <- order(DM[i,]) ADM[ i, nid[2:(k[i]+1)] ] <- DM[ i, nid[2:(k[i]+1)] ] } }else{ for (i in 1:N) { nid <- order(DM[i,]) ADM[i,nid[2:(k[i]+1)] ] <- 1 } } if(symm==TRUE){ SADM <- ADM+t(ADM) SADM[SADM==2*ADM] <- ADM[SADM==2*ADM] ADM <- SADM } return(ADM) } ADM <- as.matrix( get.adjacency(graph.famous("Thomassen")) ) #Apply LOE result.LOE <- LOE(ADM=ADM,p=2,c=0.1,method="BFGS",report=1000) #Compute the vector of numbers of nearest neighbors with each verteces true.nn <- apply(X=ADM,1,sum) #Reconstracte the adjacency matrix based on the result embedding EDM <- as.matrix( dist(result.LOE\$X) ) EADM <- rec.graph(EDM,k=true.nn ) #Compute GARI between ADM and EADM GARI(ADM,EADM) 

### Example output

Loading required package: MASS

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

decompose, spectrum

The following object is masked from 'package:base':

union

initial  value 7.531723
final  value 3.124988
converged
 0.5652314


loe documentation built on May 2, 2019, 3:28 a.m.