library(oddnet)library(igraph)#>#> Attaching package: 'igraph'#> The following objects are masked from 'package:stats':#>#> decompose, spectrum#> The following object is masked from 'package:base':#>#> union
Synthetic data
We create a sequence of temporal networks based on the Erdos Renyiconstruction and insert an anomaly at location 50. For this series, wemake the edge probability increase from 0.01 to 0.2.
set.seed(1)networks<-list()p.or.m.seq<-seq(from =0.01,to =0.2,length.out =100)p.or.m.seq[50]<- p.or.m.seq[50]+0.2# anomalous networkfor(iin1:100){ gr<- igraph::erdos.renyi.game(100,p.or.m = p.or.m.seq[i]) networks[[i]]<- igraph::as_adjacency_matrix(gr)}
Let’s plot a couple of networks.
Plotting
# Plottingnetwork_1<- networks[[1]]gr<- igraph::graph_from_adjacency_matrix(network_1)plot(gr,layout = layout_with_fr,vertex.size=3,vertex.label=NA,edge.arrow.size=0.2,main ="Network 1")
network_30<- networks[[30]]gr<- igraph::graph_from_adjacency_matrix(network_30)plot(gr,layout = layout_with_fr,vertex.size=3,vertex.label=NA,edge.arrow.size=0.2,main ="Network 30")
network_80<- networks[[80]]gr<- igraph::graph_from_adjacency_matrix(network_80)plot(gr,layout = layout_with_fr,vertex.size=3,vertex.label=NA,edge.arrow.size=0.2,main ="Network 80")
The networks have increased in connectivity because the edgeprobability increases over time. Let’s look at the anomalous network att = 50.
# Plottingnetwork_a<- networks[[50]]gr<- igraph::graph_from_adjacency_matrix(network_a)plot(gr,layout = layout_with_fr,vertex.size=3,vertex.label=NA,edge.arrow.size=0.2,main ="Network 50 - Anomaly")
Features
Both networks at t = 50 and t = 80 look alike. Let’s explore theirdegree distributions.
network_80<- networks[[80]]gr<- igraph::graph_from_adjacency_matrix(network_80)hist(degree(gr))
network_a<- networks[[50]]gr<- igraph::graph_from_adjacency_matrix(network_a)hist(degree(gr))
We see a clear difference in the degree distributions of the twonetworks. Let’s look at the average degree of the network sequence.
avg_deg<-rep(0,100)max_deg<-rep(0,100)for(iin1:100){ network<- networks[[i]] gr<- igraph::graph_from_adjacency_matrix(network) avg_deg[i]<-mean(degree(gr)) max_deg[i]<-max(degree(gr))}plot(avg_deg,type ="l")
We clearly see the anomaly at 50. Oddnet is a feature-based method.By computing many features it finds anomalies using time series methods.Let’s find the anomalous networks using oddnet.
Anomalies
anomalous_networks(networks)#> Warning in sqrt(diag(best$var.coef)): NaNs produced#> Warning in sqrt(diag(best$var.coef)): NaNs produced#> Leave-out-out KDE outliers using lookout algorithm#>#> Call: lookout::lookout(X = dfpca[, 1:dd], alpha = alpha)#>#> Outliers Probability#> 1 50 0.007779304
We see the correct anomaly is identified with low conditionalprobability.