Spectral-Ranking-for-Abnormality

Implementation of the Spectral Ranking for Abnormality (SRA) algorithm as described in the paper K. Nian, H. Zhang, A. Tayal, T. F. Coelman, Y. Li, (2014) 'Unsupervised Spectral Ranking for Anomaly and Application to Auto Insurance Fraud Detection'

Example1

load libraries

library(kernlab) library(ggplot2)

load data

data(promotergene)

transform numeric data to categorical data

df=as.data.frame(sapply(promotergene[,-1],catcalinhara))

compute hamming distance kernel matrix

hammingkernelMatrix = hammingkernel2(df,lambda = .6)

Perform spectral ranking

SpectralAnomaly = sra(hammingkernelMatrix, Xi = .4)

plot

g = ggplot(SpectralAnomaly$EigenSpace,aes(x=np_Eigenvector_1, y = np_Eigenvector_2,color=ifelse(sign(SpectralAnomaly$Anomaly)==-1,1,SpectralAnomaly$Anomaly+1))) + geom_point() + scale_color_gradient("Anomaly",trans="log",low="blue",high="red") g = g + ggtitle(paste("mFLAG= ",SpectralAnomaly$mFLAG)) g = g + theme(legend.title = element_text(face="plain"), legend.text = element_text(color = "white")) g

Example2

mushroom=read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/mushroom/agaricus-lepiota.data", header=FALSE, sep=",") mush.split=split(mushroom,mushroom$V1) mush.e=mush.split[[1]] mush.p=mush.split[[2]] mush.p=mush.p[sample(nrow(mush.p),300),] mushroom =rbind(mush.e,mush.p)

should have 300 poisonous mushrooms

table(mushroom$V1)

transform numeric data to categorical data

df=as.data.frame(sapply(mushroom[,-1],catcalinhara))

compute hamming distance kernel matrix

ptm <- proc.time() hammingkernelMatrix = hammingkernel(df,lambda = .5) proc.time() - ptm

Perform spectral ranking

ptm <- proc.time() SpectralAnomaly = sra(hammingkernelMatrix, Xi = .1) proc.time() - ptm

plot

g = ggplot(SpectralAnomaly$EigenSpace,aes(x=np_Eigenvector_1, y = np_Eigenvector_2,color=ifelse(sign(SpectralAnomaly$Anomaly)==-1,1,SpectralAnomaly$Anomaly+1))) + geom_point() + scale_color_gradient("Anomaly",trans="log",low="black",high="red") g = g + ggtitle(paste("mFLAG= ",SpectralAnomaly$mFLAG)) g = g + theme(legend.title = element_text(face="plain"), legend.text = element_text(color = "white")) g

use both first non-principal eigenvectors for the anomaly score

g = ggplot(SpectralAnomaly$EigenSpace,aes(x=np_Eigenvector_1, y = np_Eigenvector_2,color=ifelse(sign(SpectralAnomaly$Anomaly)==-1,1,SpectralAnomaly$Anomaly+1+max(abs(SpectralAnomaly$EigenSpace[,"np_Eigenvector_2"])) - abs(SpectralAnomaly$EigenSpace[,"np_Eigenvector_2"])))) + geom_point() + scale_color_gradient("Anomaly",low="black",high="red") g = g + ggtitle(paste("mFLAG= ",SpectralAnomaly$mFLAG)) g = g + theme(legend.title = element_text(face="plain"), legend.text = element_text(color = "white")) g

Test set AUC

library(ROCR) ROCRpred = prediction(SpectralAnomaly$Anomaly, mushroom$V1) perf = performance(ROCRpred, "tpr", "fpr") plot(perf,colorize=T,print.cutoffs.at=seq(0,1,by=0.05),main=paste("AUC: ",as.numeric(performance(ROCRpred, "auc")@y.values)))

Example3

breastcancer=read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data", header=FALSE, sep=",")

should have 357 benign cases and 212 malignant

table(breastcancer$V2)

transform numeric data to categorical data

df=as.data.frame(sapply(breastcancer[,c(-1,-2)],catcalinhara))

compute hamming distance kernel matrix

ptm <- proc.time() hammingkernelMatrix = hammingkernel(df,lambda = .8) proc.time() - ptm

Perform spectral ranking

ptm <- proc.time() SpectralAnomaly = sra(hammingkernelMatrix, Xi = .4) proc.time() - ptm

plot

g = ggplot(SpectralAnomaly$EigenSpace,aes(x=np_Eigenvector_1, y = np_Eigenvector_2,color=ifelse(sign(SpectralAnomaly$Anomaly)==-1,1,SpectralAnomaly$Anomaly+1))) + geom_point() + scale_color_gradient("Anomaly",trans="log",low="black",high="red") g = g + ggtitle(paste("mFLAG= ",SpectralAnomaly$mFLAG)) g = g + theme(legend.title = element_text(face="plain"), legend.text = element_text(color = "white")) g

Test set AUC

library(ROCR) ROCRpred = prediction(SpectralAnomaly$Anomaly, breastcancer$V2) perf = performance(ROCRpred, "tpr", "fpr") plot(perf,colorize=T,print.cutoffs.at=seq(0,1,by=0.2),main=paste("AUC: ",as.numeric(performance(ROCRpred, "auc")@y.values)))