DataMining_AnomalyDetection.Rmd

---
title: "Anomaly Detection"
author: "Parash Upreti"
date: "July 13, 2016"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


## Anomaly Detection in R

Distance to k-Nearest Neighbor as Outlier Score

First Example Data Set

```{r}
set.seed(5364)
x1=rnorm(50)
y1=rnorm(50)
mydata1=data.frame(x=c(x1,6),y=c(y1,6))
plot(mydata1,pch=16)

#Distance Matrix
D=as.matrix(dist(mydata1))

#Distance to kth nearest neighbor (k=5)
kdist=1:51

for(i in 1:51){
  kdist[i]=(sort(D[i,]))[6]
}
```

Plotting data

```{r,fig=T}
library(proto)
library(ggplot2)
library(gridExtra)

#Ordinary plot
ggplot(data=mydata1,aes(x=x,y=y,size=3))+geom_point()

#Plot with Color Determined by kdist
ggplot(data=mydata1,aes(x=x,y=y,col=kdist,size=3))+geom_point()

#Gradient Plot (Heatmap)
ggplot(data=mydata1,aes(x=x,y=y,col=kdist,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("black", "red"))

ggplot(data=mydata1,aes(x=x,y=y,col=kdist,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("blue", "red"))

#Using Size to Represent kdist
ggplot(data=mydata1,aes(x=x,y=y,size=kdist))+geom_point()

#Density curve for Outlier Scores (kdist)
plot(density(kdist))
```

Finding Rows with Outliers

```{r}
(1:51)[kdist>=6]

#my.kdist function

my.kdist=function(data,k){
  n=nrow(data)
  D=as.matrix(dist(data))
  kdist=1:n
  for(i in 1:n){
    kdist[i]=(sort(D[i,]))[k+1]
  }
  return(kdist)
}

temp=my.kdist(mydata1,5)
cor(temp,kdist)
range(temp-kdist)
```

Second Example Data Set

```{r, fig=T}
set.seed(5364)
x1=rnorm(50)
y1=rnorm(50)
x2=0.5*rnorm(5)+10
y2=0.5*rnorm(5)+10
set.seed(5364)
mydata2=data.frame(x=c(x1,x2),y=c(y1,y2))
plot(mydata2,pch=16)

#Plot using kdist with k=5
kdist=my.kdist(mydata2,5)

ggplot(data=mydata2,aes(x=x,y=y,col=kdist,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("black", "red"))

plot(density(kdist))
(1:55)[kdist>=8]

#Plot using kdist with k=4
kdist=my.kdist(mydata2,4)

ggplot(data=mydata2,aes(x=x,y=y,col=kdist,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("black", "red"))

plot(density(kdist))
```

Third Example Data Set

```{r, fig=T}
set.seed(5366)
x1=rnorm(10)
y1=rnorm(10)
x2=0.1*rnorm(10)+10
y2=0.1*rnorm(10)
mydata3=data.frame(x=c(x1,x2,6),y=c(y1,y2,5))
plot(mydata3,pch=16)

#Detecting Outliers
kdist=my.kdist(mydata3,5)

ggplot(data=mydata3,aes(x=x,y=y,col=kdist,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("blue", "red"))

plot(density(kdist))
(1:nrow(mydata3))[kdist>=4]

```

### Density as an Outlier Score

Writing a density function

```{r, fig=T}
my.density=function(data,k){
  n=nrow(data)
  D=as.matrix(dist(data))
  density=1:n
  for(i in 1:n){
    knn.distances=(sort(D[i,]))[2:(k+1)]
    density[i]=(mean(knn.distances))^(-1)
  }
  return(density)
}

mydata3.density=my.density(mydata3,5)

ggplot(data=mydata3,aes(x=x,y=y,col=mydata3.density,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("blue", "red"))

ggplot(data=mydata3,aes(x=x,y=y,col=mydata3.density,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("red","blue"))

plot(density(mydata3.density))
```


### Average Relative Density as an Outlier Score
### Local Outlier Factor Method (LOF)           

```{r, fig=T}
library(DMwR)

outlier.scores=lofactor(mydata3,k=5)

ggplot(data=mydata3,aes(x=x,y=y,col=outlier.scores,size=3))+geom_point()+
  scale_colour_gradientn(colours=c("blue","red"))

plot(density(outlier.scores))
```

### Exploring Outliers in Iris Data with LOF

Remove Species Labels

```{r, fig=T}
attach(iris)
iris.x=iris[,1:4]
outlier.scores=lofactor(iris.x,k=5)

plot(density(outlier.scores))
sum(outlier.scores>=1.7)
sort(outlier.scores)

outliers=(outlier.scores>=1.7)

coloring=rep("black",150)
coloring[outliers]=c("red","green","blue")

plot(iris.x,col=coloring)
#text()
```