The "Elbow" Method for Clustering Evaluation

Description

Determining the number of clusters in a data set by the "elbow" rule.

Usage

## find a good k given thresholds of EV and its increment.
elbow(x,inc.thres,ev.thres,precision=3,print.warning=TRUE)

## a wrapper of `elbow' testing multiple thresholds.
elbow.batch(x,inc.thres=c(0.01,0.05,0.1),
ev.thres=c(0.95,0.9,0.8,0.75,0.67,0.5,0.33),precision=3)

## S3 method for class 'elbow'
plot(x,elbow.obj=NULL,main,xlab="k",
ylab="Explained_Variance",type="b",pch=20,col.abline="red",
lty.abline=3,if.plot.new=TRUE,print.info=TRUE,
mar=c(4,5,3,3),omi=c(0.75,0,0,0),...)

Arguments

Details

Determining the number of clusters in a data set by the "elbow" rule and thresholds in the explained variance (EV) and its increment.

Value

Both elbow and elbow.btach return a ‘elbow’ object (if a "good" k exists), which is a list containing the following components

, and with an attribute ‘meta’ that contains

See Also

css and css.hclust for computing Clustering Sum-of-Squares.

Examples

## load library
require("GMD")

## simulate data around 12 points in Euclidean space
pointv <- data.frame(x=c(1,2,2,4,4,5,5,6,7,8,9,9),
y=c(1,2,8,2,4,4,5,9,9,8,1,9))
set.seed(2012)
mydata <- c()
for (i in 1:nrow(pointv)){
  mydata <- rbind(mydata,cbind(rnorm(10,pointv[i,1],0.1),
rnorm(10,pointv[i,2],0.1)))
}
mydata <- data.frame(mydata); colnames(mydata) <- c("x","y")
plot(mydata,type="p",pch=21, main="Simulated data")

## determine a "good" k using elbow
dist.obj <- dist(mydata[,1:2])
hclust.obj <- hclust(dist.obj)
css.obj <- css.hclust(dist.obj,hclust.obj)
elbow.obj <- elbow.batch(css.obj)
print(elbow.obj)

## make partition given the "good" k
k <- elbow.obj$k; cutree.obj <- cutree(hclust.obj,k=k)
mydata$cluster <- cutree.obj

## draw a elbow plot and label the data
dev.new(width=12, height=6)
par(mfcol=c(1,2),mar=c(4,5,3,3),omi=c(0.75,0,0,0))
plot(mydata$x,mydata$y,pch=as.character(mydata$cluster),
col=mydata$cluster,cex=0.75,main="Clusters of simulated data")
plot(css.obj,elbow.obj,if.plot.new=FALSE)

## clustering with more relaxed thresholds (, resulting a smaller "good" k)
elbow.obj2 <- elbow.batch(css.obj,ev.thres=0.90,inc.thres=0.05)
mydata$cluster2 <- cutree(hclust.obj,k=elbow.obj2$k)

dev.new(width=12, height=6)
par(mfcol=c(1,2), mar=c(4,5,3,3),omi=c(0.75,0,0,0))
plot(mydata$x,mydata$y,pch=as.character(mydata$cluster2),
col=mydata$cluster2,cex=0.75,main="Clusters of simulated data")
plot(css.obj,elbow.obj2,if.plot.new=FALSE)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GMD)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GMD/elbow.Rd_%03d_medium.png", width=480, height=480)
> ### Name: elbow
> ### Title: The "Elbow" Method for Clustering Evaluation
> ### Aliases: elbow elbow.batch plot.elbow
> 
> ### ** Examples
> 
> ## load library
> require("GMD")
> 
> ## simulate data around 12 points in Euclidean space
> pointv <- data.frame(x=c(1,2,2,4,4,5,5,6,7,8,9,9),
+ y=c(1,2,8,2,4,4,5,9,9,8,1,9))
> set.seed(2012)
> mydata <- c()
> for (i in 1:nrow(pointv)){
+   mydata <- rbind(mydata,cbind(rnorm(10,pointv[i,1],0.1),
+ rnorm(10,pointv[i,2],0.1)))
+ }
> mydata <- data.frame(mydata); colnames(mydata) <- c("x","y")
> plot(mydata,type="p",pch=21, main="Simulated data")
> 
> ## determine a "good" k using elbow
> dist.obj <- dist(mydata[,1:2])
> hclust.obj <- hclust(dist.obj)
> css.obj <- css.hclust(dist.obj,hclust.obj)
> elbow.obj <- elbow.batch(css.obj)
> print(elbow.obj)
$k
[1] 7

$ev
[1] 0.9795881

$inc.thres
[1] 0.01

$ev.thres
[1] 0.95

attr(,"description")
[1] "A "good" k=7 (EV=0.98) is detected when the EV is no less than 0.95\nand the increment of EV is no more than 0.01 for a bigger k.\n"
attr(,"class")
[1] "elbow" "list" 
> 
> ## make partition given the "good" k
> k <- elbow.obj$k; cutree.obj <- cutree(hclust.obj,k=k)
> mydata$cluster <- cutree.obj
> 
> ## draw a elbow plot and label the data
> dev.new(width=12, height=6)
dev.new(): using pdf(file="Rplots976.pdf")
> par(mfcol=c(1,2),mar=c(4,5,3,3),omi=c(0.75,0,0,0))
> plot(mydata$x,mydata$y,pch=as.character(mydata$cluster),
+ col=mydata$cluster,cex=0.75,main="Clusters of simulated data")
> plot(css.obj,elbow.obj,if.plot.new=FALSE)
There were 50 or more warnings (use warnings() to see the first 50)
> 
> ## clustering with more relaxed thresholds (, resulting a smaller "good" k)
> elbow.obj2 <- elbow.batch(css.obj,ev.thres=0.90,inc.thres=0.05)
> mydata$cluster2 <- cutree(hclust.obj,k=elbow.obj2$k)
> 
> dev.new(width=12, height=6)
dev.new(): using pdf(file="Rplots977.pdf")
> par(mfcol=c(1,2), mar=c(4,5,3,3),omi=c(0.75,0,0,0))
> plot(mydata$x,mydata$y,pch=as.character(mydata$cluster2),
+ col=mydata$cluster2,cex=0.75,main="Clusters of simulated data")
> plot(css.obj,elbow.obj2,if.plot.new=FALSE)
There were 50 or more warnings (use warnings() to see the first 50)
> 
> 
> 
> 
> 
> dev.off()
png 
  2 
>