K-means introduction in R: code used for post: http://btovar.com/2015/04/introduction-to-k-means-in-r/

kmeans_introduction.R

# ***********************************************
# ***********************************************
# Author: Benjamin Tovar
# Date: April 20, 2015
# Post: http://btovar.com/2015/04/introduction-to-k-means-in-r/ ‎
# ***********************************************
# ***********************************************

library(ggplot2)
library(reshape)

#####################################################
# Case study 1: the basics of the K-means in R
#####################################################

set.seed(1121)
## Set three vectors, each with 100 entries
l <- 100
## x with a mean of 1 and a sd of 0.5
x <- rnorm(l,1,0.5)
mean(x);var(x);sd(x);summary(x)

## y with a mean of 5 and a sd of 1
y <- rnorm(l,5,1)
mean(y);var(y);sd(y);summary(y)

## z with a mean of 4 and a sd of 0.4
z <- rnorm(l,4,0.4)
mean(z);var(z);sd(z);summary(z)

# set dataset
dataset <- data.frame(x=x,y=y,z=z)
dataset_m <- melt(dataset)
dataset_m <- cbind(id=1:(l*3),dataset_m)
colnames(dataset_m) <- c("id","class","value")

# Now plot the distribution of the artificial dataset in order to check out the 
# distribution of the entries in the dataset:

ggplot(dataset_m) + 
	aes(x=value) + 
	geom_density(aes(fill="red",colour="red"),alpha=0.4) +
	theme(legend.position="none") + 
	labs(title="Density plot of all values (omitting classes)")

ggplot(dataset_m) + 
	aes(x=value) + 
	geom_density(aes(fill=class,colour=class),alpha=0.4) +
	labs(title="Density plot for all classes")

# Scatter plot of dataset
ggplot(dataset_m) + 
	aes(x=id,y=value) + 
	geom_point(aes(shape=class),size=2.5,alpha=0.9) +
	labs(title="Scatter plot of dataset")


## set the number of centroids with parameter k
k <- 2
## run the Kmeans algorithm
km <- kmeans(dataset_m$value,centers=k)
dataset_km <- cbind(dataset_m,cluster=as.factor(km$cluster))

# plot each sample
ggplot(dataset_km) + 
	aes(x=id,y=value) + 
	geom_point(aes(shape=class,colour=cluster),size=2.5,alpha=0.9) +
	labs(title="Dataset K-means clustering | k=2")


## set the number of centroids with parameter k
k <- 3
## run the Kmeans algorithm
km <- kmeans(dataset_m$value,centers=k)
dataset_km <- cbind(dataset_m,cluster=as.factor(km$cluster))

# plot each sample
ggplot(dataset_km) + 
	aes(x=id,y=value) + 
	geom_point(aes(shape=class,colour=cluster),size=2.5,alpha=0.9) +
	labs(title="Dataset K-means clustering | k=3")

## set the number of centroids with parameter k
k <- 4
## run the Kmeans algorithm
km <- kmeans(dataset_m$value,centers=k)
dataset_km <- cbind(dataset_m,cluster=as.factor(km$cluster))

# plot each sample
ggplot(dataset_km) + 
	aes(x=id,y=value) + 
	geom_point(aes(shape=class,colour=cluster),size=2.5,alpha=0.9) +
	labs(title="Dataset K-means clustering | k=4")

##############
# COMPUTE THE BEST VALUE
# FOR PARAMETER K
##############

# TRAIN THE MODEL ITERATING THE VALUES OF K
max_k_size <- 10
error <- numeric(max_k_size)
for (i in 1:max_k_size){ 
	error[i] <- sum(kmeans(dataset,centers=i)$withinss)
}
# set data frame object
error <- data.frame(k=1:max_k_size,error=error)

ggplot(error) + 
	aes(x=k,y=error) +
	geom_point(colour="#f96161",size=3) + 
	ylim(0,150) + 
	scale_x_continuous(breaks=seq(0, 15, 1)) + 
	geom_line(colour="#f96161") +
	labs(title="Error calibration curve",
			x="Number of Clusters (k)",
			y="Within groups sum of squares") +
	geom_vline(xintercept=3,colour="#32ab9f", linetype = "longdash")