k-means Clustering and Custergram with R. K Means Clustering is an unsupervised learning algorithm that tries to cluster data based on their similarity. Unsupervised learning means that there is no outcome to be predicted, and the algorithm just tries to find patterns in the data. In k means clustering, we have the specify the number of clusters we want the data to be grouped into. The algorithm randomly assigns each observation to a cluster, and finds the centroid of each cluster. ref:https://www.r-bloggers.com/k-means-clustering-in-r/ ref:https://rpubs.com/FelipeRego/K-Means-Clustering ref:https://www.r-bloggers.com/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-code/

1. prepared by Volkan OBAN
K-Means Clustering with R
library(datasets)
data(attitude)
attitude
rating complaints privileges learning raises critical advance
1 43 51 30 39 61 92 45
2 63 64 51 54 63 73 47
3 71 70 68 69 76 86 48
4 61 63 45 47 54 84 35
5 81 78 56 66 71 83 47
6 43 55 49 44 54 49 34
7 58 67 42 56 66 68 35
8 71 75 50 55 70 66 41
9 72 82 72 67 71 83 31
10 67 61 45 47 62 80 41
11 64 53 53 58 58 67 34
12 67 60 47 39 59 74 41
13 69 62 57 42 55 63 25
14 68 83 83 45 59 77 35
15 77 77 54 72 79 77 46
16 81 90 50 72 60 54 36
17 74 85 64 69 79 79 63
18 65 60 65 75 55 80 60
19 65 70 46 57 75 85 46
20 50 58 68 54 64 78 52
21 50 40 33 34 43 64 33
22 64 61 52 62 66 80 41
23 53 66 52 50 63 80 37
24 40 37 42 58 50 57 49
25 63 54 42 48 66 75 33
26 66 77 66 63 88 76 72
27 78 75 58 74 80 78 49
28 48 57 44 45 51 83 38
29 85 85 71 71 77 74 55
30 82 82 39 59 64 78 39
datset.seed(7)
cl = kmeans(dat, 6, nstart=100)
cl
> cl = kmeans(dat, 3, nstart=100)
>
> # Examine the result of the clustering algorithm
> cl

2. K-means clustering with 3 clusters of sizes 11, 2, 17
Cluster means:
privileges learning
1 61.45455 69.09091
2 75.50000 49.50000
3 45.11765 48.94118
Clustering vector:
[1] 3 3 1 3 1 3 3 3 1 3 3 3 3 2 1 1 1 1 3 2 3 1 3 3 3 1 1 3 1 3
Within cluster sum of squares by cluster:
[1] 783.6364 153.0000 1732.7059
(between_SS / total_SS = 68.0 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifaul
plot(dat, col =(cl$cluster +1) , main="K-Means result with 3 clusters", pch
=20, cex=2)

3. > mydata <- dat
> wss <- (nrow(mydata)-1)*sum(apply(mydata,2,var))
> for (i in 2:15) wss[i] <- sum(kmeans(mydata,
+ centers=i)$withinss)
> plot(1:15, wss, type="b", xlab="Number of Clusters",
+ ylab="Within groups sum of squares",
+ main="Assessing the Optimal Number of Clusters with the Elbow Method
",
+ pch=20, cex=2)
Ref:https://rpubs.com/FelipeRego/K-Means-Clustering
Felipe Rego

4. > clustergram.kmeans <- function(Data, k, ...)
+ {
+ # this is the type of function that the clustergram
+ # function takes for the clustering.
+ # using similar structure will allow implementation of differe
nt clustering algorithms
+
+ # It returns a list with two elements:
+ # cluster = a vector of length of n (the number of subjects/items)
+ # indicating to which cluster each item belong
s.
+ # centers = a k dimensional vector. Each element is 1 number that re
present that cluster
+ # In our case, we are using the weighted mean
of the cluster dimensions by
+ # Using the first component (loading) of the P
CA of the Data.
+
+ cl <- kmeans(Data, k,...)
+
+ cluster <- cl$cluster
+ centers <- cl$centers %*% princomp(Data)$loadings[,1] # 1 number per
center
+ # here we are using the weighted mean for each
+
+ return(list(
+ cluster = cluster,
+ centers = centers
+ ))
+ }
>
> clustergram.plot.matlines <- function(X,Y, k.range,
+ x.range, y.range , COL,
+ add.center.points , centers.points)
+ {
+ plot(0,0, col = "white", xlim = x.range, ylim = y.range,
+ axes = F,
+ xlab = "Number of clusters (k)", ylab = "PCA weighted Mean of th
e clusters", main = "Clustergram of the PCA-weighted Mean of the clusters k
-mean clusters vs number of clusters (k)")
+ axis(side =1, at = k.range)
+ axis(side =2)
+ abline(v = k.range, col = "grey")
+
+ matlines(t(X), t(Y), pch = 19, col = COL, lty = 1, lwd = 1.5)
+
+ if(add.center.points)
+ {
+ require(plyr)
+
+ xx <- ldply(centers.points, rbind)
+ points(xx$y~xx$x, pch = 19, col = "red", cex = 1.3)
+
+ # add points
+ # temp <- l_ply(centers.points, function(xx) {
+ # with(xx,points(y~x, pch = 19, col = "red", cex = 1.3))
+ # points(xx$y~xx$x, pch = 19, col = "red", cex = 1.3)
+ # return(1)
+ # })
+ # We assign the lapply to a variable (temp) only to suppress the
lapply "NULL" output
+ }

5. + }
>
>
>
> clustergram <- function(Data, k.range = 2:10 ,
+ clustering.function = clustergram.kmeans,
+ clustergram.plot = clustergram.plot.matlines,
+ line.width = .004, add.center.points = T)
+ {
+ # Data - should be a scales matrix. Where each column belongs to a d
ifferent dimension of the observations
+ # k.range - is a vector with the number of clusters to plot the clust
ergram for
+ # clustering.function - this is not really used, but offers a bases t
o later extend the function to other algorithms
+ # Although that would more work on the code
+ # line.width - is the amount to lift each line in the plot so they wo
n't superimpose eachother
+ # add.center.points - just assures that we want to plot points of the
cluster means
+
+ n <- dim(Data)[1]
+
+ PCA.1 <- Data %*% princomp(Data)$loadings[,1] # first principal comp
onent of our data
+
+ if(require(colorspace)) {
+ COL <- heat_hcl(n)[order(PCA.1)] # line colors
+ } else {
+ COL <- rainbow(n)[order(PCA.1)] # line colors
+ warning('Please consider installing the package "colorspace" for
prittier colors')
+ }
+
+ line.width <- rep(line.width, n)
+
+ Y <- NULL # Y matrix
+ X <- NULL # X matrix
+
+ centers.points <- list()
+
+ for(k in k.range)
+ {
+ k.clusters <- clustering.function(Data, k)
+
+ clusters.vec <- k.clusters$cluster
+ # the.centers <- apply(cl$centers,1, mean)
+ the.centers <- k.clusters$centers
+
+ noise <- unlist(tapply(line.width, clusters.vec, cumsum))[order(s
eq_along(clusters.vec)[order(clusters.vec)])]
+ # noise <- noise - mean(range(noise))
+ y <- the.centers[clusters.vec] + noise
+ Y <- cbind(Y, y)
+ x <- rep(k, length(y))
+ X <- cbind(X, x)
+
+ centers.points[[k]] <- data.frame(y = the.centers , x = rep(k , k
))
+ # points(the.centers ~ rep(k , k), pch = 19, col = "red", cex
= 1.5)
+ }

6. +
+
+ x.range <- range(k.range)
+ y.range <- range(PCA.1)
+
+ clustergram.plot(X,Y, k.range,
+ x.range, y.range , COL,
+ add.center.points , centers.points)
+
+
+ }
> set.seed(250)
> data("attitude")
> Data <- scale(attitude[,-5])
> clustergram(Data, k.range = 2:8, line.width = 0.004)

7. > par(cex.lab = 1.2, cex.main = .7)
> par(mfrow = c(3,2))
> for(i in 1:6) clustergram(Data, k.range = 2:8 , line.width = .004, add.ce
nter.points = T)