# Interpret the visualization of k-mean clusters

Following my posted data here, I conducted a k-mean clustering analysis. I refereed to this post: How to produce a pretty plot of the results of k-means cluster analysis? for the clusters visualization

# Read and Sort Input Data
mydata <- read.csv(file="three_county_6_25.csv", head=TRUE, sep=",") # read input data
mydata2 <- scale(mydata)  # Normalize the data

# Determine number of clusters
wssplot(mydata2)
set.seed(1234)
nc <- NbClust(mydata2, min.nc=2, max.nc=15, method="kmeans")
table(nc$Best.n[1,]) # Do K-means clustering set.seed(1234) fit.km <- kmeans(mydata2, centers = 3, nstart=25) # Visualize the clusters # Fig 1 plotcluster(mydata2, fit.km$cluster)
# Fig 2
clusplot(mydata2, fit.km$cluster, color=TRUE, shade=TRUE,labels=2, lines=0) # Fig 3 with(mydata, pairs(mydata2, col=c(1:3)[fit.km$cluster]))


The NbClust indicates 2 clusters:

Here are the visualization of clusters:

I am not sure how to interpret the clusters visualization result. 1) The 1st cluster plot is doing "Centroid Plot against 1st 2 discriminant functions". It seemed the clusters showed three groups. 2) The 2nd cluster plot "vary parameters for most readable graph" (referred from Quick-R: Cluster Analysis).

## 1 Answer

The data contains correlations.

k-means cannot handle correlations, and failed badly.

Either split your data manually based on the visualization (the left looks reasonable), or use a different algorithm capable of handling linear elongated clusters.

• Do you think if I do PCA on the data, then do k-means on the PCs, will that solve the correlation problems? I saw a post indicated this solution: stats.stackexchange.com/questions/92985/…
– enaJ
Jun 26 '15 at 18:01
• Sometimes. Sometimes not. Visualize again, and check if A) the results look much better in the visualization, and B) the plot exhibits a real elbow. No elbow in the plot usually indicates that kmeans didn't work. Jun 26 '15 at 20:22
• Also, could you guide me to understand why the correlation will fail k-means? I did a quick search, but don't have the fortune to find the exact answer: stats.stackexchange.com/search?q=k+mean+correlation
– enaJ
Jun 26 '15 at 21:27
• Correlation roughly means scaling one axis, but not another. K-means is very sensitive to rescaling axes differently. Jun 26 '15 at 22:05