What The Process Looks Like

This figure shows what our k-means clustering might produce after the first clustering run.

After our final run, we see that the cluster centers have moved locations. The cluster assignments for some of our data points have also therefore changed.

K-means R Code for Example 1

In the following, we’ll use some sample data. If you have your own data in an Excel file, just import it using the “Import Dataset” button in the RStudio console in the upper right. Then change the variable name to the one you want to examine.

We’ll use the “kmeans” function. The first argument is the data we want to use to create our cluster. The second is simply the number of centers (clusters) we want.

That’s really all you need to do your own cluster analysis.

### Creating some example data

set.seed(101)
t1 <- runif(20, 0, 3.5)
t2 <- rnorm(20, 5, 2)
t3 <- rnorm(20, 6, 2)
t4 <- rnorm(40, 15, 3)
data <- c(t1, t2, t3, t4)

# Creating the k-means assignments

k <- kmeans(x = data, centers = 4) # x is the data, centers is the number of cluster centers
#str(k) # use the "str" function here to see all the output provided.

Let’s look at some of the output of the kmeans clustering algorithm available. We not only see how many people are in each cluster but also identify where the cluster centers are.

k$size # see how many values are in each cluster

## [1] 16 22 30 32

k$centers # the cluster center values that determine the assignments to a cluster

##        [,1]
## 1 18.015877
## 2 13.586993
## 3  6.402419
## 4  2.053784

Note that the actual cluster number itself does not really mean anything. It’s arbitrary. What is NOT arbitrary, however, are the clustering assigments. Like values are grouped with like values.

We can see what this means in practice with a histogram plot using a different color for each cluster assignment. The clustering clearly fits the data better than some arbitrary split.

Note that I am showing the plotting code here for those playing along at home. Regardless of whether you are coding or not, the key lesson is that the cluster labels provide a nice way to group people by company tenure or whatever other variable you are looking at.

library(RColorBrewer) # I like these colors more

h <- hist(data, breaks = 40, plot = F) #making the histogram and saving as a variable
temp <- sort(k$centers) # getting the centers
m1 <- c(mean(temp[1:2]), mean(temp[2:3]), mean(temp[3:4])) # finding the midpoints for coloring

cuts <- cut(h$breaks,breaks = c(-Inf, m1, Inf)) # assigning the breaks of the histogram to cluster

# Plotting the histogram with some pretty colors from R Color Brewer
plot(h, col = brewer.pal(4,"Set1")[cuts],  
     main = "Company Tenure Histogram \n Colored By Cluster") 

Saving the Output to a CSV File

Now we can put our cluster assignment data together with our original data and then save it as a csv file. This is useful if we want to use our new cluster data in a program like Excel. The order of the cluster assignment data from k$cluster follows the same order as our original data.

data_all <- cbind(data, k$cluster) #binding them as columns
write.csv(x = data_all, file = "our_filename.csv")

Quick Template for Clustering with Your Own Data

Use this template to run a kmeans with your own data and then save that data as a csv file.

your_data <- read.csv("your_file_name_here") # you can use the "Import Dataset"  button
vars <- c(1,2,3,4) # or whatever columns you want to include; you can also use variable names 

k <- kmeans(your_data[,vars]) # Run the cluster analysis

your_data_2 <- cbind(your_data,k$cluster) #add the cluster label output to your data 
write.csv(x = your_data_2, file = "your_new_filename.csv") # write your data to a csv

Will K-Means Always Produce the Best Answer?

Not always, but it generally works pretty darn well.

The first step in the process is randomly choosing the initial cluster center locations. This means that sometimes the output is influenced to some degree by that random starting point.

In rare cases, the answer will be substandard relative to other possible clustering outcomes.

In practice, you should always first set your random seed as I have done here before running kmeans. This will let you always reproduce the result you get.

In addition, I find it helpful to try some different random seeds to make sure the answers I am getting are broadly consistent across different runs.

Indeed, in creating this post, I found that every so often I got poor results. The solution was to set that random seed. Generally, though kmeans is fairly robust and you should get pretty similar results with different runs regardless of the random starting point. Just be sure to cover your bases.

How Do I Choose the Number of Centers? A Simple Approach in 4 Steps

The simple approach to answering this begins with what you intend to actually do with the data. Clustering is great, but if you don’t begin with the end in mind, you are wasting your time.

1. Ask yourself how many clusters would be useful. If you are looking at ways to split up your initial trainee course into separate sections according to early performance, you might first think about how many instructors you have. If you only have three instructors, then choosing 2-3 clusters would probably make more sense than 7 or 8. If, on the other hand, you are talking about simply understanding the structure of your workfore, a few more clusters might be useful.
2. Look at the sizes of each cluster. If you have a group of 24 people but one cluster contains only 3 people take a closer look. They might be really different and worth separating out or you just might have too many clusters.
3. Relatedly, look at the values of the cluster center themselves and visualize. Are the differences practically meaningful? Consider test scores on scale of 0-100%. If the cluster1 center value is 87% and the cluster 2 center value is 89%, is that a difference that really matters? If those differences are not meaningful, reduce the number of clusters and rerun it. Please note that this method of determining how clusters really only works with 1 or 2 variables. Anything more and you won’t be able to properly visualize it.
4. Don’t be afraid to experiment. Try a few clusters, try a bunch. See what makes sense to you and what will be useful for those who need to act on your new insights. For typical HR analytics needs, you will get surprising impact from just a few.

There is a more complicated approach but it is beyond our current scope. In brief, it looks at the decreasing explanatory power of adding more clusters. My advice is to start small and get comfortable with kmeans first. Then you can start to dig deeper if you need to. I provide some links at the end if you want to learn more.

How Many Variables Can I Use in K-means?

As I mentioned earlier, for most HR uses you will probably only use 2-5 variables. You can, however, greatly expand this up to dozens or, in principle, even hundreds or thousands. When you get into the hundreds or thousands of variables, you might run into something called “the curse of dimensionality” but this is not really relevant for HR analytics.

Can I Use Data with Different Scales?

Yes, BUT you need to get them on the same scale first. This is called normalization.

Why do you need to do this for items on vastly different scales? K-means works by reducing the distance between the data points and the cluster centers. Variables with larger scales can swamp the calculations and dominate the cluster calculations.

For example, suppose I am clustering employees according to tenure at the company and salary. Tenure is at the scale of individual years but salary is in the tens of thousands of dollars. If we just threw it all in, the clustering would be driven by the salary variable because the numbers are just larger. Normalizing our data first takes care of this problem.

To normalize a variable, just subtract the mean value for that variable from each value. Then divide those values by the standard deviation. You will end up with a variable that has a mean of 0 and a standard deviation of 1 for each of your normalized variables. The cluster assignment outcomes will correspond to each case just as before.

If you are not familiar with standard deviations, click here for an earlier introductory post.

Here is some sample code if you need to normalize a variable.

a <- runif(20, 0, 100) #Use your own variable here. 
norm_a <- (a-mean(a))/sd(a) #normalizing that data