Exercise

# Selecting number of clusters

The k-means algorithm assumes the number of clusters as part of the input. If you know the number of clusters in advance (e.g. due to certain business constraints) this makes setting the number of clusters easy. However, as you saw in the video, if you do not know the number of clusters and need to determine it, you will need to run the algorithm multiple times, each time with a different number of clusters. From this, you can observe how a measure of model quality changes with the number of clusters.

In this exercise, you will run `kmeans()`

multiple times to see how model quality changes as the number of clusters changes. Plots displaying this information help to determine the number of clusters and are often referred to as *scree plots*.

The ideal plot will have an *elbow* where the quality measure improves more slowly as the number of clusters increases. This indicates that the quality of the model is no longer improving substantially as the model complexity (i.e. number of clusters) increases. In other words, the elbow indicates the number of clusters inherent in the data.

Instructions

**100 XP**

The data, `x`

, is still available in your workspace.

- Build 15
`kmeans()`

models on`x`

, each with a different number of clusters (ranging from 1 to 15). Set`nstart = 20`

for all model runs and save the total within cluster sum of squares for each model to the`i`

th element of`wss`

. - Run the code provided to create a scree plot of the
`wss`

for all 15 models. - Take a look at your scree plot. How many clusters are inherent in the data? Set
`k`

equal to the number of clusters at the location of the elbow.