# How to visualise optimal number of Clusters in R

When performing cluster analysis, one of the most important decisions to make is how many clusters to create. A cluster is a group of data points that are similar to one another. Determining the optimal number of clusters can be challenging, as it depends on the specific data and the research question.

One way to determine the optimal number of clusters is by visualizing the data using a technique called the elbow method. This method involves plotting the explained variation as a function of the number of clusters, and picking the elbow of the curve as the number of clusters to use. The explained variation is a measure of how much of the total variation in the data is explained by the clusters.

The idea behind the elbow method is that as the number of clusters increases, the explained variation will also increase, but at some point, the increase will not be as significant. The point at which this happens is the elbow of the curve, and this is the number of clusters that should be chosen. The graph of explained variation versus the number of clusters is called the “elbow plot” and it is a useful tool for visualizing the optimal number of clusters.

Another way to determine the optimal number of clusters is by using the silhouette method. This method is based on the silhouette coefficient, which measures the similarity of each data point to its own cluster compared to other clusters. The silhouette coefficient ranges from -1 to 1, where a high value means that the data point is well-matched to its own cluster and poorly matched to neighboring clusters, and a low value means that the data point is poorly matched to its own cluster and well-matched to neighboring clusters. The optimal number of clusters is the one that maximizes the average silhouette coefficient.

In summary, determining the optimal number of clusters is an important step in cluster analysis. The elbow method and the silhouette method are two common techniques used to determine the optimal number of clusters in R. The elbow method involves plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use. The silhouette method measures the similarity of each data point to its own cluster compared to other clusters and the optimal number of clusters is the one that maximizes the average silhouette coefficient. Both methods are useful for visualizing the optimal number of clusters and can help you to make a more informed decision when performing cluster analysis.

In this Applied Machine Learning Recipe, you will learn: How to visualise optimal number of Clusters in R.