K-Means Clustering is an Unsupervised Learning algorithm, which groups the unlabeled dataset into different clusters. Here K defines the number of pre-defined clusters that need to be created in the process, as if K=2, there will be two clusters, and for K=3, there will be three clusters, and so on.
How to choose the value of K?
One of the most challenging tasks in this clustering algorithm is to choose the right values of k. What should be the right k-value? How to choose the k-value? Let us find the answer to these questions. If you are choosing the k values randomly, it might be correct or may be wrong. If you will choose the wrong value then it will directly affect your model performance. So there are two methods by which you can select the right value of k.
Elbow Method: Elbow is one of the most famous methods by which you can select the right value of k and boost your model performance. We also perform the hyperparameter tuning to chose the best value of k. Let us see how this elbow method works. It is an empirical method to find out the best value of k. it picks up the range of values and takes the best among them. It calculates the sum of the square of the points and calculates the average distance.
Silhouette Method: The silhouette method is somewhat different. The elbow method it also picks up the range of the k values and draws the silhouette graph. It calculates the silhouette coefficient of every point. It calculates the average distance of points within its cluster a (i) and the average distance of the points to its next closest cluster called b (i).
Note : The a (i) value must be less than the b (i) value, that is ai<<bi.
Now, we have the values of a (i) and b (i). we will calculate the silhouette coefficient by using the below formula.
in Worst Case s(i) = -1
s(i) = [b(i) - a(i)] / [(larger of b(i) and a(i)]
a(i) = average distance inside cluster
b(i) = average distance nearest other cluster