How we choose K in K-mean clustering?

There are three methods to select the K for K-Kmean Clustering-

  1. Elbow Method
  2. Gap Statistic method
  3. Average Silhouette Width method

There are different approaches to fix the ‘K’ value in K-means clustering. In those 3 techniques are famous/ widely used by research community. I will name these techniques here. For detailed analysis view respected papers

  1. Elbow/knee method
  2. Silhouette method
  3. Gap statistics

The best answer is " Based on application for which you are targeting" or you can propose your own with some changes to above techniques. Run some test cases and check which one suits well for your case.