https://www.oreilly.com/library/view/statistics-for-machine/9781788295758/c71ea970-0f3c-4973-8d3a-b09a7a6553c1.xhtml

University of Michigan - Ann Arbor

One popular way to determine the optimal number of k is by using the elbow method. To use this method, you will run K means n times, each time adding another cluster. After each iteration you graph a score for that number of k. The point in the graph where there is an “elbow” is the point of optimal clusters. The picture below shows an example graph that would be used for determining the number of clusters -- in this example case 3 clusters is optimal


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