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I have used K means clustering. In order to find the best value for K, I've looked at the changes of inertia value vs K and also changes of average Silhouette number vs K. The graph for inertia seems to indicate there are 5 clusters in the data. However, the average Silhouette number reaches a minimum at 5. So, how does one interpret this? If there are 5 clusters in the data, shouldn't the average Silhouette number have a maximum at 5 (not a minimum)?

Thanks

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These are only heuristics.

The are not very reliable, and often fail. They will not detect if you did not preprocess your data well.

So instead of looking at some number, look at your data instead.

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