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I am clustering a large amount of high-dimensional data using KMeans (and the Euclidean distance metric), and then calculating the silhouette score and the Euclidean distance to the calculated cluster center for each point. What is the best method for determine which data point in each cluster is the best representation of that cluster?

I think it's either the point with the lowest Euclidean distance to the cluster center, or the point with the highest silhouette score for the cluster, but I don't know which one it is. In fact, why are they different points at all?

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