Under ideal spherical clusters, the additive penalty coefficient must satisfy N rho^2 / K < lambda < N L^2 / (2K), and a parameter-free multiplicative penalty naturally favors the true cluster count.
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Number of Clusters in a Dataset: A Regularized K-means Approach
Under ideal spherical clusters, the additive penalty coefficient must satisfy N rho^2 / K < lambda < N L^2 / (2K), and a parameter-free multiplicative penalty naturally favors the true cluster count.