Validating Clusters with the Lower Bound for Sum-of-Squares Error

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K -means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on the observed sum-of-squares error as compared to the minimum sum-of-squares error.