  Several clustering methods (e.g., Normalized Cut and Ratio Cut) divide the
Min Cut cost function by a cluster dependent factor (e.g., the size or the
degree of the clusters), in order to yield a more balanced partitioning. We,
instead, investigate adding such regularizations to the original cost function.
We first consider the case where the regularization term is the sum of the
squared size of the clusters, and then generalize it to adaptive regularization
of the pairwise similarities. This leads to shifting (adaptively) the pairwise
similarities which might make some of them negative. We then study the
connection of this method to Correlation Clustering and then propose an
efficient local search optimization algorithm with fast theoretical convergence
rate to solve the new clustering problem. In the following, we investigate the
shift of pairwise similarities on some common clustering methods, and finally,
we demonstrate the superior performance of the method by extensive experiments
on different datasets.
