We propose a data clustering model reduced from variational approach. This new clustering
model, a regularized k-means, is an extension from the classical k-means model. It uses the
sum-of-squares error for assessing fidelity, and the number of data in each cluster is used as
a regularizer. The model automatically gives a reasonable number of clusters by a choice of
a parameter. We explore various properties of this classification model and present different
numerical results. This model is motivated by an application to scale segmentation. A typical …