A Binary Linear ProgrammingBased KMeans Approach for the Capacitated Centered Clustering Problem The kmeans algorithm is one of the most popular clustering algorithms in the machine learning community. Its simplicity and scalability make it the primary choice for many clustering applications. We introduce here a variant of the kmeans algorithm that can account for complex side constraints. The key idea is to use binary linear programming for assigning objects to clusters. Unlike existing extensions of the kmeans algorithm that are designed for accommodating specific types of constraints, our approach can be applied to a wide range of constrained clustering problems with minor modifications. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it to a stateoftheart algorithm on a test set that comprises 18 instances of the capacitated centered clustering problem. The proposed approach performed particularly well on largesized instances with more than 100 clusters. It even found new bestknown solutions for the four largest instances in the test set.

Efficient Algorithms for Constrained Clustering with Side Information Clustering as an unsupervised machine learning method has broad applications within the area of data science and natural language processing. In this paper, we use background knowledge or side information of the data as constraints to improve clustering accuracy. Following the representation method as in 15, we first format the side information as mustlink set and cannotlink set. Then we propose a constrained kmeans algorithm for clustering the data. The key idea of our algorithm for clustering mustlink data sets is to treat each set as a data with large volume, which is, to assign a set of mustlink data as a whole to the center closest to its mass center. In contrast, the key for clustering cannotlink data set is to transform the assignment of the involved data points to the computation of a minimum weight perfect matching. At last, we carried out numerical simulation to evaluate our algorithms for constrained kmeans on UCI datasets. The experimental results demonstrate that our method outperforms the previous constrained kmeans as well as the classical kmeans in both clustering accuracy and runtime.