Group Labeling Methodology Using Distancebased Data Grouping Algorithms Clustering algorithms are often used to form groups based on the similarity of their members. In this context, understanding a group is just as important as its composition. Identifying, or labeling groups can assist with their interpretation and, consequently, guide decisionmaking efforts by taking into account the features from each group. Interpreting groups can be beneficial when it is necessary to know what makes an element a part of a given group, what are the main features of a group, and what are the differences and similarities among them. This work describes a method for finding relevant features and generate labels for the elements of each group, uniquely identifying them. This way, our approach solves the problem of finding relevant definitions that can identify groups. The proposed method transforms the standard output of an unsupervised distancebased clustering algorithm into a Pertinence Degree (GP), where each element of the database receives a GP concerning each formed group. The elements with their GPs are used to formulate ranges of values for their attributes. Such ranges can identify the groups uniquely. The labels produced by this approach averagedxc2xa0  94  .  83%xc2xa0  of correct answers for the analyzed databases, allowing a natural interpretation of the generated definitions.

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.