Clustering is an unsupervised machine learning problem that is widely studied in different contexts of business and science. The complexity of real-world data, often characterized by high dimensionality, poses significant challenges to traditional clustering methods. Feature selection is the most used technique to cope with the high dimensionality in clustering problems. Most feature selection methods select a common set of features to define all clusters, which is called global feature selection. Localized feature selection methods consider that the relevant set of features may differ across the clusters and select a set of features for each cluster separately. In this study, we address a clustering problem that aims to group data points and select a cluster center and a set of relevant features for each cluster. The objective is to minimize the sum of Euclidean distances between data points and their cluster center over each cluster's relevant set of features. We propose two Mixed-Integer Second-Order Cone Programming formulations, a matheuristic method, and a heuristic method for the problem. We evaluate the computational performance of the proposed methods on generated data sets.

This is a joint work with Dr.Sinan Gürel and Dr. Cem İyigün.

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