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On a Nonconvex Distance-Based Clustering Problem

Авторы: Gruzdeva T., Ushakov A.

Журнал: Lecture Notes in Computer Science: 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022

Том: 13367


Год: 2022

Отчётный год: 2022


Местоположение издательства:


Аннотация: Clustering is one of the basic data analysis tools and an important subroutine in many machine learning tasks. Probably, the most well-known and popular clustering model is the Euclidean minimum-sum-of-squares clustering problem, also known as the k-means problem. Clustering with Bregman divergences is a generalization of the k-means problem where the distances between data items and closest cluster centers are computed according to any Bregman divergence, rather than the squared Euclidean distance. In this paper, we consider a mathematical programming problem of clustering with Bregman divergences. We propose several representations of the problem in the form of a DC (difference of convex) program and develop a DC programming approach to solve it. We provide particular DC representations and particular DC solution algorithms for several widely-known Bregman divergences.

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