AUTHOR=Gabissa Adugna Fita , Obsu Legesse Lemecha 

TITLE=A DC programming to two-level hierarchical clustering with ℓ1 norm

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1445390

DOI=10.3389/fams.2024.1445390

ISSN=2297-4687

ABSTRACT=<p>The main challenge in solving clustering problems using mathematical optimization techniques is the non-smoothness of the distance measure used. To overcome this challenge, we used Nesterov's smoothing technique to find a smooth approximation of the ℓ<sub>1</sub> norm. In this study, we consider a bi-level hierarchical clustering problem where the similarity distance measure is induced from the ℓ<sub>1</sub> norm. As a result, we are able to design algorithms that provide optimal cluster centers and headquarter (HQ) locations that minimize the total cost, as evidenced by the obtained numerical results.</p>