A Dc Optimization Approach For Constrained Bi-Level Hierarchical Clustering With 1 Norm

Abstract

Clustering problems often face challenges due to the non-smooth nature of distance measures like the 1 norm. To address this issue, we employ nesterov's partial smoothing technique to approximate the 1 norm with a smoother function, thereby facilitating more effective mathematical optimization. This dissertation presents two main contributions. We model and solved clustering problems where nodes are identified as cluster centers to minimize the overall 1 distance between nodes within clusters. The proposed approach uses nesterov's technique to smooth the 1 norm and improve optimization efficiency. We investigate two network topologies for bi-level hierarchical clustering. The first topology chooses cluster centers first, then a headquarter from cluster centers that functions as both a cluster center and a headquarter node that minimize the 1 distances within the network.