An Algorithm for Clustering Using L1-Norm Based on Hyperbolic Smoothing Technique

Cluster analysis deals with the problem of organization of a collection of objects into clusters based on a similarity measure, which can be defined using various distance functions. The use of different similarity measures allows one to find different cluster structures in a data set. In this article, an algorithm is developed to solve clustering problems where the similarity measure is defined using the L1‐norm. The algorithm is designed using the nonsmooth optimization approach to the clustering problem. Smoothing techniques are applied to smooth both the clustering function and the L1‐norm. The algorithm computes clusters sequentially and finds global or near global solutions to the clustering problem. Results of numerical experiments using 12 real‐world data sets are reported, and the proposed algorithm is compared with two other clustering algorithms.