The presence of noise or outliers in data sets may heavily affect the performance of clustering algorithms and lead to unsatisfactory results. The majority of conventional clustering algorithms are sensitive to noise and outliers. Robust clustering algorithms often overcome difficulties associated with noise and outliers and find true cluster structures. We introduce a soft trimming approach for the hard clustering problem where its objective is modeled as a sum of the cluster function and a function represented as a composition of the algebraic and distance functions. We utilize the composite function to estimate the degree of the significance of each data point in clustering. A robust clustering algorithm based on the new model and a procedure for generating starting cluster centers is developed. We demonstrate the performance of the proposed algorithm using some synthetic and real-world data sets containing noise and outliers. We also compare its performance with that of some well-known clustering techniques. Results show that the new algorithm is robust to noise and outliers and finds true cluster structures.

The research by Dr. Adil M. Bagirov is supported by the Australian Government through the Australian Research Council's Discovery Projects funding scheme (Project No. DP190100580) . The authors express their gratitude to three anonymous referees for their invaluable comments, which have contributed to enhancing the quality of the paper.

Australian Government through the Australian Research Council's Discovery Projects funding scheme [DP190100580]