Development of assessment criteria for clustering algorithms

In this paper, new measures—called clustering performance measures (CPMs)—for assessing the reliability of a clustering algorithm are proposed. These CPMs are defined using a validation measure, which determines how well the algorithm works with a given set of parameter values, and a repeatability measure, which is used for studying the stability of the clustering solutions and has the ability to estimate the correct number of clusters in a dataset. These proposed CPMs can be used to evaluate clustering algorithms that have a structure bias to certain types of data distribution as well as those that have no structure biases. Additionally, we propose a novel cluster validity index, V _I index, which is able to handle non-spherical clusters. Five clustering algorithms on different types of real-world data and synthetic data are evaluated. The first dataset type refers to a communications signal dataset representing one modulation scheme under a variety of noise conditions, the second represents two breast cancer datasets, while the third type represents different synthetic datasets with arbitrarily shaped clusters. Additionally, comparisons with other methods for estimating the number of clusters indicate the applicability and reliability of the proposed cluster validity V _I index and repeatability measure for correct estimation of the number of clusters.

Asoke K. NandiEmail:

---

Sameh A. Salem   graduated with a BSc degree in Communications and Electronics Engineering and an MSc in Communications and Electronics Engineering, both from Helwan University, Cairo, Egypt, in May 1998 and October 2003, respectively. He is currently pursuing PhD degree in the Signal Processing and Communications Group, Department of Electrical Engineering and Electronics, The University of Liverpool, UK. His research interests include clustering algorithms, machine learning, and parallel computing. Asoke K. Nandi   received PhD degree from the University of Cambridge (Trinity College), Cambridge, UK, in 1979. He held several research positions in Rutherford Appleton Laboratory (UK), European Organisation for Nuclear Research (Switzerland), Department of Physics, Queen Mary College (London, UK) and Department of Nuclear Physics (Oxford, UK). In 1987, he joined the Imperial College, London, UK, as the Solartron Lecturer in the Signal Processing Section of the Electrical Engineering Department. In 1991, he joined the Signal Processing Division of the Electronic and Electrical Engineering Department in the University of Strathclyde, Glasgow, UK, as a Senior Lecturer; subsequently, he was appointed as a Reader in 1995 and a Professor in 1998. In March 1999, he moved to the University of Liverpool, Liverpool, UK to take up his appointment with David Jardine, Chair of Signal Processing in the Department of Electrical Engineering and Electronics. In 1983, he was a member of the UA1 team at CERN that discovered the three fundamental particles known as W⁺, W⁻ and Z⁰ providing the evidence for the unification of the electromagnetic and weak forces, which was recognised by the Nobel Committee for Physics in 1984. Currently, he is the Head of the Signal Processing and Communications Research Group with interests in the areas of non-Gaussian signal processing, communications, and machine learning research. With his group he has been carrying out research in machine condition monitoring, signal modelling, system identification, communication signal processing, biomedical signals, ultrasonics, blind source separation, and blind deconvolution. He has authored or co-authored over 350 technical publications, including two books “Automatic Modulation Recognition of Communications Signals” (Kluwer Academic, Boston, MA, 1996) and “Blind Estimation Using Higher-Order Statistics” (Kluwer Academic, Boston, MA, 1999) and over 140 journal papers. Professor Nandi was awarded the Mounbatten Premium, Division Award of the Electronics and Communications Division, of the Institution of Electrical Engineers of the UK in 1998 and the Water Arbitration Prize of the Institution of Mechanical Engineers of the UK in 1999. He is a Fellow of the Cambridge Philosophical Society, the Institution of Engineering and Technology, the Institute of Mathematics and its applications, the Institute of Physics, the Royal Society for Arts, the Institution of Mechanical Engineers, and the British Computer Society.