Speaker: Academician Nikhil R Pal
Title: What and when can we gain from the kernel versions of c-means algorithm?
Time: 10:30 am, July 30, 2022 (Saturday)
Abstract:
Different kernelized versions of c-means (hard and fuzzy) clustering algorithms have been proposed. Here we focus on kernel-clustering of only n-dimensional object data. First, we raise a basic question: should we really cluster any given object data in the kernel space? Our answer answer is NO! We shall provide our line of arguments. We shall establish that when we try to cluster in a transformed space, we must know if it could help us to find the clusters present in the original data X. To get any benefit from kernel clustering (or clustering in any other transformed space) we need to answer this question first; otherwise, we may find completely irrelevant clusters without knowing it and thereby making kernel clustering useless. This issue is a philosophical one and is neither dependent on the choice of clustering algorithm nor on the particular transformation (kernel function) used. Except for 2D/3D data, we do not have any “easy” way to answer the question and for 2D/3D data since we can look at the data we really do not really get any benefit from kernel clustering. So it appears that there is no benefit from kernel clustering unless we can answer some basic questions! We demonstrate and justify our claims using both synthetic and real data sets with visual assessment as well as with Normalized Mutual Information (NMI), Adjusted Rand Index (ARI) and cluster instability. We propose to use Sammon's nonlinear projection method to get a crude visual representation of the data in the kernel space. We discuss the issue of how to choose appropriate parameters of the kernel function, but we could not provide a solution to this problem. Finally, we discuss how the kernel parameters and the algorithmic parameters interact.
Personal Introduction:
Nikhil R. Pal is a Professor in the Electronics and Communication Sciences Unit and is the Head of the Center for Artificial Intelligence and Machine Learning of the Indian Statistical Institute. His current research interest includes brain science, computational intelligence, machine learning and data mining. He was the Editor-in-Chief of the IEEE Transactions on Fuzzy Systems for the period January 2005-December 2010. He has served/been serving on the editorial /advisory board/ steering committee of several journals including the International Journal of Approximate Reasoning, Applied Soft Computing, International Journal of Neural Systems, Fuzzy Sets and Systems, IEEE Transactions on Fuzzy Systems and the IEEE Transactions on Cybernetics. He is a recipient of the 2015 IEEE Computational Intelligence Society (CIS) Fuzzy Systems Pioneer Award and 2021 IEEE CIS Meritorious Service Award. He has given many plenary/keynote speeches in different premier international conferences in the area of computational intelligence. He has served as the General Chair, Program Chair, and co-Program chair of several conferences. He has been a Distinguished Lecturer of the IEEE CIS (2010-2012, 2016-2018, 2022-2024) and was a member of the Administrative Committee of the IEEE CIS (2010-2012). He has served as the Vice-President for Publications of the IEEE CIS (2013-2016) and the President of the IEEE CIS (2018-2019). He is a Fellow of the West Bengal Academy of Science and Technology, Institution of Electronics and Tele Communication Engineers, National Academy of Sciences, India, Indian National Academy of Engineering, Indian National Science Academy, International Fuzzy Systems Association (IFSA), The World Academy of Sciences, and a Fellow of the IEEE, USA. (www.isical.ac.in/~nikhil)
[Editor: Xiaohan Liu]