The power spectral density (PSD) of a signal is often used as a feature for signal classification for which a distance measure must be chosen to compare the similarity between the signal features. We reason that PSD matrices have structural constraints and describe a manifold in the signal space. Thus, the widely used Euclidean distance may not be ppropriate. A more suitable measure is the Riemannian distance on the manifold. Here, we examine the geometry of the PSD manifold and develop a closed-form Riemannian distance between two PSD matrices on the manifold. We employ this new measure for the classification of EEG signals in the determination of a patient’s sleep state. To best facilitate the classification of similar and dissimilar EEG signal sets, we develop an optimal weighting for RD which aims to render signals in different classes more separable while those in the same class more compact. The results are highly encouraging, having the accuracy of classification greatly improved from those using other measures.
Kon Max Wong received his BSc(Eng), DIC, PhD, and DSc(Eng) degrees, all in electrical engineering, from the University of London, England, in 1969, 1972, 1974 and 1995, respectively. He started working at the Transmission Division of Plessey Telecommunications Research Ltd., England, in 1969. In October 1970 he was on leave from Plessey pursuing postgraduate studies and research at Imperial College of Science and Technology, London. In 1972, he rejoined Plessey as a research engineer and worked on digital signal processing and signal transmission. In 1976, he joined the Department of Electrical Engineering at the Technical University of Nova Scotia, Canada, and in 1981, moved to McMaster University, Hamilton, Canada, where he has been a Professor since 1985 and served as Chairman of the Department of Electrical and Computer Engineering in 1986–87, 1988–94 and 2003?08. Professor Wong was on leave as Visiting Professor at the Department of Electronic Engineering of the Chinese University of Hong Kong from 1997 to 1999. At present, he holds the Canada Research Chair in Signal Processing at McMaster University. His research interest is in signal processing and communication theory and has published over 240 papers in the area.
Professor Wong was the recipient of the IEE Overseas Premium for the best paper in 1989, and is also the co-author of the papers that received the IEEE Signal Processing Society “Best Young Author” awards of 2006 and 2008. He is a Fellow of IEEE, a Fellow of the Institution of Electrical Engineers, a Fellow of the Royal Statistical Society, and a Fellow of the Institute of Physics. More recently, he has also been elected as Fellow of the Canadian Academy of Engineering as well as Fellow of the Royal Society of Canada. He was an Associate Editor of the IEEE Transaction on Signal Processing, 1996–98 and served as Chair of the Sensor Array and Multi-channel Signal Processing Technical Committee of the IEEE Signal Processing Society in 2002–04. Professor Wong was the recipient of the Alexander Von Humboldt International Research Award in 2010 and of the McMaster Engineering Research Achievement Award in 2011.