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Clustering Brain-Network Time Series by Riemannian Geometry | IEEE Journals & Magazine | IEEE Xplore

Abstract:

This paper advocates Riemannian multi-manifold modeling for network-wide time-series analysis: Dynamic brainnetwork data yield features which are viewed as points in or c...Show More

Abstract:

This paper advocates Riemannian multi-manifold modeling for network-wide time-series analysis: Dynamic brainnetwork data yield features which are viewed as points in or close to a union of a finite number of submanifolds of a Riemannian manifold. Distinguishing disparate time series amounts then to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for network-wide dynamic time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positive-definite matrices. Capitalizing on recently developed research on Riemannian-submanifold clustering, an algorithm is provided to differentiate time series based on their Riemannian-geometry properties. Extensive numerical tests on synthetic and real fMRI data demonstrate that the proposed framework outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.
Page(s): 519 - 533
Date of Publication: 16 November 2017

ISSN Information:

Funding Agency:

Author image of Konstantinos Slavakis
Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
Konstantinos Slavakis (M’08–SM’12) received the Ph.D. degree in electrical and electronic Engineering from Tokyo Institute of Technology, Tokyo, Japan. He joined University at Buffalo (SUNY) as an Associate Professor in 2015. He has served IEEE Transactions on Signal Processing as an Associate Editor (AE) (2009–2013) as well as a Senior AE (2010–2015). He is currently an AE of the EURASIP Signal Processing Journal and...Show More
Konstantinos Slavakis (M’08–SM’12) received the Ph.D. degree in electrical and electronic Engineering from Tokyo Institute of Technology, Tokyo, Japan. He joined University at Buffalo (SUNY) as an Associate Professor in 2015. He has served IEEE Transactions on Signal Processing as an Associate Editor (AE) (2009–2013) as well as a Senior AE (2010–2015). He is currently an AE of the EURASIP Signal Processing Journal and...View more
Author image of Shiva Salsabilian
Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, NJ, USA
Shiva Salsabilian received the B.Sc. degree in Electrical Engineering (Electronics) from Shahrekord University, Isfahan, Iran, in 2008 and the M.Sc. degree in Electrical Engineering (Communication Systems) from the Isfahan University of Technology, Isfahan, Iran, in 2011. She is currently working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, Rutgers University, State University of N...Show More
Shiva Salsabilian received the B.Sc. degree in Electrical Engineering (Electronics) from Shahrekord University, Isfahan, Iran, in 2008 and the M.Sc. degree in Electrical Engineering (Communication Systems) from the Isfahan University of Technology, Isfahan, Iran, in 2011. She is currently working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, Rutgers University, State University of N...View more
Author image of David S. Wack
Department of Nuclear Medicine and the Department of Biomedical Engineering, University at Buffalo, NY, USA
David S. Wack was born in Buffalo, NY, USA, in 1966. He received the B.A. degree in Applied Mathematics and a MusB in music performance (Percussion) in 1989, and the M.A. degree in applied Mathematics in 1992 from University at Buffalo, Buffalo, NY, USA, and the Ph.D. in communicative disorders and sciences (Hearing Science), in 2010. He is currently an Associate Professor in the Department of Nuclear Medicine and Bio...Show More
David S. Wack was born in Buffalo, NY, USA, in 1966. He received the B.A. degree in Applied Mathematics and a MusB in music performance (Percussion) in 1989, and the M.A. degree in applied Mathematics in 1992 from University at Buffalo, Buffalo, NY, USA, and the Ph.D. in communicative disorders and sciences (Hearing Science), in 2010. He is currently an Associate Professor in the Department of Nuclear Medicine and Bio...View more
Author image of Sarah F. Muldoon
Department of Mathematics and the Computational and Data-Enabled Science and Eng. Program, University at Buffalo, NY, USA
Sarah Muldoon joined the Department of Mathematics, University at Buffalo, Buffalo, NY, USA, as an Assistant Professor in 2015. She joined as the core faculty in the Computational and Data-Enabled Sciences and Engineering Program. Her research interests include intersection of experiment and theory with a focus on applications of network theory to neuroscience data, with a specific interest in epilepsy. She has spent ...Show More
Sarah Muldoon joined the Department of Mathematics, University at Buffalo, Buffalo, NY, USA, as an Assistant Professor in 2015. She joined as the core faculty in the Computational and Data-Enabled Sciences and Engineering Program. Her research interests include intersection of experiment and theory with a focus on applications of network theory to neuroscience data, with a specific interest in epilepsy. She has spent ...View more
Author image of Henry E. Baidoo-Williams
Vocal Technologies, Inc, Buffalo, NY, USA
Henry E. Baidoo-Williams was born in 1980 in Takoradi, Ghana. He received the B.Sc. degree in Electrical and Electronic Eng. from the Kwame Nkrumah Univ. of Science and Technology (Ghana), in 2005, and the Ph.D. in Electrical and Computer Eng. from the Univ. of Iowa in 2015. Between 2005 and 2006, he was an Intelligent Networks Engineer at Huawei Technologies, Ghana. He was a Design Engineer at the Electricity Company...Show More
Henry E. Baidoo-Williams was born in 1980 in Takoradi, Ghana. He received the B.Sc. degree in Electrical and Electronic Eng. from the Kwame Nkrumah Univ. of Science and Technology (Ghana), in 2005, and the Ph.D. in Electrical and Computer Eng. from the Univ. of Iowa in 2015. Between 2005 and 2006, he was an Intelligent Networks Engineer at Huawei Technologies, Ghana. He was a Design Engineer at the Electricity Company...View more
Author image of Jean M. Vettel
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA
Jean M. Vettel received the Ph.D. degree in cognitive neuroscience from Brown University, funded by an NSF Graduate Fellowship (2004–2007) and a DoD SMART Fellowship (2007–2009), following a lab position at Washington Univ. in St. Louis and BA from Carnegie Mellon. Since Sept 2009, she has been a civilian neuroscientist at Army Research Laboratory and currently serves as a senior science lead in the Future Soldier Tec...Show More
Jean M. Vettel received the Ph.D. degree in cognitive neuroscience from Brown University, funded by an NSF Graduate Fellowship (2004–2007) and a DoD SMART Fellowship (2007–2009), following a lab position at Washington Univ. in St. Louis and BA from Carnegie Mellon. Since Sept 2009, she has been a civilian neuroscientist at Army Research Laboratory and currently serves as a senior science lead in the Future Soldier Tec...View more
Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, USA
Matthew Cieslak photograph and biography not available at the time of publication.
Matthew Cieslak photograph and biography not available at the time of publication.View more
Author image of Scott T. Grafton
Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, USA
Scott T. Grafton received the B.A.S. degree in mathematics and psychobiology from the University of California at Santa Cruz, CA, USA, in 1980 and the MD degree from the University of Southern California (USC), Los Angeles, CA, USA, in 1984. After completing residency in Neurology at University of Washington in 1988, he completed a Nuclear Medicine residency and functional imaging research fellowship at the University...Show More
Scott T. Grafton received the B.A.S. degree in mathematics and psychobiology from the University of California at Santa Cruz, CA, USA, in 1980 and the MD degree from the University of Southern California (USC), Los Angeles, CA, USA, in 1984. After completing residency in Neurology at University of Washington in 1988, he completed a Nuclear Medicine residency and functional imaging research fellowship at the University...View more

Author image of Konstantinos Slavakis
Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
Konstantinos Slavakis (M’08–SM’12) received the Ph.D. degree in electrical and electronic Engineering from Tokyo Institute of Technology, Tokyo, Japan. He joined University at Buffalo (SUNY) as an Associate Professor in 2015. He has served IEEE Transactions on Signal Processing as an Associate Editor (AE) (2009–2013) as well as a Senior AE (2010–2015). He is currently an AE of the EURASIP Signal Processing Journal and Journal on Advances in Signal Processing. He has been a member of the IEEE Signal Processing Theory and Methods technical committee (TC) [’12–’17] and he is a member of the EURASIP Signal and Data Analytics for Machine Learning (SiG-DML) TC. His research interests are in the areas of signal processing, machine learning and data analytics.
Konstantinos Slavakis (M’08–SM’12) received the Ph.D. degree in electrical and electronic Engineering from Tokyo Institute of Technology, Tokyo, Japan. He joined University at Buffalo (SUNY) as an Associate Professor in 2015. He has served IEEE Transactions on Signal Processing as an Associate Editor (AE) (2009–2013) as well as a Senior AE (2010–2015). He is currently an AE of the EURASIP Signal Processing Journal and Journal on Advances in Signal Processing. He has been a member of the IEEE Signal Processing Theory and Methods technical committee (TC) [’12–’17] and he is a member of the EURASIP Signal and Data Analytics for Machine Learning (SiG-DML) TC. His research interests are in the areas of signal processing, machine learning and data analytics.View more
Author image of Shiva Salsabilian
Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, NJ, USA
Shiva Salsabilian received the B.Sc. degree in Electrical Engineering (Electronics) from Shahrekord University, Isfahan, Iran, in 2008 and the M.Sc. degree in Electrical Engineering (Communication Systems) from the Isfahan University of Technology, Isfahan, Iran, in 2011. She is currently working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, Rutgers University, State University of New Jersey, New Brunswick, NJ, USA. From 2015 to 2016, she was with the Department of Electrical Engineering,  University at Buffalo (SUNY). Her research interests include Digital Signal Processing and Functional Brain Imaging.
Shiva Salsabilian received the B.Sc. degree in Electrical Engineering (Electronics) from Shahrekord University, Isfahan, Iran, in 2008 and the M.Sc. degree in Electrical Engineering (Communication Systems) from the Isfahan University of Technology, Isfahan, Iran, in 2011. She is currently working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, Rutgers University, State University of New Jersey, New Brunswick, NJ, USA. From 2015 to 2016, she was with the Department of Electrical Engineering,  University at Buffalo (SUNY). Her research interests include Digital Signal Processing and Functional Brain Imaging.View more
Author image of David S. Wack
Department of Nuclear Medicine and the Department of Biomedical Engineering, University at Buffalo, NY, USA
David S. Wack was born in Buffalo, NY, USA, in 1966. He received the B.A. degree in Applied Mathematics and a MusB in music performance (Percussion) in 1989, and the M.A. degree in applied Mathematics in 1992 from University at Buffalo, Buffalo, NY, USA, and the Ph.D. in communicative disorders and sciences (Hearing Science), in 2010. He is currently an Associate Professor in the Department of Nuclear Medicine and Biomedical Engineering, and is a member of the Toshiba Stroke and Vascular Research Center, at SUNY at Buffalo. In 1992, he joined the Center for Positron Emission Tomography, a joint venture between the VA Western New York Healthcare Center and SUNY at Buffalo, as a Computer Specialist and Lecturer. He was promoted to Assistant Professor in the Dept. of Nuclear Medicine at SUNY at Buffalo in 1998 and was promoted to Associate Professor in 2013. His dissertation used functional MRI to locate neural correlates of binaural hearing. Dr. Wacks research interests are in neuro-imaging analysis and algorithm methods, and he is currently investigating machine learning and query by image algorithms. Additionally, he is conducting neuro-imaging studies investigating binaural listening and also chronic pain.
David S. Wack was born in Buffalo, NY, USA, in 1966. He received the B.A. degree in Applied Mathematics and a MusB in music performance (Percussion) in 1989, and the M.A. degree in applied Mathematics in 1992 from University at Buffalo, Buffalo, NY, USA, and the Ph.D. in communicative disorders and sciences (Hearing Science), in 2010. He is currently an Associate Professor in the Department of Nuclear Medicine and Biomedical Engineering, and is a member of the Toshiba Stroke and Vascular Research Center, at SUNY at Buffalo. In 1992, he joined the Center for Positron Emission Tomography, a joint venture between the VA Western New York Healthcare Center and SUNY at Buffalo, as a Computer Specialist and Lecturer. He was promoted to Assistant Professor in the Dept. of Nuclear Medicine at SUNY at Buffalo in 1998 and was promoted to Associate Professor in 2013. His dissertation used functional MRI to locate neural correlates of binaural hearing. Dr. Wacks research interests are in neuro-imaging analysis and algorithm methods, and he is currently investigating machine learning and query by image algorithms. Additionally, he is conducting neuro-imaging studies investigating binaural listening and also chronic pain.View more
Author image of Sarah F. Muldoon
Department of Mathematics and the Computational and Data-Enabled Science and Eng. Program, University at Buffalo, NY, USA
Sarah Muldoon joined the Department of Mathematics, University at Buffalo, Buffalo, NY, USA, as an Assistant Professor in 2015. She joined as the core faculty in the Computational and Data-Enabled Sciences and Engineering Program. Her research interests include intersection of experiment and theory with a focus on applications of network theory to neuroscience data, with a specific interest in epilepsy. She has spent extensive time working in experimental neurobiology labs and now runs a research group that couples theoretical advancement, computational modeling, and data-intensive analysis to study the relationship between structure and function in brain networks. She is the member of the Neuroscience Program.
Sarah Muldoon joined the Department of Mathematics, University at Buffalo, Buffalo, NY, USA, as an Assistant Professor in 2015. She joined as the core faculty in the Computational and Data-Enabled Sciences and Engineering Program. Her research interests include intersection of experiment and theory with a focus on applications of network theory to neuroscience data, with a specific interest in epilepsy. She has spent extensive time working in experimental neurobiology labs and now runs a research group that couples theoretical advancement, computational modeling, and data-intensive analysis to study the relationship between structure and function in brain networks. She is the member of the Neuroscience Program.View more
Author image of Henry E. Baidoo-Williams
Vocal Technologies, Inc, Buffalo, NY, USA
Henry E. Baidoo-Williams was born in 1980 in Takoradi, Ghana. He received the B.Sc. degree in Electrical and Electronic Eng. from the Kwame Nkrumah Univ. of Science and Technology (Ghana), in 2005, and the Ph.D. in Electrical and Computer Eng. from the Univ. of Iowa in 2015. Between 2005 and 2006, he was an Intelligent Networks Engineer at Huawei Technologies, Ghana. He was a Design Engineer at the Electricity Company of Ghana between 2006 and 2009. He was engaged as an Adjunct Assistant Professor of Electrical and Computer Engineering at the Univ. of Iowa, U.S.A. in 2015. Between 2016 and 2017, he held a joint postdoctoral research associate position at the Univ. at Buffalo and the U.S. Army research Laboratory, Aberdeen proving ground. He is currently R&D lead at Vocal Technologies, Inc. for acoustic beamforming and speech recognition algorithms for real time operating systems. He is a member of IEEE. His research interests are in signal processing, design of algorithms, pattern recognition, communication systems and optimization techniques.
Henry E. Baidoo-Williams was born in 1980 in Takoradi, Ghana. He received the B.Sc. degree in Electrical and Electronic Eng. from the Kwame Nkrumah Univ. of Science and Technology (Ghana), in 2005, and the Ph.D. in Electrical and Computer Eng. from the Univ. of Iowa in 2015. Between 2005 and 2006, he was an Intelligent Networks Engineer at Huawei Technologies, Ghana. He was a Design Engineer at the Electricity Company of Ghana between 2006 and 2009. He was engaged as an Adjunct Assistant Professor of Electrical and Computer Engineering at the Univ. of Iowa, U.S.A. in 2015. Between 2016 and 2017, he held a joint postdoctoral research associate position at the Univ. at Buffalo and the U.S. Army research Laboratory, Aberdeen proving ground. He is currently R&D lead at Vocal Technologies, Inc. for acoustic beamforming and speech recognition algorithms for real time operating systems. He is a member of IEEE. His research interests are in signal processing, design of algorithms, pattern recognition, communication systems and optimization techniques.View more
Author image of Jean M. Vettel
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA
Jean M. Vettel received the Ph.D. degree in cognitive neuroscience from Brown University, funded by an NSF Graduate Fellowship (2004–2007) and a DoD SMART Fellowship (2007–2009), following a lab position at Washington Univ. in St. Louis and BA from Carnegie Mellon. Since Sept 2009, she has been a civilian neuroscientist at Army Research Laboratory and currently serves as a senior science lead in the Future Soldier Technologies Division under ARLs Human Sciences campaign. In support of ARLs Open Campus, Jean was appointed as adjunct faculty at Univ. of California, Santa Barbara in 2014 and a visiting scholar at Univ. of Pennsylvania in 2015. Her collaborative research investigates methods to quantify brain connectivity that accounts for task performance variability both within- and between-individuals and then uses these brain metrics in novel neurotechnology approaches to enhance performance and enable fundamental innovations in adaptive technology.
Jean M. Vettel received the Ph.D. degree in cognitive neuroscience from Brown University, funded by an NSF Graduate Fellowship (2004–2007) and a DoD SMART Fellowship (2007–2009), following a lab position at Washington Univ. in St. Louis and BA from Carnegie Mellon. Since Sept 2009, she has been a civilian neuroscientist at Army Research Laboratory and currently serves as a senior science lead in the Future Soldier Technologies Division under ARLs Human Sciences campaign. In support of ARLs Open Campus, Jean was appointed as adjunct faculty at Univ. of California, Santa Barbara in 2014 and a visiting scholar at Univ. of Pennsylvania in 2015. Her collaborative research investigates methods to quantify brain connectivity that accounts for task performance variability both within- and between-individuals and then uses these brain metrics in novel neurotechnology approaches to enhance performance and enable fundamental innovations in adaptive technology.View more
Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, USA
Matthew Cieslak photograph and biography not available at the time of publication.
Matthew Cieslak photograph and biography not available at the time of publication.View more
Author image of Scott T. Grafton
Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA, USA
Scott T. Grafton received the B.A.S. degree in mathematics and psychobiology from the University of California at Santa Cruz, CA, USA, in 1980 and the MD degree from the University of Southern California (USC), Los Angeles, CA, USA, in 1984. After completing residency in Neurology at University of Washington in 1988, he completed a Nuclear Medicine residency and functional imaging research fellowship at the University of California at Los Angeles, CA, USA1991. He was a faculty member and developed brain imaging programs in the Schools of Medicine, USC, Emory University, and Dartmouth College before joining the faculty at the University of California, Santa Barbara in 2006, where he directs the UCSB Brain Imaging Center. He directs an interdisciplinary research program at the interface of learning theory, the organization of skilled action, network science, and multimodal brain imaging. He is recognized for developing novel analysis tools that are used to characterize plasticity and learning, particularly in the human motor system. Clinically, these tools are also being used to identify changes in brain connectivity during stroke recovery, after mild traumatic brain injury and after repeated sub-concussive head impacts that are part of normal athletics. He holds the Bedrosian-Coyne Presidential Chair in Neuroscience at the UCSB. He is Co-Director at the Institute for Collaborative Biotechnologies, which draws on bio-inspiration and innovative bioengineering solutions for both non-medical and medical challenges posed by the defense and medical communities.
Scott T. Grafton received the B.A.S. degree in mathematics and psychobiology from the University of California at Santa Cruz, CA, USA, in 1980 and the MD degree from the University of Southern California (USC), Los Angeles, CA, USA, in 1984. After completing residency in Neurology at University of Washington in 1988, he completed a Nuclear Medicine residency and functional imaging research fellowship at the University of California at Los Angeles, CA, USA1991. He was a faculty member and developed brain imaging programs in the Schools of Medicine, USC, Emory University, and Dartmouth College before joining the faculty at the University of California, Santa Barbara in 2006, where he directs the UCSB Brain Imaging Center. He directs an interdisciplinary research program at the interface of learning theory, the organization of skilled action, network science, and multimodal brain imaging. He is recognized for developing novel analysis tools that are used to characterize plasticity and learning, particularly in the human motor system. Clinically, these tools are also being used to identify changes in brain connectivity during stroke recovery, after mild traumatic brain injury and after repeated sub-concussive head impacts that are part of normal athletics. He holds the Bedrosian-Coyne Presidential Chair in Neuroscience at the UCSB. He is Co-Director at the Institute for Collaborative Biotechnologies, which draws on bio-inspiration and innovative bioengineering solutions for both non-medical and medical challenges posed by the defense and medical communities.View more

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