title: Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals.
abstract: This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.
authors.affiliation: Boston Children's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA.
authors.forename: Burak
authors.initials: B
authors.lastname: Erem
authors.affiliation: Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Ramon
authors.initials: R
authors.lastname: Martinez Orellana
authors.affiliation: Boston Children's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA.
authors.forename: Damon E
authors.initials: DE
authors.lastname: Hyde
authors.affiliation: Boston Children's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA.
authors.forename: Jurriaan M
authors.initials: JM
authors.lastname: Peters
authors.affiliation: Boston Children's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA.
authors.forename: Frank H
authors.initials: FH
authors.lastname: Duffy
authors.affiliation: General University Hospital, Charles University, 128 08 Prague, Czech Republic.
authors.forename: Petr
authors.initials: P
authors.lastname: Stovicek
authors.affiliation: Boston Children's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA.
authors.forename: Simon K
authors.initials: SK
authors.lastname: Warfield
authors.affiliation: University of Utah, Salt Lake City, Utah 84112, USA.
authors.forename: Rob S
authors.initials: RS
authors.lastname: MacLeod
authors.affiliation: Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Gilead
authors.initials: G
authors.lastname: Tadmor
authors.affiliation: Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Dana H
authors.initials: DH
authors.lastname: Brooks
mesh_terms: D001921:Brain / Q000502:physiology; D004562:Electrocardiography; D004569:Electroencephalography; D055724:Electrophysiological Phenomena; D006321:Heart / Q000502:physiology; D006801:Humans; D000069550:Machine Learning; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted; D059629:Signal-To-Noise Ratio; D013997:Time Factors