2019/08/02 by Mustaffa Alfatlawi, Alfatlawi, Mustaffa, Vaibhav Srivastava +1 · 3 citations
Computer Science · Neuroscience · #Blind Source Separation Techniques #EEG and Brain-Computer Interfaces #FOS: Electrical engineering #FOS: Mathematics #Neural dynamics and brain function #Optimization and Control (math.OC) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1908.01047
openalex publication_date 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low\ndimensional linear time invariant dynamics underlying high-dimensional data.\nFor systems in which such underlying low-dimensional dynamics is time-varying,\na time-invariant approximation of such dynamics computed through standard DMD\ntechniques may not be appropriate. We focus on DMD techniques for such\ntime-varying systems and develop incremental algorithms for systems without and\nwith exogenous control inputs. We build upon the work in [35] to scenarios in\nwhich high dimensional data are governed by low dimensional time-varying\ndynamics. We consider two classes of algorithms that rely on (i) a discount\nfactor on previous observations, and (ii) a sliding window of observations. Our\nalgorithms leverage existing techniques for incremental singular value\ndecomposition and allow us to determine an appropriately reduced model at each\ntime and are applicable even if data matrix is singular. We apply the developed\nalgorithms for autonomous systems to Electroencephalographic (EEG) data and\ndemonstrate their effectiveness in terms of reconstruction and prediction. Our\nalgorithms for non-autonomous systems are illustrated using randomly generated\nlinear time-varying systems.\n