Singular Spectrum Analysis of Biomedical Signals Singular Spectrum Analysis of Biomedical Signals Saeid Sanei and Hossein Hassani CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20151109 International Standard Book Number-13: 978-1-4665-8928-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xi 1 Introduction 1 1.1 Physiological,Biological, and Biochemical Processes . . . . . 1 1.2 Major Topics in Physiologicaland Biological Signal Processing 2 1.3 Biological Signals and Systems . . . . . . . . . . . . . . . . . 10 1.4 Decomposition of Signals and Extraction of the Sources of In- terest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Quantification of Evolution and Prediction of Future Trends 11 1.6 Data and Trends; Rhythmic, Noisy, or Chaotic? . . . . . . . 12 1.7 Generation of Surrogate Data . . . . . . . . . . . . . . . . . 13 1.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 13 Bibliography 15 2 Singular Spectrum Analysis 17 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Univariate SSA . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1 Stage 1: Decomposition . . . . . . . . . . . . . . . . . 19 2.2.2 Stage 2: Reconstruction . . . . . . . . . . . . . . . . . 22 2.2.3 Selection of L and r in Univariate Cases . . . . . . . . 24 2.2.3.1 Singular Values. . . . . . . . . . . . . . . . . 25 2.2.3.2 Pairwise Scatterplots . . . . . . . . . . . . . 26 2.2.3.3 PeriodogramAnalysis . . . . . . . . . . . . . 27 2.2.3.4 Separability. . . . . . . . . . . . . . . . . . . 27 2.2.4 SSA Forecasting Algorithm . . . . . . . . . . . . . . . 29 2.3 Multivariate SSA . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.1 MSSA: Vertical Form . . . . . . . . . . . . . . . . . . 32 2.3.2 MSSA: Horizontal Form . . . . . . . . . . . . . . . . . 33 2.4 Optimal Values of L and r in MSSA . . . . . . . . . . . . . . 35 2.4.1 L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4.2 r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5 Extensions of SSA . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5.1 SSA-Based Causality Tests . . . . . . . . . . . . . . . 38 2.5.1.1 Forecasting Accuracy Criteria . . . . . . . . 38 2.5.1.2 Direction of Change Based Criteria . . . . . 40 v vi Contents 2.5.2 Change Point Detection . . . . . . . . . . . . . . . . . 42 2.5.3 Automated Selection of L and r . . . . . . . . . . . . 42 2.5.4 SSA Based on Minimum Variance . . . . . . . . . . . 43 2.5.5 SSA Based on Perturbation Theory . . . . . . . . . . 44 2.5.6 Two Dimensional SSA . . . . . . . . . . . . . . . . . . 45 2.5.7 SSA Based on L -Norm . . . . . . . . . . . . . . . . . 45 1 Bibliography 47 3 SSA Application to Sleep Scoring 51 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Stages of Sleep . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.1 NREM Sleep . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.2 REM Sleep . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 The Influence of Circadian Rhythms . . . . . . . . . . . . . . 57 3.4 Sleep Deprivation . . . . . . . . . . . . . . . . . . . . . . . . 59 3.5 PsychologicalEffects . . . . . . . . . . . . . . . . . . . . . . 60 3.6 DetectionandMonitoringofBrainAbnormalitiesDuringSleep by EEG Analysis . . . . . . . . . . . . . . . . . . . . . . . . 61 3.7 SSA for Sleep Scoring . . . . . . . . . . . . . . . . . . . . . . 62 3.7.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 62 3.7.2 Tensor-BasedSSA . . . . . . . . . . . . . . . . . . . . 63 3.7.3 EMD . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.7.4 TSSA-EMD . . . . . . . . . . . . . . . . . . . . . . . . 67 3.7.5 Application to Sleep EEG . . . . . . . . . . . . . . . . 68 3.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 69 Bibliography 73 4 Adaptive SSA and its Application to Biomedical Source Separation 77 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 Adaptive Line Enhancement . . . . . . . . . . . . . . . . . . 78 4.3 SSA-BasedALEanditsApplicationtoSeparationofECGfrom Recorded EMG . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 Incorporating Sparsity Constraint . . . . . . . . . . . . . . . 81 4.5 Comparing Basic ALE and SSA-Based ALE . . . . . . . . . 82 4.5.1 Simulated Signals. . . . . . . . . . . . . . . . . . . . . 82 4.5.2 Real Signals (EMG Corrupted by ECG Artefact) . . . 84 4.6 Application of Sparsity Constraint . . . . . . . . . . . . . . . 86 4.7 An Adaptive SSA-Based System for Classification of Narrow Frequency Band Signals . . . . . . . . . . . . . . . . . . . . . 87 4.7.1 Recursive Least Squares . . . . . . . . . . . . . . . . . 88 4.7.2 Application to Sleep Scoring . . . . . . . . . . . . . . 89 4.7.3 Experimental Results . . . . . . . . . . . . . . . . . . 89 4.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 91 Contents vii Bibliography 93 5 Applications to Biometric Identification and Recognition 95 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.2 Gait Recognition . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2.1 Gait Modelling and Recognition . . . . . . . . . . . . 98 5.2.2 PsychophysicalConsiderations . . . . . . . . . . . . . 98 5.3 Model Free Methods . . . . . . . . . . . . . . . . . . . . . . . 99 5.3.1 Temporal Correspondence . . . . . . . . . . . . . . . . 100 5.3.2 Spatio-Temporal Motion . . . . . . . . . . . . . . . . . 101 5.3.3 Model-Based Approaches . . . . . . . . . . . . . . . . 105 5.3.4 Approaches to Pose Recovery . . . . . . . . . . . . . . 108 5.4 Combination of Gait with Other Biometrics . . . . . . . . . 113 5.5 Gait Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.6 Gait Analysis for Clinical Rehabilitation . . . . . . . . . . . 114 5.7 Assessing Limb Function for Stroke Patients . . . . . . . . . 115 5.8 SSA Application for Recognition and Characterisation of Stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.9 Use of Multivariate SSA for Joint Analysis of 3D Trajectories 125 5.10 Gait Analysis Using Ear-WornSensor Data . . . . . . . . . . 125 5.10.1 Discrimination of Gait Pattern . . . . . . . . . . . . . 131 5.11 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 133 Bibliography 135 6 Complex-Valued SSA for Detection of Event Related Potentials from EEG 145 6.1 Brief Literature . . . . . . . . . . . . . . . . . . . . . . . . . 146 6.2 Complex-Valued Matrix Variables Z and Z∗ . . . . . . . . . 147 6.3 Augmented Complex Statistics . . . . . . . . . . . . . . . . . 148 6.4 Analytic Signals . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.5 Complex-Valued Derivatives . . . . . . . . . . . . . . . . . . 151 6.6 Generalized Complex-Valued Matrix Derivatives . . . . . . . 152 6.7 Augmented Complex-Valued Matrix Variables . . . . . . . . 153 6.8 Singular Spectrum Analysis of P300 for Classification . . . . 154 6.8.1 Augmented Complex SSA Algorithm . . . . . . . . . . 155 6.9 Experimental Results . . . . . . . . . . . . . . . . . . . . . . 157 6.10 Some Concluding Remarks . . . . . . . . . . . . . . . . . . . 159 6.11 Extension to Hypercomplex Domain . . . . . . . . . . . . . . 159 6.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Bibliography 165 viii Contents 7 SSA Change Point Detection and Eye Fundus Image Analysis 171 7.1 Ocular Fundus Abnormalities . . . . . . . . . . . . . . . . . . 172 7.2 Ocular Fundus Images . . . . . . . . . . . . . . . . . . . . . . 173 7.3 Diabetic Retinopathy Images . . . . . . . . . . . . . . . . . . 175 7.4 Analysis of Fundus Images and Detection of Retinopathy Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 7.4.1 Potential Vessel Distribution Map . . . . . . . . . . . 180 7.4.2 Blood Vessel Reconstruction and Linking the Vessel Segments . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.4.3 Post Processing . . . . . . . . . . . . . . . . . . . . . . 183 7.4.4 Implementation and Results . . . . . . . . . . . . . . . 184 7.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 185 Bibliography 187 8 Prediction of Medical and Physiological Trends 191 8.1 Conventional Approaches for Time Series Prediction . . . . . 192 8.1.1 Multiple Linear Regression . . . . . . . . . . . . . . . 192 8.1.2 Recurrent Neural Networks . . . . . . . . . . . . . . . 194 8.1.3 Hidden Markov Model . . . . . . . . . . . . . . . . . . 195 8.1.4 Holt–Winters Exponential Smoothing Model . . . . . 196 8.2 SSA Application for Prediction . . . . . . . . . . . . . . . . . 198 8.3 How Is SSA Used in Prediction? . . . . . . . . . . . . . . . . 198 8.4 Application of SSA-Based Prediction to Real Biomedical Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 8.4.1 Prediction of Pharmaceutical Product . . . . . . . . . 202 8.4.2 Predicting Ambulance Demand . . . . . . . . . . . . . 204 8.4.3 Progressof Alzheimer’s Disease and Prediction of Crit- ical State of the Patient . . . . . . . . . . . . . . . . . 206 8.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 209 Bibliography 211 9 SSA Application on Genetic Studies 215 9.1 Genomic Signal Processing . . . . . . . . . . . . . . . . . . . 215 9.1.1 Problems in Genomic Signal Processing . . . . . . . . 218 9.1.2 Frequency Domain Analysis . . . . . . . . . . . . . . . 219 9.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 9.3 Singular Spectrum Analysis and Colonial Theory . . . . . . . 222 9.3.1 Stage 1: Decomposition . . . . . . . . . . . . . . . . . 224 9.3.2 Stage 2: Reconstruction . . . . . . . . . . . . . . . . . 225 9.4 Signal Extraction and Filtering . . . . . . . . . . . . . . . . . 227 9.5 SSA Based on Minimum Variance . . . . . . . . . . . . . . . 227 9.6 SSA Combined with AR Model . . . . . . . . . . . . . . . . 228 9.7 Application of Two Dimensional SSA . . . . . . . . . . . . . 230 Contents ix 9.8 Eigenvalues Identification in SSA Signal Extraction . . . . . 231 9.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 234 Bibliography 239 10 Conclusions and Suggestions for Future Research 245 Index 247