Fuzzy Recurrence Plots and Networks with Applications in Biomedicine

Description

This book presents an original combination of three well-known methodological approaches for nonlinear data analysis: recurrence, networks, and fuzzy logic. After basic concepts of these three approaches are introduced, this book presents recently developed methods known as fuzzy recurrence plots and fuzzy recurrence networks.  Computer programs written in MATLAB, which implement the basic algorithms, are included to facilitate the understanding of the developed ideas. Several applications of these techniques to biomedical problems, ranging from cancer and neurodegenerative disease to depression, are illustrated to show the potential of fuzzy recurrence methods. This book opens a new door to theorists in complex systems science as well as specialists in medicine, biology, engineering, physics, computer science, geosciences, and social economics to address issues in experimental nonlinear signal and data processing. Foreword Preface References Acknowledgements Contents About the Author 1 Phase Space in Chaos and Nonlinear Dynamics 1.1 Phase Space 1.2 Maps 1.3 Attractors 1.4 Time Delay 1.5 Embedding Dimension 1.6 Phase-Space Reconstruction References 2 Recurrence Plots 2.1 Recurrence Plots 2.2 Cross and Joint Recurrence Plots 2.3 Recurrence Networks 2.4 Recurrence Quantification Analysis References 3 Fuzzy Logic 3.1 Fuzzy Sets 3.2 Operations on Fuzzy Sets 3.3 Fuzzy Relations 3.4 The Fuzzy c-Means Algorithm 3.5 Cluster Validity for the FCM 3.6 Illustrations References 4 Fuzzy Recurrence Plots 4.1 Fuzzy Recurrence Plots 4.1.1 Mathematical Formulation 4.1.2 Computer Code 4.1.3 Illustrations 4.2 Fuzzy Cross Recurrence Plots 4.2.1 Computer Code 4.2.2 Illustrations 4.3 Fuzzy Joint Recurrence Plots 4.3.1 Computer Code 4.3.2 Illustrations 4.4 Texture Analysis of Fuzzy Recurrence Plots References 5 Fuzzy Recurrence Networks 5.1 Unweighted Fuzzy Recurrence Networks 5.1.1 Computer Code 5.1.2 Illustrations 5.2 Fuzzy Weighted Recurrence Networks 5.2.1 Computer Code 5.2.2 Illustrations 5.3 Fuzzy Weighted Recurrence Networks of Multichannel Data 5.3.1 Computer Code 5.3.2 Illustrations References 6 Entropy Algorithms 6.1 Approximate Entropy and Sample Entropy 6.2 Multiscale Entropy 6.3 Time-Shift Multiscale Entropy 6.4 Illustrations 6.4.1 Analysis of Time Series with Known Properties 6.4.2 Analysis of Physiological Signals 6.4.3 Remarks References 7 Applications in Biomedicine 7.1 Protein Expression by Immunohistochemistry in Rectal Cancer Patients 7.1.1 Rectal Cancer Patients 7.1.2 Immunochemistry and Image Extraction 7.1.3 Results 7.2 The Recurrence Dynamics of Personalized Depression 7.2.1 Time-Series Data 7.2.2 Tensor Decomposition of Mental-State Dynamics 7.2.3 Results 7.3 Classification of Short Time Series with Deep Learning … 7.3.1 LSTM Neural Networks with FRPs 7.3.2 Database 7.3.3 Results 7.4 Analysis of Computer-Keystroke Time Series 7.5 Visualization and Classification of Gait Dynamics 7.5.1 Database 7.5.2 Results 7.6 Recurrence of White Matter Lesions on MRI 7.6.1 2D-FWRN 7.6.2 Results 7.7 Nonlinear Dynamics of Photoplethysmogram in Parkinson's Disease References Index