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Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters

Book Description

Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters such as complex-valued neural networks, quantum neural networks, quaternary neural networks, and Clifford neural networks, which have been developing in recent years.

Table of Contents

  1. Copyright
  2. Editorial Advisory Board
  3. List of Reviewers
  4. Foreword
  5. Preface
  6. Acknowledgment
  7. Complex-Valued Neural Network Models and Their Analysis
    1. Complex-Valued Boltzmann Manifold
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE COMPLEX-VALUED HOPFIELD NETWORKS
      5. THE COMPLEX_VALUED BOLTZMANN MACHINES
      6. INFORMATION GEOMETRY
      7. INFORMATION GEOMETRY OF THE COMPLEX_VALUED BOLTZMANN MACHINES
      8. CONCLUSION
      9. FUTURE RESEARCH DIRECTIONS
      10. REFERENCES
      11. ADDITIONAL READING
    2. Complex-Valued Neural Network and Inverse Problems
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. COMPLEX-VALUED NETWORK INVERSION
      5. SAMPLE PROBLEMS FOR COMPLEX-VALUED NETWORK INVERSION
      6. CONCLUSION
      7. FUTURE RESEARCH DIRECTIONS
      8. REFERENCES
      9. ADDITIONAL READING
    3. Kolmogorov's Spline Complex Network and Adaptive Dynamic Modeling of Data
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE CEA METHOD
      5. NEURAL NETS BASED ON THE KOLMOGOROV'S SUPERPOSITION THEOREM
      6. CONCLUSION
      7. FUTURE RESEARCH DIRECTIONS
      8. REFERENCES
      9. ADDITIONAL READINGS
      10. ENDNOTES
    4. A Complex-Valued Hopfield Neural Network: Dynamics and Applications
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE REAL-VALUED HOPFIELD NETWORK
      5. INTERPRETATION OF THE COMPLEX STATE
      6. COMPLEX-VALUED HOPFIELD NEURAL NETWORK
      7. LEARNING: ONE-SHOT AND ADAPTIVE
      8. NETWORK DYNAMICS: THE TWO NETWORK MODES
      9. NETWORK APPLICATIONS
      10. CHNN FOR CHAOTIC SYNCHRONIZATION
      11. CONCLUSION
      12. FUTURE RESEARCH DIRECTIONS
      13. ACKNOWLEDGMENT
      14. REFERENCES
      15. ADDITIONAL READING
      16. MATHEMATICAL APPENDIX
    5. Global Stability Analysis for Complex-Valued Recurrent Neural Networks and Its Application to Convex Optimization Problems
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. COMPLEX-VALUED NEURAL NETWORKS
      5. GLOBAL ASYMPTOTIC STABILITY CONDITIONS
      6. APPLICATION TO CONVEX PROGRAMMING PROBLEMS
      7. NUMERICAL EXAMPLE
      8. CONCLUSION
      9. FUTURE RESEARCH DIRECTIONS
      10. REFERENCES
      11. ADDITIONAL READINGS
      12. APPENDIX: PROOF OF PROPERTY 2
    6. Models of Complex-Valued Hopfield-Type Neural Networks and Their Dynamics
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. HOPFIELD TYPE NEURAL NETWORKS
      5. MODEL OF COMPLEX-VALUED NEURAL NETWORKS OF HOPFIELD TYPE
      6. ENERGY FUNCTION FOR COMPLEX-VALUED NEURAL NETWORKS
      7. EXISIENSE CONDITION OF ENERGY FUNCTION ON ACTIVATION FUNCTIONS
      8. APPLICATION OF ENERGY FUNCTION
      9. CONCLUSION
      10. FUTURE RESEARCH DIRECTIONS
      11. ACKNOWLEDGMENT
      12. REFERENCES
      13. ADDITIONAL READING
      14. ENDNOTE
  8. Applications of Complex-Valued Neural Networks
    1. Complex-Valued Symmetric Radial Basis Function Network for Beamforming
      1. ABSTRACT
      2. INTRODUCION
      3. BACKGROUND
      4. CLUSTERING-BASED SYMMETRIC RBF BEAMFORMING
      5. SYMMETRIC RBF BEAMFORMING CONSTRUCTION BASED ON OFS
      6. CONCLUSION
      7. FUTURE RESEARCH DIRECTIONS
      8. REFERENCES
      9. ADDITIONAL READING
      10. APPENDIX
    2. Complex-Valued Neural Networks for Equalization of Communication Channels
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. SYSTEM MODEL FOR EQUALIZATION PROBLEM
      5. RBFN EQUALIZER
      6. COMPLEX-VALUED NEURAL NETWORKS FOR BLIND EQUALIZATION
      7. COMPLEX VALUED RECURRENT EQUALIZER
      8. EQUALIZATION OF TIME VARYING CHANNELS
      9. CONCLUSION
      10. FUTURE RESEARCH DIRECTIONS
      11. REFERENCES
      12. ADDITIONAL READING
    3. Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE LEARNING ALGORITHM OF THE COMPLEX-VALUED NEURAL NETWORKS
      5. APPLICATIONS IN COMMUNICATION SIGNAL PROCESSING
      6. CONCLUSION
      7. FUTURE RESEARCH DIRECTION
      8. REFERENCES
      9. ADDITIONAL READING
      10. APPENDIX
      11. NNGA
      12. NNDDMMA
    4. Image Reconstruction by the Complex-Valued Neural Networks: Design by Using Generalized Projection Rule
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. NEW LEARNING ALGORITHMS FOR THE CVHAMS
      5. GENERALIZED PROJECTION RULES FOR CVHAMS
      6. A STRATEGY TO FURTHER IMPROVE THE RECALL CAPABILITY OF THE CVHAMS
      7. GENERALIZED INVERSE TECHNIQUE FOR IBAMS
      8. EXPERIMENTAL RESULTS
      9. CONCLUDING REMARKS
      10. FUTURE RESEARCH DIRECTIONS
      11. REFERENCES
      12. ADDITIONAL READING
    5. A Method of Estimation for Magnetic Resonance Spectroscopy Using Complex-Valued Neural Networks
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. MATHEMATICAL MODEL OF THE NMR SIGNAL AND ESTIMATION OF SPECTRA
      5. DESIGN OF A COMPLEX-VALUED HOPFIELD NEURAL NETWORK AS A SPECTRAL ESTIMATOR
      6. SEQUENTIAL EXTENSION OF SECTION (SES)
      7. SIMULATIONS
      8. DISCUSSION
      9. CONCLUSION
      10. FUTURE RESEARCH DIRECTIONS
      11. REFERENCES
      12. ADDITIONAL READING
    6. Flexible Blind Signal Separation in the Complex Domain
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. THE COMPLEX ENVIRONMENT
      5. THE FLEXIBLE ACTIVATION FUNCTION
      6. THE DE-MIXING ALGORITHM AND SEPARATION ARCHITECTURE
      7. RESULTS
      8. CONCLUSION
      9. FUTURE RESEARCH DIRECTION
      10. REFERENCES
      11. ADDITIONAL READING
      12. ENDNOTES
      13. APPENDIX
  9. Models with High-Dimensional Parameters
    1. Qubit Neural Network: Its Performance and Applications
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. QUANTUM COMPUTING AND NEURON MODEL
      5. QUBIT NEURAL NETWORK
      6. LEARNING PERFORMANCES: QUBIT NN VS. CLASSICAL NNS
      7. PRACTICAL APPLICATIONS
      8. CONCLUSION
      9. FUTURE RESEARCH DIRECTIONS
      10. ACKNOWLEDGMENT
      11. REFERENCES
      12. ADDITIONAL READING
    2. Neuromorphic Adiabatic Quantum Computation
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. NEUROMORPHIC ADIABATIC QUANTUM COMPUTATION
      5. APPLICATION TO COMBINATORIAL OPTIMIZATION PROBLEMS
      6. QUANTUM HEBB LEARNING
      7. HARDWARE IMPLEMENTATION
      8. CONCLUSION
      9. FUTURE RESEARCH DIRECTIONS
      10. REFERENCES
      11. ADDITIONAL READING
    3. Attractors and Energy Spectrum of Neural Structures Based on the Model of the Quantum Harmonic Oscillator
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. EQUIVALENCE OF SCHRÖDINGER'S EQUATION TO A DIFFUSION PROCESS
      5. INTERACTING DIFFUSING PARTICLES AS A MODEL OF NEURAL NETWORKS
      6. COMPATIBILITY WITH PRINCIPLES OF QUANTUM MECHANICS
      7. ATTRACTORS IN ASSOCIATIVE MEMORIES BASED ON THE Q.H.O. MODEL
      8. SPECTRAL ANALYSIS OF ASSOCIATIVE MEMORIES THAT FOLLOW THE Q.H.O. MODEL
      9. SIMULATION TESTS
      10. CONCLUSION
      11. FUTURE RESEARCH DIRECTIONS
      12. REFERENCES
      13. ADDITIONAL READING
    4. Quaternionic Neural Networks: Fundamental Properties and Applications
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. QUATERNIONIC MULTILAYER NEURAL NETWORK
      5. HOPFIELD-TYPE QUATERNIONIC NEURAL NETWORK
      6. CONCLUSION
      7. FUTURE RESEARCH DIRECTIONS
      8. ACKNOWLEDGMENT
      9. REFERENCES
      10. ADDITIONAL READING
  10. Compilation of References
  11. About the Contributors
  12. Index