Root-Power Mean Aggregation-Based Neuron in Quaternionic Domain

ABSTRACT

This paper illustrates the new structure of artificial neuron based on root-power mean (RPM) aggregation for quaternionic-valued signals and also presented an efficient learning process of neural networks with quaternionic-valued RPM neurons. The main aim of this neuron is to present the potential capability of a nonlinear aggregation operation on the quaternionic-valued signals in neuron cell. A wide spectrum of aggregation ability of RPM in between minima and maxima has a beautiful property of changing its degree of compensation in the natural way which emulates the various existing neuron models as its special cases. Further, the quaternionic resilient propagation algorithm (ℍ-RPROP) with error-dependent weight backtracking step significantly accelerates the training speed and exhibits better approximation accuracy. The wide spectra of benchmark problem are considered to evaluate the performance of proposed quaternionic RPM neuron with ℍ-RPROP learning algorithm.

KEYWORDS:

• Approximation
• Quasi-arithmetic means
• Quaternionic resilient propagation
• Quaternionic-valued back-propagation
• Quaternionic-valued function
• Quaternionic-valued multilayer perceptron
• Root-power means in quaternionic domain (ℍ)
• Three-dimensional face recognition

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Sushil Kumar

Sushil Kumar is pursuing his PhD degree in computational intelligence area from HBTU Kanpur, India, and completed his MTech degree in modelling and simulation from DIAT-DRDO Pune, India. He is currently a teacher fellow in Department of Computer Science and Engineering of HBTU Kanpur, India. He is also leading the Nature-inspired Computational Intelligence Research Group (NCIRG) at HBTU. His areas of research include high-dimensional neurocomputing, computational intelligence, machine learning and computer vision focused on biometrics, and 3D imaging. He has published several research papers in these areas.

Bipin Kumar Tripathi

Bipin Kumar Tripathi completed his PhD degree in computational intelligence from IIT Kanpur, India, and MTech degree in computer science and engineering from IIT Delhi, India. Dr Tripathi is currently serving as a professor in Department of Computer Science and Engineering of HBTU Kanpur, India. He is also leading the Nature-inspired Computational Intelligence Research Group (NCIRG) at HBTI. His areas of research include high-dimensional neurocomputing, computational neuroscience, intelligent system design, machine learning and computer vision focused on biometrics, and 3D imaging. He has published several research papers in these areas in many peer-reviewed journals including IEEE Transaction, Elsevier, Springer, and other international conferences. He has also contributed book chapters in different international publications and patent in his area. He is continuously serving as PC for many international conferences and as a reviewer of several international journals.

Email: [email protected]