A fully complex-valued radial basis function classifier for real-valued classification problems

In this paper, we investigate the decision making ability of a fully complex-valued radial basis function (FC-RBF) network in solving real-valued classification problems. The FC-RBF classifier is a single hidden layer fully complex-valued neural network with a nonlinear input layer, a nonlinear hidden layer, and a linear output layer. The neurons in the input layer of the classifier employ the phase encoded transformation to map the input features from the Real domain to the Complex domain. The neurons in the hidden layer employ a fully complex-valued Gaussian-like activation function of the type of hyperbolic secant (sech). The classification ability of the classifier is first studied analytically and it is shown that the decision boundaries of the FC-RBF classifier are orthogonal to each other. Then, the performance of the FC-RBF classifier is studied experimentally using a set of real-valued benchmark problems and also a real-world problem. The study clearly indicates the superior classification ability of the FC-RBF classifier.

[1]  S. N. Omkar,et al.  Rule extraction for classification of acoustic emission signals using Ant Colony Optimisation , 2008, Eng. Appl. Artif. Intell..

[2]  R. Remmert,et al.  Theory of Complex Functions , 1990 .

[3]  Hongming Zhou,et al.  Optimization method based extreme learning machine for classification , 2010, Neurocomputing.

[4]  Narasimhan Sundararajan,et al.  A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks , 2006, IEEE Transactions on Neural Networks.

[5]  Narasimhan Sundararajan,et al.  Communication channel equalization using complex-valued minimal radial basis function neural networks , 2002, IEEE Trans. Neural Networks.

[6]  Kazuyuki Murase,et al.  Ensemble of single-layered complex-valued neural networks for classification tasks , 2009, Neurocomputing.

[7]  Tülay Adali,et al.  Fully Complex Multi-Layer Perceptron Network for Nonlinear Signal Processing , 2002, J. VLSI Signal Process..

[8]  Claudio Moraga,et al.  Multilayer Feedforward Neural Network Based on Multi-valued Neurons (MLMVN) and a Backpropagation Learning Algorithm , 2006, Soft Comput..

[9]  N Sundararajan,et al.  Adaptive beamforming using complex-valued Radial Basis Function neural networks , 2009, TENCON 2009 - 2009 IEEE Region 10 Conference.

[10]  Narasimhan Sundararajan,et al.  A sequential multi-category classifier using radial basis function networks , 2008, Neurocomputing.

[11]  Narasimhan Sundararajan,et al.  A self-regulated learning in Fully Complex-valued Radial Basis Function Networks , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[12]  N. Sundararajan,et al.  Complex-valued growing and pruning rbf neural networks for communication channel equalisation , 2006 .

[13]  Sundaram Suresh,et al.  Lift coefficient prediction at high angle of attack using recurrent neural network , 2003 .

[14]  Y Lu,et al.  A Sequential Learning Scheme for Function Approximation Using Minimal Radial Basis Function Neural Networks , 1997, Neural Computation.

[15]  Dustin Boswell,et al.  Introduction to Support Vector Machines , 2002 .

[16]  V. Mani,et al.  Acoustic emmision signal classiefiation using fuzzy C-means clustering - Neural Information Processing, 2002. ICONIP '02. Proceedings of the 9th International Conference o , 2004 .

[17]  K. R. Ramakrishnan,et al.  Parallel Magnetic Resonance Imaging using Neural Networks , 2007, 2007 IEEE International Conference on Image Processing.

[18]  Bernard Mulgrew,et al.  Complex-valued radial basic function network, Part I: Network architecture and learning algorithms , 1994, Signal Process..

[19]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[20]  Narasimhan Sundararajan,et al.  A Sequential Learning Algorithm for Complex-Valued Self-Regulating Resource Allocation Network-CSRAN , 2011, IEEE Transactions on Neural Networks.

[21]  Sheng Chen,et al.  Complex Valued Radial Basis Function Network: Application to Digital Communications Channel Equalisation (part II) , 1994 .

[22]  Narasimhan Sundararajan,et al.  Risk-sensitive loss functions for sparse multi-category classification problems , 2008, Inf. Sci..

[23]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[24]  Tohru Nitta.  On the inherent property of the decision boundary in complex-valued neural networks , 2003, Neurocomputing.

[25]  Kavita Burse,et al.  Channel Equalization Using Neural Networks: A Review , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[26]  F. Ares,et al.  Analysis, synthesis, and diagnostics of antenna arrays through complex-valued neural networks , 2006 .

[27]  R. Venkatesh Babu,et al.  No-reference image quality assessment using modified extreme learning machine classifier , 2009, Appl. Soft Comput..

[28]  Paramasivan Saratchandran,et al.  A new learning algorithm with logarithmic performance index for complex-valued neural networks , 2009, Neurocomputing.

[29]  Jacek M. Zurada,et al.  Blur Identification by Multilayer Neural Network Based on Multivalued Neurons , 2008, IEEE Transactions on Neural Networks.

[30]  Tohru Nitta,et al.  Solving the XOR problem and the detection of symmetry using a single complex-valued neuron , 2003, Neural Networks.

[31]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[32]  H. J. Kim,et al.  A sequential learning algorithm for self-adaptive resource allocation network classifier , 2010, Neurocomputing.

[33]  B. Mulgrew,et al.  Complex-valued radial basis function network, Part II: Application to digital communications channel equalisation , 1994, Signal Process..

[34]  Narasimhan Sundararajan,et al.  An efficient sequential learning algorithm for growing and pruning RBF (GAP-RBF) networks , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[35]  Kazuyuki Murase,et al.  Single-layered complex-valued neural network for real-valued classification problems , 2009, Neurocomputing.

[36]  N. Sundararajan,et al.  A fully complex-valued radial basis function network and its learning algorithm. , 2009 .

[37]  Saleem A. Kassam,et al.  Channel Equalization Using Adaptive Complex Radial Basis Function Networks , 1995, IEEE J. Sel. Areas Commun..