U sing Singular Regions and Search Pruning

[1]  Héctor J. Sussmann,et al.  Uniqueness of the weights for minimal feedforward nets with a given input-output map , 1992, Neural Networks.

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

[3]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[4]  Tohru Nitta,et al.  Reducibility of the Complex-valued Neural Network , 2004 .

[5]  Ryohei Nakano,et al.  Fast and Stable Learning Utilizing Singular Regions of Multilayer Perceptron , 2013, Neural Processing Letters.

[6]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[7]  Akira Hirose,et al.  Complex-Valued Neural Networks , 2006, Studies in Computational Intelligence.

[8]  Henry Leung,et al.  The complex backpropagation algorithm , 1991, IEEE Trans. Signal Process..

[9]  Tohru Nitta,et al.  Local minima in hierarchical structures of complex-valued neural networks , 2013, Neural Networks.

[10]  Clark C. Guest,et al.  Modification of backpropagation networks for complex-valued signal processing in frequency domain , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[11]  Kazuyuki Murase,et al.  Wirtinger Calculus Based Gradient Descent and Levenberg-Marquardt Learning Algorithms in Complex-Valued Neural Networks , 2011, ICONIP.

[12]  Ryohei Nakano,et al.  Learning Method Utilizing Singular Region of Multilayer Perceptron , 2011, IJCCI.

[13]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

[14]  Kenji Fukumizu,et al.  Local minima and plateaus in hierarchical structures of multilayer perceptrons , 2000, Neural Networks.