Convergence analysis of online gradient method for BP neural networks

Wu, Wei; Wang, Jian; Cheng, Mingsong; Li, Zhengxue

doi:10.1016/j.neunet.2010.09.007

Cited by 145 publications

(37 citation statements)

References 19 publications

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“…Assumption (A1) means the condition on boundedness of ∥w k ∥, which is often used in the literature (Aizenberg, 2010(Aizenberg, , 2011Gori & Maggini, 1996;Shao & Zheng, 2011;Wu et al, 2005Wu et al, , 2011Xu et al, 2010), and can be removed when adding a penalty term to the error function . Assumption (A2) indicates that complex coefficient polynomials can be used as the activation function, which removes the Schwarz symmetry condition in Adali et al (2008), Leung and Haykin (1991) and Zhang, Liu et al (2014).…”

Section: Convergence Analysismentioning

confidence: 99%

“…Convergence of the real-valued learning algorithm has been widely studied (Shao & Zheng, 2011;Wang, Yang, & Wu, 2011;Wu, Fan, & Zurada, 2014;Wu, Feng, Li, & Xu, 2005;Wu, Wang, Cheng, & Li, 2011). However, in the complex domain, in addition to the conflict between boundedness and analyticity of the activation function, another challenge is that the traditional mean value theorem does not hold in the complex domain (e.g., f (z) = e z with…”

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of an augmented algorithm for fully complex-valued neural networks

Zhang

Mandic

2015

Neural Networks

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Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convergence analysis of an augmented algorithm for fully complex-valued neural networks

Zhang

Mandic

2015

Neural Networks

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“…The traditional BPNN frame [12][13][14] often consists of input layer, hidden layer, and output layer. It sometimes contains more than one hidden layer; the outputs of each layer are sent directly to each neuron of the next layer [15]; it also may contain a bias neuron that produces constant outputs but receives no inputs.…”

Section: Network Framementioning

confidence: 99%

An Evaluation Model for Tailings Storage Facilities Using Improved Neural Networks and Fuzzy Mathematics

Tian

Chen

2014

Journal of Applied Mathematics

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With the development of mine industry, tailings storage facility (TSF), as the important facility of mining, has attracted increasing attention for its safety problems. However, the problems of low accuracy and slow operation rate often occur in current TSF safety evaluation models. This paper establishes a reasonable TSF safety evaluation index system and puts forward a new TSF safety evaluation model by combining the theories for the analytic hierarchy process (AHP) and improved back-propagation (BP) neural network algorithm. The varying proportions of cross validation were calculated, demonstrating that this method has better evaluation performance with higher learning efficiency and faster convergence speed and avoids the oscillation in the training process in traditional BP neural network method and other primary neural network methods. The entire analysis shows the combination of the two methods increases the accuracy and reliability of the safety evaluation, and it can be well applied in the TSF safety evaluation.

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“…Artificial neural network (ANN) is a mathematical model for biomimetic neural network [6][7][8]. It can effectively deal with tangible and intangible information during mode recognition through sample training, in particular dealing with the multilayer feed-forward network (or BP (Back Propagation) neural network [9][10][11][12] through error back propagation training. The multilayer feed-forward network is widely applied in engineering and has provided new solution to facial image recognition featured by massive data, multiple factors and multi-features.…”

Section: Introductionmentioning

confidence: 99%