Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian ne...Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.展开更多
A κ-regular graph is called panfactorical, or even panfactorical respectively, if for every integer s, 1 ≤ s ≤ κ,there exists an s-factor, or 2[s/2 ]-factor, in this graph. A criterion for checking an γ-regular g...A κ-regular graph is called panfactorical, or even panfactorical respectively, if for every integer s, 1 ≤ s ≤ κ,there exists an s-factor, or 2[s/2 ]-factor, in this graph. A criterion for checking an γ-regular graph to be panfactorical or even panfactorical is established. It is proved that every Cayley graph of odd degree is panfactorical and every Cayley graph of even degree is even panfactorical by using this criterion. For a dihedral group, we prove that every connected Cayley graph on this group is panfactorial.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41374118)the Research Fund for the Higher Education Doctoral Program of China(Grant No.20120162110015)+3 种基金the China Postdoctoral Science Foundation(Grant No.2015M580700)the Hunan Provincial Natural Science Foundation,the China(Grant No.2016JJ3086)the Hunan Provincial Science and Technology Program,China(Grant No.2015JC3067)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B138)
文摘Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
文摘A κ-regular graph is called panfactorical, or even panfactorical respectively, if for every integer s, 1 ≤ s ≤ κ,there exists an s-factor, or 2[s/2 ]-factor, in this graph. A criterion for checking an γ-regular graph to be panfactorical or even panfactorical is established. It is proved that every Cayley graph of odd degree is panfactorical and every Cayley graph of even degree is even panfactorical by using this criterion. For a dihedral group, we prove that every connected Cayley graph on this group is panfactorial.
