Figure 1.
Internal structure of the convolutional neural networks
-
Previous Article
Stock price fluctuation prediction method based on time series analysis
- DCDS-S Home
- This Issue
-
Next Article
Wireless sensor network energy efficient coverage method based on intelligent optimization algorithm
August & September
2019, 12(4&5): 901-914.
doi: 10.3934/dcdss.2019060
An efficient face recognition algorithm using the improved convolutional neural network
Qingdao Vocational and Technical College of Hotel Management, Qingdao 266100, China |
This paper concentrates on the problem of human face recognition problem, which is a crucial problem in computer vision. In this paper, the semi-supervised learning based convolutional neural network is used to implement the face recognition system with high efficiency. Convolutional neural networks denote a multi-layer neural network, in which each layer is made up of multiple two-dimension planes and each plane consists of a lot of independent neurons. To extract the rich and discriminative information of human face images, the sparse Laplacian filter learning is utilized to learn the filters of the network with a large scale unlabeled human face images. Afterwards, a softmax classifier layer is trained by multi-task learning using only a small number of labeled human face images as the output layer. In the end, a series of experiments are conducted to test the performance of our proposed algorithm. Experimental results show that face recognition accuracy of the proposed improved CNN method performs better than other methods.
Keywords:
Face recognition,
convolutional neural network,
semi-supervised learning,
softmax classifier,
sparse Laplacian filter.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
Honggang Yu. An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S,
2019, 12
(4&5)
: 901-914.
doi: 10.3934/dcdss.2019060
![]()
References:
| [1] |
O. Abdel-Hamid, A.-R. Mohamed, H. Jiang, L. Deng, G. Penn and D. Yu, Convolutional neural networks for speech recognition, IEEE-ACM Transactions on Audio Speech and Language Processing, 22 (2014), 1533-1545. Google Scholar |
| [2] |
R. T. G. Alexander, B. E. Schwenker and S. Marinai, Object detection and feature base learning with sparse convolutional neural networks, Artificial Neural Networks in Pattern Recognition, Proceedings, 4087 (2006), 221-232. Google Scholar |
| [3] |
A. Amal, L. S. Lebai, V. Ibrahim and F.-Ma. Fernando, Towards a robust affect recognition: Automatic facial expression recognition in 3D faces, Expert Systems With Applications, 42 (2015), 3056-3066. Google Scholar |
| [4] |
S. Bashbaghi, E. Granger, R. Sabourin and G. A. Bilodeau, Dynamic ensembles of exemplar-SVMs for still-to-video face recognition, Pattern Recognition, 69 (2017), 61-81. Google Scholar |
| [5] |
P. N. Belhumeur, J. P. Hespanha and D. Kriegman, Eigenfaces vs. fisherfaces: Recognition using class specific linear projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19 (1997), 711-720. Google Scholar |
| [6] |
D. Cai, X. He and J. Han, Semi-supervised discriminant analysis, IEEE 11th International Conference on Computer Vision, 2007, 1–7. Google Scholar |
| [7] |
F. L. Cao, X. S. Feng and J. W. Zhao, Sparse representation for robust face recognition by dictionary decomposition, Journal of Visual Communication and Image Representation, 46 (2017), 260-268. Google Scholar |
| [8] |
C. Cernazanu-Glavan and S. Holban, Segmentation of bone structure in x-ray images using convolutional neural network, Advances In Electrical And Computer Engineering, 13 (2013), 87-94. Google Scholar |
| [9] |
X. Chen, S. Xiang, C.-L. Liu and C.-H. Pan, Vehicle detection in satellite images by hybrid deep convolutional neural networks, IEEE Geoscience and Remote Sensing Letters, 11 (2014), 1797-1801. Google Scholar |
| [10] |
M. De-la-Torre, E. Granger, V. W. Radtke Paulo, R. Sabourin and O. Gorodnichy Dmitry, Partially-supervised learning from facial trajectories for face recognition in video surveillance, Information Fusion, 24 (2015), 31-53. Google Scholar |
| [11] |
S. Elaiwat, M. Bennamoun, F. Boussaid and A. El-Sallam, A Curve let-based approach for textured 3D face recognition, Pattern Recognition, 48 (2015), 1235-1246. Google Scholar |
| [12] |
C. Fang, Z. Y. Zhao, P. Zhou and Z. C. Lin, Feature learning via partial differential equation with applications to face recognition, Pattern Recognition, 69 (2017), 14-25. Google Scholar |
| [13] |
X. He, S. Yan, Y. Hu, P. Niyogi and H.-J. Zhang, Face recognition using Laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (), 328-340. Google Scholar |
| [14] |
N. Hoangvu, W. Yang, F. Shen and C. Sun, Kernel Low-Rank Representation for face recognition, Neurocomputing, 155 (2015), 32-42. Google Scholar |
| [15] |
T. Hong-Phuc and M. Duranton, Paindavoine Michel, Efficient Data Encoding for Convolutional Neural Network application, ACM Transactions on Architecture and Code Optimization, 11 (2014), Article No. 49. Google Scholar |
| [16] |
W. Hwang, X. Huang, S. Z. Li and K. Junmo, Face recognition using Extended Curvature Gabor classifier bunch, Pattern Recognition, 48 (2015), 1247-1260. Google Scholar |
| [17] |
W. L. Huang and H. J. Yin, Robust face recognition with structural binary gradient patterns, Pattern Recognition, 68 (2017), 126-140. Google Scholar |
| [18] |
S. Ji, W. Xu, M. Yang and K. Yu, 3D convolutional neural networks for human action recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 221-231. Google Scholar |
| [19] |
J. Jin, K. Fu and C. Zhang, Traffic sign recognition with hinge loss trained convolutional neural networks, IEEE Transactions on Intelligent Transportation Systems, 15 (2014), 1991-2000. Google Scholar |
| [20] |
F. Johannes, M. Karlheinz and S. Johannes, A convolutional neural network tolerant of synaptic faults for low-power analog hardware, Artificial Neural Networks in Pattern Recognition, Proceedings, 4087 (2006), 122-132. Google Scholar |
| [21] |
I.-J. Kim and X. Xie, Handwritten Hangul recognition using deep convolutional neural networks, International Journal on Document Analysis and Recognition, 18 (2015), 1-13. Google Scholar |
| [22] |
T. Larrain, J. S. Bernhard, D. Mery and K. W. Bowyer, Face recognition using sparse fingerprint classification algorithm, Ieee Transactions on Information Forensics and Security, 12 (2017), 1646-1657. Google Scholar |
| [23] |
A. Levinskis, Convolutional neural network feature reduction using wavelet transform, Electronics & Electrical Engineering, 19 (2013), p61. Google Scholar |
| [24] |
L. Li, M. Wang, X. Ding, J. Lian and Y. Zong, Convolutional neural network applied to traversability analysis of vehicles, Advances in Mechanical Engineering, 2013, Article No. 542832. Google Scholar |
| [25] |
Y. Lu, N. Zeng, Y. Liu and N. Zhang, A hybrid wavelet neural network and switching particle swarm optimization algorithm for face direction recognition, Neurocomputing, 155 (2015), 219-224. Google Scholar |
| [26] |
Q. Mao, M. Dong, Z. Huang and Y. Zhan, Learning salient features for speech emotion recognition using convolutional neural networks, IEEE Transactions On Multimedia, 16 (2014), 2203-2213. Google Scholar |
| [27] |
S. Rajbhandari, Z. Ghassemlooy and M. Angelova, Adaptive soft' sliding block decoding of convolutional code using the artificial neural network, Transactions on Emerging Telecommunications Technologies, 23 (2012), 672-677. Google Scholar |
| [28] |
T. N. Sainath, B. Kingsbury, G. Saon, H. Soltau, A.-R. Mohamed, G. Dahl and B. Ramabhadran, Deep convolutional neural networks for large-scale speech tasks, Neural Networks, 64 (2015), 39-48. Google Scholar |
| [29] |
J. Shi and C. Qi, From local geometry to global structure: Learning latent subspace for low-resolution face image recognition, IEEE Signal Processing Letters, 22 (2015), 554-558. Google Scholar |
| [30] |
P. Swietojanski, A. Ghoshal and S. Renals, Convolutional neural networks for distant speech recognition, IEEE Signal Processing Letters, 21 (2014), 1120-1124. Google Scholar |
| [31] |
F. H. C. Tivive, A. Bouzerdoum, I. Be King, J. Wang, L. Chan and D. L. Wang, Rotation invariant face detection using convolutional neural networks, Neural Information Processing, PT 2, Proceedings, 4233 (2006), 260-269. Google Scholar |
| [32] |
F. H. C. Tivive and A. Bouzerdoum, Efficient training algorithms for a class of shunting inhibitory convolutional neural networks, IEEE Transactions on Neural Networks, 16 (2005), 541-556. Google Scholar |
| [33] |
U. C. Turhal and A. Duysak, Cross grouping strategy based 2DPCA method for face recognition, Applied Soft Computing, 29 (2015), 270-279. Google Scholar |
| [34] |
M. Turk and A. Pentland, Eigenfaces for recognition, Journal of Cognitive Neuroscience, 3 (1991), 71-86. Google Scholar |
| [35] |
S. N. Zeng, J. P. Gou and L. M. Deng, An antinoise sparse representation method for robust face recognition via joint l(1) and l(2) regularization, Expert Systems with Applications, 82 (2017), 1-9. Google Scholar |
| [36] |
W. Zhang, R. Li, H. Deng, L. Wang, W. Lin, S. Ji and D. Shen, Deep convolutional neural networks for multi-modality isointense infant brain image segmentation, Neuroimage, 108 (2015), 214-224. Google Scholar |
| [37] |
X. Zhao, N. Evans and J. Dugelay, Semi-supervised face recognition with LDA self-training, 18th IEEE International Conference on Image Processing (ICIP), 2011, 3041–3044. Google Scholar |
show all references
References:
| [1] |
O. Abdel-Hamid, A.-R. Mohamed, H. Jiang, L. Deng, G. Penn and D. Yu, Convolutional neural networks for speech recognition, IEEE-ACM Transactions on Audio Speech and Language Processing, 22 (2014), 1533-1545. Google Scholar |
| [2] |
R. T. G. Alexander, B. E. Schwenker and S. Marinai, Object detection and feature base learning with sparse convolutional neural networks, Artificial Neural Networks in Pattern Recognition, Proceedings, 4087 (2006), 221-232. Google Scholar |
| [3] |
A. Amal, L. S. Lebai, V. Ibrahim and F.-Ma. Fernando, Towards a robust affect recognition: Automatic facial expression recognition in 3D faces, Expert Systems With Applications, 42 (2015), 3056-3066. Google Scholar |
| [4] |
S. Bashbaghi, E. Granger, R. Sabourin and G. A. Bilodeau, Dynamic ensembles of exemplar-SVMs for still-to-video face recognition, Pattern Recognition, 69 (2017), 61-81. Google Scholar |
| [5] |
P. N. Belhumeur, J. P. Hespanha and D. Kriegman, Eigenfaces vs. fisherfaces: Recognition using class specific linear projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19 (1997), 711-720. Google Scholar |
| [6] |
D. Cai, X. He and J. Han, Semi-supervised discriminant analysis, IEEE 11th International Conference on Computer Vision, 2007, 1–7. Google Scholar |
| [7] |
F. L. Cao, X. S. Feng and J. W. Zhao, Sparse representation for robust face recognition by dictionary decomposition, Journal of Visual Communication and Image Representation, 46 (2017), 260-268. Google Scholar |
| [8] |
C. Cernazanu-Glavan and S. Holban, Segmentation of bone structure in x-ray images using convolutional neural network, Advances In Electrical And Computer Engineering, 13 (2013), 87-94. Google Scholar |
| [9] |
X. Chen, S. Xiang, C.-L. Liu and C.-H. Pan, Vehicle detection in satellite images by hybrid deep convolutional neural networks, IEEE Geoscience and Remote Sensing Letters, 11 (2014), 1797-1801. Google Scholar |
| [10] |
M. De-la-Torre, E. Granger, V. W. Radtke Paulo, R. Sabourin and O. Gorodnichy Dmitry, Partially-supervised learning from facial trajectories for face recognition in video surveillance, Information Fusion, 24 (2015), 31-53. Google Scholar |
| [11] |
S. Elaiwat, M. Bennamoun, F. Boussaid and A. El-Sallam, A Curve let-based approach for textured 3D face recognition, Pattern Recognition, 48 (2015), 1235-1246. Google Scholar |
| [12] |
C. Fang, Z. Y. Zhao, P. Zhou and Z. C. Lin, Feature learning via partial differential equation with applications to face recognition, Pattern Recognition, 69 (2017), 14-25. Google Scholar |
| [13] |
X. He, S. Yan, Y. Hu, P. Niyogi and H.-J. Zhang, Face recognition using Laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (), 328-340. Google Scholar |
| [14] |
N. Hoangvu, W. Yang, F. Shen and C. Sun, Kernel Low-Rank Representation for face recognition, Neurocomputing, 155 (2015), 32-42. Google Scholar |
| [15] |
T. Hong-Phuc and M. Duranton, Paindavoine Michel, Efficient Data Encoding for Convolutional Neural Network application, ACM Transactions on Architecture and Code Optimization, 11 (2014), Article No. 49. Google Scholar |
| [16] |
W. Hwang, X. Huang, S. Z. Li and K. Junmo, Face recognition using Extended Curvature Gabor classifier bunch, Pattern Recognition, 48 (2015), 1247-1260. Google Scholar |
| [17] |
W. L. Huang and H. J. Yin, Robust face recognition with structural binary gradient patterns, Pattern Recognition, 68 (2017), 126-140. Google Scholar |
| [18] |
S. Ji, W. Xu, M. Yang and K. Yu, 3D convolutional neural networks for human action recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 221-231. Google Scholar |
| [19] |
J. Jin, K. Fu and C. Zhang, Traffic sign recognition with hinge loss trained convolutional neural networks, IEEE Transactions on Intelligent Transportation Systems, 15 (2014), 1991-2000. Google Scholar |
| [20] |
F. Johannes, M. Karlheinz and S. Johannes, A convolutional neural network tolerant of synaptic faults for low-power analog hardware, Artificial Neural Networks in Pattern Recognition, Proceedings, 4087 (2006), 122-132. Google Scholar |
| [21] |
I.-J. Kim and X. Xie, Handwritten Hangul recognition using deep convolutional neural networks, International Journal on Document Analysis and Recognition, 18 (2015), 1-13. Google Scholar |
| [22] |
T. Larrain, J. S. Bernhard, D. Mery and K. W. Bowyer, Face recognition using sparse fingerprint classification algorithm, Ieee Transactions on Information Forensics and Security, 12 (2017), 1646-1657. Google Scholar |
| [23] |
A. Levinskis, Convolutional neural network feature reduction using wavelet transform, Electronics & Electrical Engineering, 19 (2013), p61. Google Scholar |
| [24] |
L. Li, M. Wang, X. Ding, J. Lian and Y. Zong, Convolutional neural network applied to traversability analysis of vehicles, Advances in Mechanical Engineering, 2013, Article No. 542832. Google Scholar |
| [25] |
Y. Lu, N. Zeng, Y. Liu and N. Zhang, A hybrid wavelet neural network and switching particle swarm optimization algorithm for face direction recognition, Neurocomputing, 155 (2015), 219-224. Google Scholar |
| [26] |
Q. Mao, M. Dong, Z. Huang and Y. Zhan, Learning salient features for speech emotion recognition using convolutional neural networks, IEEE Transactions On Multimedia, 16 (2014), 2203-2213. Google Scholar |
| [27] |
S. Rajbhandari, Z. Ghassemlooy and M. Angelova, Adaptive soft' sliding block decoding of convolutional code using the artificial neural network, Transactions on Emerging Telecommunications Technologies, 23 (2012), 672-677. Google Scholar |
| [28] |
T. N. Sainath, B. Kingsbury, G. Saon, H. Soltau, A.-R. Mohamed, G. Dahl and B. Ramabhadran, Deep convolutional neural networks for large-scale speech tasks, Neural Networks, 64 (2015), 39-48. Google Scholar |
| [29] |
J. Shi and C. Qi, From local geometry to global structure: Learning latent subspace for low-resolution face image recognition, IEEE Signal Processing Letters, 22 (2015), 554-558. Google Scholar |
| [30] |
P. Swietojanski, A. Ghoshal and S. Renals, Convolutional neural networks for distant speech recognition, IEEE Signal Processing Letters, 21 (2014), 1120-1124. Google Scholar |
| [31] |
F. H. C. Tivive, A. Bouzerdoum, I. Be King, J. Wang, L. Chan and D. L. Wang, Rotation invariant face detection using convolutional neural networks, Neural Information Processing, PT 2, Proceedings, 4233 (2006), 260-269. Google Scholar |
| [32] |
F. H. C. Tivive and A. Bouzerdoum, Efficient training algorithms for a class of shunting inhibitory convolutional neural networks, IEEE Transactions on Neural Networks, 16 (2005), 541-556. Google Scholar |
| [33] |
U. C. Turhal and A. Duysak, Cross grouping strategy based 2DPCA method for face recognition, Applied Soft Computing, 29 (2015), 270-279. Google Scholar |
| [34] |
M. Turk and A. Pentland, Eigenfaces for recognition, Journal of Cognitive Neuroscience, 3 (1991), 71-86. Google Scholar |
| [35] |
S. N. Zeng, J. P. Gou and L. M. Deng, An antinoise sparse representation method for robust face recognition via joint l(1) and l(2) regularization, Expert Systems with Applications, 82 (2017), 1-9. Google Scholar |
| [36] |
W. Zhang, R. Li, H. Deng, L. Wang, W. Lin, S. Ji and D. Shen, Deep convolutional neural networks for multi-modality isointense infant brain image segmentation, Neuroimage, 108 (2015), 214-224. Google Scholar |
| [37] |
X. Zhao, N. Evans and J. Dugelay, Semi-supervised face recognition with LDA self-training, 18th IEEE International Conference on Image Processing (ICIP), 2011, 3041–3044. Google Scholar |
Figure 2.
Flowchart of the proposed CNN based human face recognition system
Figure 3.
Rate of face recognition on the test dataset of ORL database
Figure 4.
Rate of face recognition on the unlabeled training dataset of ORL database
Figure 5.
Rate of face recognition on the test dataset of Yale database
Figure 6.
Rate of face recognition on the unlabeled training dataset of Yale database
Figure 7.
Rate of face recognition on the test dataset of Extended Yale B database
Figure 8.
Rate of face recognition on the unlabeled training dataset of Extended Yale B database
Figure 9.
Average face recognition accuracy for different methods
Table 1.
Description of the CNN baseline model
| Name | Description |
| Input layer | |
| Convolution 1 | |
| Convolution 2 | |
| Convolution 3 | |
| Pooling 1 | |
| Pooling 2 | |
| Fully connected 1 | HalfRect Units with 64 output neurons |
| Fully connected 2 | 10 output neurons |
| Name | Description |
| Input layer | |
| Convolution 1 | |
| Convolution 2 | |
| Convolution 3 | |
| Pooling 1 | |
| Pooling 2 | |
| Fully connected 1 | HalfRect Units with 64 output neurons |
| Fully connected 2 | 10 output neurons |
Table 2.
The face recognition accuracy using the CMU PIE database (mean $\pm$ std.dev%)
| Approach | Unlabeled set | Test set |
| Fisherface | 21.8 |
21.8 |
| Laplacianface | 35.9 |
34.8 |
| SDA | 41.8 |
43.8 |
| LDA self-training | 48.9 |
50.3 |
| CNN | 36.8 |
38.7 |
| The improved CNN | 91.8 |
92.1 |
| Approach | Unlabeled set | Test set |
| Fisherface | 21.8 |
21.8 |
| Laplacianface | 35.9 |
34.8 |
| SDA | 41.8 |
43.8 |
| LDA self-training | 48.9 |
50.3 |
| CNN | 36.8 |
38.7 |
| The improved CNN | 91.8 |
92.1 |
| [1] |
Liming Yang, Yannan Chao. A new semi-supervised classifier based on maximum vector-angular margin. Journal of Industrial & Management Optimization, 2017, 13 (2) : 609-622. doi: 10.3934/jimo.2016035 |
| [2] |
Shuhua Xu, Fei Gao. Weighted two-phase supervised sparse representation based on Gaussian for face recognition. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1385-1400. doi: 10.3934/dcdss.2015.8.1385 |
| [3] |
Zhuwei Qin, Fuxun Yu, Chenchen Liu, Xiang Chen. How convolutional neural networks see the world --- A survey of convolutional neural network visualization methods. Mathematical Foundations of Computing, 2018, 1 (2) : 149-180. doi: 10.3934/mfc.2018008 |
| [4] |
Ning Zhang, Qiang Wu. Online learning for supervised dimension reduction. Mathematical Foundations of Computing, 2019, 2 (2) : 95-106. doi: 10.3934/mfc.2019008 |
| [5] |
Huining Qiu, Xiaoming Chen, Wanquan Liu, Guanglu Zhou, Yiju Wang, Jianhuang Lai. A fast $\ell_1$-solver and its applications to robust face recognition. Journal of Industrial & Management Optimization, 2012, 8 (1) : 163-178. doi: 10.3934/jimo.2012.8.163 |
| [6] |
Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891 |
| [7] |
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655 |
| [8] |
Weiping Li, Haiyan Wu, Jie Yang. Intelligent recognition algorithm for social network sensitive information based on classification technology. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1385-1398. doi: 10.3934/dcdss.2019095 |
| [9] |
Cai-Tong Yue, Jing Liang, Bo-Fei Lang, Bo-Yang Qu. Two-hidden-layer extreme learning machine based wrist vein recognition system. Big Data & Information Analytics, 2017, 2 (1) : 59-68. doi: 10.3934/bdia.2017008 |
| [10] |
Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420 |
| [11] |
King Hann Lim, Hong Hui Tan, Hendra G. Harno. Approximate greatest descent in neural network optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 327-336. doi: 10.3934/naco.2018021 |
| [12] |
Shyan-Shiou Chen, Chih-Wen Shih. Asymptotic behaviors in a transiently chaotic neural network. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 805-826. doi: 10.3934/dcds.2004.10.805 |
| [13] |
Ndolane Sene. Fractional input stability and its application to neural network. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 853-865. doi: 10.3934/dcdss.2020049 |
| [14] |
Sangye Lungten, Wil H. A. Schilders, Joseph M. L. Maubach. Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 227-239. doi: 10.3934/naco.2014.4.227 |
| [15] |
Simone Göttlich, Stephan Knapp. Semi-Markovian capacities in production network models. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3235-3258. doi: 10.3934/dcdsb.2017090 |
| [16] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
| [17] |
Hui-Qiang Ma, Nan-Jing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 645-660. doi: 10.3934/jimo.2015.11.645 |
| [18] |
Yixin Guo, Aijun Zhang. Existence and nonexistence of traveling pulses in a lateral inhibition neural network. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1729-1755. doi: 10.3934/dcdsb.2016020 |
| [19] |
Jianhong Wu, Ruyuan Zhang. A simple delayed neural network with large capacity for associative memory. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 851-863. doi: 10.3934/dcdsb.2004.4.851 |
| [20] |
Sanjay K. Mazumdar, Cheng-Chew Lim. A neural network based anti-skid brake system. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 321-338. doi: 10.3934/dcds.1999.5.321 |
2018 Impact Factor: 0.545
Tools
Metrics
Other articles
by authors
[Back to Top]