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186 results on '"Fan, Hongtao"'

40. An artificial neural network approach for a class of time-fractional diffusion and diffusion-wave equations.

Author

Ye, Yinlin, Fan, Hongtao, Li, Yajing, Huang, Ao, and He, Weiheng

Subjects
HEAT equation, ERROR functions
Abstract

In this paper, the artificial neural network method is applied to solve the time-fractional diffusion and diffusion-wave equations. This method combines Taylor series and neural network method, and uses the terms of different power terms of Taylor series as neurons. An error function is given to update the weights of the proposed neural network. In addition, in order to balance the contributions of different error terms in the error function, we propose an adaptive weight adjustment method. In the end, four numerical examples are given to demonstrate the effectiveness of proposed method in solving the time-fractional diffusion and diffusion-wave equations. [ABSTRACT FROM AUTHOR]

Published
2023
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45. Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function

Author

Zhang, Hongbing, Liu, Xinyi, Liu, Chang, Fan, Hongtao, Li, Yajing, and Zhu, Xinyun

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Image and Video Processing (eess.IV), FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Computer Vision and Pattern Recognition, Electrical Engineering and Systems Science - Image and Video Processing, Machine Learning (cs.LG)
Abstract

Non-convex relaxation methods have been widely used in tensor recovery problems, and compared with convex relaxation methods, can achieve better recovery results. In this paper, a new non-convex function, Minimax Logarithmic Concave Penalty (MLCP) function, is proposed, and some of its intrinsic properties are analyzed, among which it is interesting to find that the Logarithmic function is an upper bound of the MLCP function. The proposed function is generalized to tensor cases, yielding tensor MLCP and weighted tensor $L\gamma$-norm. Consider that its explicit solution cannot be obtained when applying it directly to the tensor recovery problem. Therefore, the corresponding equivalence theorems to solve such problem are given, namely, tensor equivalent MLCP theorem and equivalent weighted tensor $L\gamma$-norm theorem. In addition, we propose two EMLCP-based models for classic tensor recovery problems, namely low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA), and design proximal alternate linearization minimization (PALM) algorithms to solve them individually. Furthermore, based on the Kurdyka-{\L}ojasiwicz property, it is proved that the solution sequence of the proposed algorithm has finite length and converges to the critical point globally. Finally, Extensive experiments show that proposed algorithm achieve good results, and it is confirmed that the MLCP function is indeed better than the Logarithmic function in the minimization problem, which is consistent with the analysis of theoretical properties., Comment: arXiv admin note: substantial text overlap with arXiv:2201.12709, arXiv:2109.12257

Published
2022

46. Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penalty

Author

Zhang, Hongbing, Liu, Xinyi, Fan, Hongtao, Li, Yajing, and Ye, Yinlin

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Machine Learning (cs.LG)
Abstract

Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the constant parameters of the MCP function as variables so that futherly improving the adaptability to the change of singular values in the LRTC problem, we propose the bivariate equivalent minimax-concave penalty (BEMCP) theorem. Applying the BEMCP theorem to tensor singular values leads to the bivariate equivalent weighted tensor $\Gamma$-norm (BEWTGN) theorem, and we analyze and discuss its corresponding properties. Besides, to facilitate the solution of the LRTC problem, we give the proximal operators of the BEMCP theorem and BEWTGN. Meanwhile, we propose a BEMCP model for the LRTC problem, which is optimally solved based on alternating direction multiplier (ADMM). Finally, the proposed method is applied to the data restorations of multispectral image (MSI), magnetic resonance imaging (MRI) and color video (CV) in real-world, and the experimental results demonstrate that it outperforms the state-of-arts methods., Comment: arXiv admin note: text overlap with arXiv:2109.12257

Published
2022

47. SLeNN-ELM: A shifted Legendre neural network method for fractional delay differential equations based on extreme learning machine.

Author

Ye, Yinlin, Li, Yajing, Fan, Hongtao, Liu, Xinyi, and Zhang, Hongbing

Subjects
FRACTIONAL differential equations, MACHINE learning, CAPUTO fractional derivatives, DELAY differential equations
Abstract

In this paper, we introduce a shifted Legendre neural network method based on an extreme learning machine algorithm (SLeNN-ELM) to solve fractional differential equations with constant and proportional delays. Based on the properties of Caputo fractional derivatives and shifted Legendre polynomials, the fractional derivatives of SLeNN can be represented analytically without other numerical techniques. SLeNN, in terms of neural network architecture, uses a function expansion block to replace the hidden layer, and thus improving the computational efficiency by reducing parameters. In terms of solving technology of neural networks, the extreme learning machine algorithm is used to replace the traditional gradient-based training algorithm. It dramatically improves our solution efficiency. In addition, the proposed method does not require parameter initialization randomly, making the neural network solution stable. Finally, three examples with constant delays and three examples with proportional delays are given, and the effectiveness and superiority of the proposed method are verified by comparison with other numerical methods. [ABSTRACT FROM AUTHOR]

Published
2023
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50. Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery

Author

Zhang, Hongbing, Liu, Xinyi, Fan, Hongtao, Li, Yajing, and Ye, Yinlin

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Machine Learning (cs.LG)
Abstract

Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to represent the data containing the internal structure of multiple factors came into being. However, different from the matrix case, constructing reasonable sparse measure of tensor is a relatively difficult and very important task. Therefore, in this paper, we propose a new tensor sparsity measure called Tensor Full Feature Measure (FFM). It can simultaneously describe the feature information of each dimension of the tensor and the related features between two dimensions, and connect the Tucker rank with the tensor tube rank. This measurement method can describe the sparse features of the tensor more comprehensively. On this basis, we establish its non-convex relaxation, and apply FFM to low rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). LRTC and TRPCA models based on FFM are proposed, and two efficient Alternating Direction Multiplier Method (ADMM) algorithms are developed to solve the proposed model. A variety of real numerical experiments substantiate the superiority of the proposed methods beyond state-of-the-arts., 13 pages, 6 figures, 5 tables

Published
2021

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