In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come...In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.展开更多
L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must ...L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must receive different colors. We focus on L(d, 1)-labeling of regular tilings for d≥3 since the cases d=0, 1 or 2 have been researched by Calamoneri and Petreschi. For all three kinds of regular tilings, we give their L (d, 1)-labeling numbers for any integer d≥3. Therefore, combined with the results given by Calamoneri and Petreschi, the L(d, 1)-labeling numbers of regular tilings for any nonnegative integer d may be determined completely.展开更多
Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground refl...Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.展开更多
Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix,...Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l_(2,1)-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cutting-edge algorithms across seven datasets corrupted with four types of noise.展开更多
基金This work was supported in part by the National Natural Science Foundation of China under Grant 61673295the Natural Science Foundation of Tianjin under Grant 18JCYBJC85200by the National College Students’ innovation and entrepreneurship project under Grant 201710060041.
文摘In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.
文摘L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must receive different colors. We focus on L(d, 1)-labeling of regular tilings for d≥3 since the cases d=0, 1 or 2 have been researched by Calamoneri and Petreschi. For all three kinds of regular tilings, we give their L (d, 1)-labeling numbers for any integer d≥3. Therefore, combined with the results given by Calamoneri and Petreschi, the L(d, 1)-labeling numbers of regular tilings for any nonnegative integer d may be determined completely.
基金supported by the National Natural Science Foundation of China(No.41422403)
文摘Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.
基金supported by the National Natural Science Foundation of China(No.62003281)the Natural Science Foundation of Chongqing,China(No.cstc2021jcyjmsxmX1169)the Science and Technology Research Program of Chongqing Municipal Education Commission(No.KJQN202200207).
文摘Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l_(2,1)-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cutting-edge algorithms across seven datasets corrupted with four types of noise.
