In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluste...In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.展开更多
By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-...By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.展开更多
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
Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empir...Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.展开更多
Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better properties.Based on Bandler’s fault ...Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better properties.Based on Bandler’s fault location method(1982), a new nonlinearly constrained L1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis L1 problem. The validity of the proposed neural networks and the fault location L1 method are illustrated by extensive computer simulations.展开更多
The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regulariza...The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.展开更多
Radial functions have become a useful tool in numerical mathematics. On the sphere they have to be identified with the zonal functions. We investigate zonal polynomials with mass concentration at the pole, in the sens...Radial functions have become a useful tool in numerical mathematics. On the sphere they have to be identified with the zonal functions. We investigate zonal polynomials with mass concentration at the pole, in the sense of their L1-norm is attaining the minimum value. Such polynomials satisfy a complicated system of nonlinear e-quations (algebraic if the space dimension is odd, only) and also a singular differential equation of third order. The exact order of decay of the minimum value with respect to the polynomial degree is determined. By our results we can prove that some nodal systems on the sphere, which are defined by a minimum-property, are providing fundamental matrices which are diagonal-dominant or bounded with respect to the ∞-norm, at least, as the polynomial degree tends to infinity.展开更多
In this work, we consider a homotopic principle for solving large-scale and dense l1underdetermined problems and its applications in image processing and classification. We solve the face recognition problem where the...In this work, we consider a homotopic principle for solving large-scale and dense l1underdetermined problems and its applications in image processing and classification. We solve the face recognition problem where the input image contains corrupted and/or lost pixels. The approach involves two steps: first, the incomplete or corrupted image is subject to an inpainting process, and secondly, the restored image is used to carry out the classification or recognition task. Addressing these two steps involves solving large scale l1minimization problems. To that end, we propose to solve a sequence of linear equality constrained multiquadric problems that depends on a regularization parameter that converges to zero. The procedure generates a central path that converges to a point on the solution set of the l1underdetermined problem. In order to solve each subproblem, a conjugate gradient algorithm is formulated. When noise is present in the model, inexact directions are taken so that an approximate solution is computed faster. This prevents the ill conditioning produced when the conjugate gradient is required to iterate until a zero residual is attained.展开更多
In the network security system,intrusion detection plays a significant role.The network security system detects the malicious actions in the network and also conforms the availability,integrity and confidentiality of da...In the network security system,intrusion detection plays a significant role.The network security system detects the malicious actions in the network and also conforms the availability,integrity and confidentiality of data informa-tion resources.Intrusion identification system can easily detect the false positive alerts.If large number of false positive alerts are created then it makes intrusion detection system as difficult to differentiate the false positive alerts from genuine attacks.Many research works have been done.The issues in the existing algo-rithms are more memory space and need more time to execute the transactions of records.This paper proposes a novel framework of network security Intrusion Detection System(IDS)using Modified Frequent Pattern(MFP-Tree)via K-means algorithm.The accuracy rate of Modified Frequent Pattern Tree(MFPT)-K means method infinding the various attacks are Normal 94.89%,for DoS based attack 98.34%,for User to Root(U2R)attacks got 96.73%,Remote to Local(R2L)got 95.89%and Probe attack got 92.67%and is optimal when it is compared with other existing algorithms of K-Means and APRIORI.展开更多
Integrated with sensors,processors,and radio frequency(RF)communication modules,intelligent bearing could achieve the autonomous perception and autonomous decision-making,guarantying the safety and reliability during ...Integrated with sensors,processors,and radio frequency(RF)communication modules,intelligent bearing could achieve the autonomous perception and autonomous decision-making,guarantying the safety and reliability during their use.However,because of the resource limitations of the end device,processors in the intelligent bearing are unable to carry the computational load of deep learning models like convolutional neural network(CNN),which involves a great amount of multiplicative operations.To minimize the computation cost of the conventional CNN,based on the idea of AdderNet,a 1-D adder neural network with a wide first-layer kernel(WAddNN)suitable for bearing fault diagnosis is proposed in this paper.The proposed method uses the l1-norm distance between filters and input features as the output response,thus making the whole network almost free of multiplicative operations.The whole model takes the original signal as the input,uses a wide kernel in the first adder layer to extract features and suppress the high frequency noise,and then uses two layers of small kernels for nonlinear mapping.Through experimental comparison with CNN models of the same structure,WAddNN is able to achieve a similar accuracy as CNN models with significantly reduced computational cost.The proposed model provides a new fault diagnosis method for intelligent bearings with limited resources.展开更多
High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurat...High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.展开更多
A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conven...A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.展开更多
The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications...The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications is style transfer.Style transfer is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image.CYCLE-GAN is a classic GAN model,which has a wide range of scenarios in style transfer.Considering its unsupervised learning characteristics,the mapping is easy to be learned between an input image and an output image.However,it is difficult for CYCLE-GAN to converge and generate high-quality images.In order to solve this problem,spectral normalization is introduced into each convolutional kernel of the discriminator.Every convolutional kernel reaches Lipschitz stability constraint with adding spectral normalization and the value of the convolutional kernel is limited to[0,1],which promotes the training process of the proposed model.Besides,we use pretrained model(VGG16)to control the loss of image content in the position of l1 regularization.To avoid overfitting,l1 regularization term and l2 regularization term are both used in the object loss function.In terms of Frechet Inception Distance(FID)score evaluation,our proposed model achieves outstanding performance and preserves more discriminative features.Experimental results show that the proposed model converges faster and achieves better FID scores than the state of the art.展开更多
文摘In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.
基金Supported by the National Natural Science Foundation of China(No:69872039)
文摘By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.
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Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.
基金Supported by Doctoral Special Fund of State Education Commissionthe National Natural Science Foundation of China,Grant No.59477001 and No.59707002
文摘Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better properties.Based on Bandler’s fault location method(1982), a new nonlinearly constrained L1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis L1 problem. The validity of the proposed neural networks and the fault location L1 method are illustrated by extensive computer simulations.
基金Supported by Open Foundation Project of Shenyang Institute of Atmospheric Environment,China Meteorological Administration(2016SYIAE14)Natural Science Foundation of Anhui Province,China(1708085QD89)National Natural Science Foundation of China(41805080)
文摘The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.
文摘Radial functions have become a useful tool in numerical mathematics. On the sphere they have to be identified with the zonal functions. We investigate zonal polynomials with mass concentration at the pole, in the sense of their L1-norm is attaining the minimum value. Such polynomials satisfy a complicated system of nonlinear e-quations (algebraic if the space dimension is odd, only) and also a singular differential equation of third order. The exact order of decay of the minimum value with respect to the polynomial degree is determined. By our results we can prove that some nodal systems on the sphere, which are defined by a minimum-property, are providing fundamental matrices which are diagonal-dominant or bounded with respect to the ∞-norm, at least, as the polynomial degree tends to infinity.
文摘In this work, we consider a homotopic principle for solving large-scale and dense l1underdetermined problems and its applications in image processing and classification. We solve the face recognition problem where the input image contains corrupted and/or lost pixels. The approach involves two steps: first, the incomplete or corrupted image is subject to an inpainting process, and secondly, the restored image is used to carry out the classification or recognition task. Addressing these two steps involves solving large scale l1minimization problems. To that end, we propose to solve a sequence of linear equality constrained multiquadric problems that depends on a regularization parameter that converges to zero. The procedure generates a central path that converges to a point on the solution set of the l1underdetermined problem. In order to solve each subproblem, a conjugate gradient algorithm is formulated. When noise is present in the model, inexact directions are taken so that an approximate solution is computed faster. This prevents the ill conditioning produced when the conjugate gradient is required to iterate until a zero residual is attained.
文摘In the network security system,intrusion detection plays a significant role.The network security system detects the malicious actions in the network and also conforms the availability,integrity and confidentiality of data informa-tion resources.Intrusion identification system can easily detect the false positive alerts.If large number of false positive alerts are created then it makes intrusion detection system as difficult to differentiate the false positive alerts from genuine attacks.Many research works have been done.The issues in the existing algo-rithms are more memory space and need more time to execute the transactions of records.This paper proposes a novel framework of network security Intrusion Detection System(IDS)using Modified Frequent Pattern(MFP-Tree)via K-means algorithm.The accuracy rate of Modified Frequent Pattern Tree(MFPT)-K means method infinding the various attacks are Normal 94.89%,for DoS based attack 98.34%,for User to Root(U2R)attacks got 96.73%,Remote to Local(R2L)got 95.89%and Probe attack got 92.67%and is optimal when it is compared with other existing algorithms of K-Means and APRIORI.
基金support provided by the China National Key Research and Development Program of China under Grant 2019YFB2004300the National Natural Science Foundation of China under Grant 51975065 and 51805051.
文摘Integrated with sensors,processors,and radio frequency(RF)communication modules,intelligent bearing could achieve the autonomous perception and autonomous decision-making,guarantying the safety and reliability during their use.However,because of the resource limitations of the end device,processors in the intelligent bearing are unable to carry the computational load of deep learning models like convolutional neural network(CNN),which involves a great amount of multiplicative operations.To minimize the computation cost of the conventional CNN,based on the idea of AdderNet,a 1-D adder neural network with a wide first-layer kernel(WAddNN)suitable for bearing fault diagnosis is proposed in this paper.The proposed method uses the l1-norm distance between filters and input features as the output response,thus making the whole network almost free of multiplicative operations.The whole model takes the original signal as the input,uses a wide kernel in the first adder layer to extract features and suppress the high frequency noise,and then uses two layers of small kernels for nonlinear mapping.Through experimental comparison with CNN models of the same structure,WAddNN is able to achieve a similar accuracy as CNN models with significantly reduced computational cost.The proposed model provides a new fault diagnosis method for intelligent bearings with limited resources.
基金supported in part by the National Natural Science Foundation of China(61702475,61772493,61902370,62002337)in part by the Natural Science Foundation of Chongqing,China(cstc2019jcyj-msxmX0578,cstc2019jcyjjqX0013)+1 种基金in part by the Chinese Academy of Sciences“Light of West China”Program,in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciencesby Technology Innovation and Application Development Project of Chongqing,China(cstc2019jscx-fxydX0027)。
文摘High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.
文摘A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.
基金This work is supported by the National Natural Science Foundation of China(No.61702226)the 111 Project(B12018)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20170200)the Fundamental Research Funds for the Central Universities(No.JUSRP11854).
文摘The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications is style transfer.Style transfer is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image.CYCLE-GAN is a classic GAN model,which has a wide range of scenarios in style transfer.Considering its unsupervised learning characteristics,the mapping is easy to be learned between an input image and an output image.However,it is difficult for CYCLE-GAN to converge and generate high-quality images.In order to solve this problem,spectral normalization is introduced into each convolutional kernel of the discriminator.Every convolutional kernel reaches Lipschitz stability constraint with adding spectral normalization and the value of the convolutional kernel is limited to[0,1],which promotes the training process of the proposed model.Besides,we use pretrained model(VGG16)to control the loss of image content in the position of l1 regularization.To avoid overfitting,l1 regularization term and l2 regularization term are both used in the object loss function.In terms of Frechet Inception Distance(FID)score evaluation,our proposed model achieves outstanding performance and preserves more discriminative features.Experimental results show that the proposed model converges faster and achieves better FID scores than the state of the art.