Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support...Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.展开更多
The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used t...The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.展开更多
Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a...Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a SVM with spline kernel function. With the help of this model, nonlinear model predictive control can be transformed to linear model predictive control, and consequently a unified analytical solution of optimal input of multi-step-ahead predictive control is possible to derive. This algorithm does not require online iterative optimization in order to be suitable for real-time control with less calculation. The simulation results of pH neutralization process and CSTR reactor show the effectiveness and advantages of the presented algorithm.展开更多
The development of forecasting models for pollution particles shows a nonlinear dynamic behavior;hence, implementation is a non-trivial process. In the literature, there have been multiple models of particulate pollut...The development of forecasting models for pollution particles shows a nonlinear dynamic behavior;hence, implementation is a non-trivial process. In the literature, there have been multiple models of particulate pollutants, which use softcomputing techniques and machine learning such as: multilayer perceptrons, neural networks, support vector machines, kernel algorithms, and so on. This paper presents a prediction pollution model using support vector machines and kernel functions, which are: Gaussian, Polynomial and Spline. Finally, the prediction results of ozone (O3), particulate matter (PM10) and nitrogen dioxide (NO2) at Mexico City are presented as a case study using these techniques.展开更多
An admissible manifold wavelet kernel is proposed to construct manifold wavelet support vector machine(MWSVM) for stock returns forecasting.The manifold wavelet kernel is obtained by incorporating manifold theory into...An admissible manifold wavelet kernel is proposed to construct manifold wavelet support vector machine(MWSVM) for stock returns forecasting.The manifold wavelet kernel is obtained by incorporating manifold theory into wavelet technique in support vector machine(SVM).Since manifold wavelet function can yield features that describe of the stock time series both at various locations and at varying time granularities,the MWSVM can approximate arbitrary nonlinear functions and forecast stock returns accurately.The applicability and validity of MWSVM for stock returns forecasting is confirmed through experiments on real-world stock data.展开更多
With the progress of deep learning research, convolutional neural networks have become the most important method in feature extraction. How to effectively classify and recognize the extracted features will directly af...With the progress of deep learning research, convolutional neural networks have become the most important method in feature extraction. How to effectively classify and recognize the extracted features will directly affect the performance of the entire network. Traditional processing methods include classification models such as fully connected network models and support vector machines. In order to solve the problem that the traditional convolutional neural network is prone to over-fitting for the classification of small samples, a CNN-TWSVM hybrid model was proposed by fusing the twin support vector machine (TWSVM) with higher computational efficiency as the CNN classifier, and it was applied to the traffic sign recognition task. In order to improve the generalization ability of the model, the wavelet kernel function is introduced to deal with the nonlinear classification task. The method uses the network initialized from the ImageNet dataset to fine-tune the specific domain and intercept the inner layer of the network to extract the high abstract features of the traffic sign image. Finally, the TWSVM based on wavelet kernel function is used to identify the traffic signs, so as to effectively solve the over-fitting problem of traffic signs classification. On GTSRB and BELGIUMTS datasets, the validity and generalization ability of the improved model is verified by comparing with different kernel functions and different SVM classifiers.展开更多
A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established...A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.展开更多
A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant i...A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.展开更多
Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlin...Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlinear system, the system model is built by using LS-SVM with linear kernel function, and then the obtained linear LS-SVM model is transformed into linear input-output relation of the controlled system. However, for the strongly nonlinear system, the off-line model of the controlled system is built by using LS-SVM with Radial Basis Function (RBF) kernel. The obtained nonlinear LS-SVM model is linearized at each sampling instant of system running, after which the on-line linear input-output model of the system is built. Based on the obtained linear input-output model, the Generalized Predictive Control (GPC) algorithm is employed to implement predictive control for the controlled plant in both algorithms. The simulation results after the presented algorithms were implemented in two different industrial processes model; respectively revealed the effectiveness and merit of both algorithms.展开更多
A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise ...A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise polluted signal is taken and the noise model assumption in logarithmic domain with Gaussian noise and impact noise is proposed. Based on the better per- formance of support vector regression （SVR） for complex signal approximation and the wavelet for signal detail expression, the wavelet kernel function is chosen as support vector kernel func- tion. Then the logarithmic SAR image is regressed with WSVR. Furthermore the regression distance is used as a judgment index of the noise type. According to the judgment of noise type every pixel can be adaptively de-noised with different filters. Through an approximation experiment for a one-dimensional complex signal, the feasibility of SAR data regression based on WSVR is con- firmed. Afterward the SAR image is treated as a two-dimensional continuous signal and filtered by an SVR with wavelet kernel function. The results show that the method proposed here reduces the radar speckle noise effectively while maintaining edge features and details well.展开更多
A method of applying support vector machine (SVM) in speech recognition was proposed, and a speech recognition system for mandarin digits was built up by SVMs. In the system, vectors were linearly extracted from speec...A method of applying support vector machine (SVM) in speech recognition was proposed, and a speech recognition system for mandarin digits was built up by SVMs. In the system, vectors were linearly extracted from speech feature sequence to make up time-aligned input patterns for SVM, and the decisions of several 2-class SVM classifiers were employed for constructing an N-class classifier. Four kinds of SVM kernel functions were compared in the experiments of speaker-independent speech recognition of mandarin digits. And the kernel of radial basis function has the highest accurate rate of 99.33%, which is better than that of the baseline system based on hidden Markov models (HMM) (97.08%). And the experiments also show that SVM can outperform HMM especially when the samples for learning were very limited.展开更多
Support Vector Machine(SVM) was demonstrated as a potentially useful tool to integrate multi-variables and to produce a predictive map for mineral deposits. The e 1071,a free R package,was used to construct a SVM with...Support Vector Machine(SVM) was demonstrated as a potentially useful tool to integrate multi-variables and to produce a predictive map for mineral deposits. The e 1071,a free R package,was used to construct a SVM with radial kernel function to integrate four evidence layers and to map prospectivity for Gangdese porphyry copper deposits.The results demonstrate that the predicted prospective target area for Cu occupies 20.5%of the total study area and contains 52.4%of the total number of known porphyry copper deposits.The results obtained展开更多
While malicious samples are widely found in many application fields of machine learning,suitable countermeasures have been investigated in the field of adversarial machine learning.Due to the importance and popularity...While malicious samples are widely found in many application fields of machine learning,suitable countermeasures have been investigated in the field of adversarial machine learning.Due to the importance and popularity of Support Vector Machines(SVMs),we first describe the evasion attack against SVM classification and then propose a defense strategy in this paper.The evasion attack utilizes the classification surface of SVM to iteratively find the minimal perturbations that mislead the nonlinear classifier.Specially,we propose what is called a vulnerability function to measure the vulnerability of the SVM classifiers.Utilizing this vulnerability function,we put forward an effective defense strategy based on the kernel optimization of SVMs with Gaussian kernel against the evasion attack.Our defense method is verified to be very effective on the benchmark datasets,and the SVM classifier becomes more robust after using our kernel optimization scheme.展开更多
In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as c...In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.展开更多
The principle of the support vector regression machine（SVR） is first analysed. Then the new data-dependent kernel function is constructed from information geometry perspective. The current waveforms change regularly...The principle of the support vector regression machine（SVR） is first analysed. Then the new data-dependent kernel function is constructed from information geometry perspective. The current waveforms change regularly in accordance with the different horizontal offset when the rotational frequency of the high speed rotational arc sensor is in the range from 15 Hz to 30 Hz. The welding current data is pretreated by wavelet filtering, mean filtering and normalization treatment. The SVR model is constructed by making use of the evolvement laws, the decision function can be achieved by training the SVR and the seam offset can be identified. The experimental results show that the precision of the offset identification can be greatly improved by modifying the SVR and applying mean filteringfrom the longitudinal direction.展开更多
In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support...In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of mul-tipliers.Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function,the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subana-lytic.Through several numerical examples,they illustrate the effectiveness of the proposed splitting algorithm.展开更多
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica...A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
Support vector machines are recognized as a powerful tool for supervised analysis and classification in different fields,particularly geophysics.In summary,SVMs are binary classifiers.Thus,for the multiclass study,the...Support vector machines are recognized as a powerful tool for supervised analysis and classification in different fields,particularly geophysics.In summary,SVMs are binary classifiers.Thus,for the multiclass study,the problem is divided into a series of binary classifications.At the end,all the results obtained from these binary classifications are combined into a one-to-one or one-to-all comparison.In this article,the strategy consists of classifying soils using their chemical composition as characteristics specific to a soil.The prediction consists of 5 classes,which are:White Clay,Red Clay,Black Clay,Granite,and Sand.The dataset is composed of basic oxides,which contribute to increasing soil salinity,acidic oxides such as silica,which do not influence soil fertility,and amphoteric oxides.These data are divided into training,test,and validation data.The one-vs-all strategy was used.The results obtained showed the strength of the one-vs-all associated with SVM on all classification metrics.The selection of the kernel as well as hyperparameters also played an important role in the prediction score.From the results obtained,the one-vs-all associated with SVM can be used for classification problems.For further studies,geolocation can be introduced to have knowledge of the evolution according to the different sectors of the same region.展开更多
文摘Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.
基金Supported by the National Natural Science Foundation of China(60473035)~~
文摘The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.
基金Supported by the State Key Development Program for Basic Research of China （No.2002CB312200） and the National Natural Science Foundation of China （No.60574019）.
文摘Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a SVM with spline kernel function. With the help of this model, nonlinear model predictive control can be transformed to linear model predictive control, and consequently a unified analytical solution of optimal input of multi-step-ahead predictive control is possible to derive. This algorithm does not require online iterative optimization in order to be suitable for real-time control with less calculation. The simulation results of pH neutralization process and CSTR reactor show the effectiveness and advantages of the presented algorithm.
文摘The development of forecasting models for pollution particles shows a nonlinear dynamic behavior;hence, implementation is a non-trivial process. In the literature, there have been multiple models of particulate pollutants, which use softcomputing techniques and machine learning such as: multilayer perceptrons, neural networks, support vector machines, kernel algorithms, and so on. This paper presents a prediction pollution model using support vector machines and kernel functions, which are: Gaussian, Polynomial and Spline. Finally, the prediction results of ozone (O3), particulate matter (PM10) and nitrogen dioxide (NO2) at Mexico City are presented as a case study using these techniques.
基金the Hunan Natural Science Foundation(No. 09JJ3129)the Hunan Key Social Science Foundation (No. 09ZDB04)the Hunan Social Science Foundation (No. 08JD28)
文摘An admissible manifold wavelet kernel is proposed to construct manifold wavelet support vector machine(MWSVM) for stock returns forecasting.The manifold wavelet kernel is obtained by incorporating manifold theory into wavelet technique in support vector machine(SVM).Since manifold wavelet function can yield features that describe of the stock time series both at various locations and at varying time granularities,the MWSVM can approximate arbitrary nonlinear functions and forecast stock returns accurately.The applicability and validity of MWSVM for stock returns forecasting is confirmed through experiments on real-world stock data.
文摘With the progress of deep learning research, convolutional neural networks have become the most important method in feature extraction. How to effectively classify and recognize the extracted features will directly affect the performance of the entire network. Traditional processing methods include classification models such as fully connected network models and support vector machines. In order to solve the problem that the traditional convolutional neural network is prone to over-fitting for the classification of small samples, a CNN-TWSVM hybrid model was proposed by fusing the twin support vector machine (TWSVM) with higher computational efficiency as the CNN classifier, and it was applied to the traffic sign recognition task. In order to improve the generalization ability of the model, the wavelet kernel function is introduced to deal with the nonlinear classification task. The method uses the network initialized from the ImageNet dataset to fine-tune the specific domain and intercept the inner layer of the network to extract the high abstract features of the traffic sign image. Finally, the TWSVM based on wavelet kernel function is used to identify the traffic signs, so as to effectively solve the over-fitting problem of traffic signs classification. On GTSRB and BELGIUMTS datasets, the validity and generalization ability of the improved model is verified by comparing with different kernel functions and different SVM classifiers.
文摘A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.
基金This work has been supported by the National Outstanding Youth Science Foundation of China (No. 60025308) and the Teach and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE,China.
文摘A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.
基金Project supported by the National Outstanding Youth ScienceFoundation of China (No. 60025308) and the Teach and ResearchAward Program for Outstanding Young Teachers in Higher EducationInstitutions of MOE, China
文摘Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlinear system, the system model is built by using LS-SVM with linear kernel function, and then the obtained linear LS-SVM model is transformed into linear input-output relation of the controlled system. However, for the strongly nonlinear system, the off-line model of the controlled system is built by using LS-SVM with Radial Basis Function (RBF) kernel. The obtained nonlinear LS-SVM model is linearized at each sampling instant of system running, after which the on-line linear input-output model of the system is built. Based on the obtained linear input-output model, the Generalized Predictive Control (GPC) algorithm is employed to implement predictive control for the controlled plant in both algorithms. The simulation results after the presented algorithms were implemented in two different industrial processes model; respectively revealed the effectiveness and merit of both algorithms.
基金supported by Shanghai Science and Technology Commission Innovation Action Plan(08DZ1205708)
文摘A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise polluted signal is taken and the noise model assumption in logarithmic domain with Gaussian noise and impact noise is proposed. Based on the better per- formance of support vector regression （SVR） for complex signal approximation and the wavelet for signal detail expression, the wavelet kernel function is chosen as support vector kernel func- tion. Then the logarithmic SAR image is regressed with WSVR. Furthermore the regression distance is used as a judgment index of the noise type. According to the judgment of noise type every pixel can be adaptively de-noised with different filters. Through an approximation experiment for a one-dimensional complex signal, the feasibility of SAR data regression based on WSVR is con- firmed. Afterward the SAR image is treated as a two-dimensional continuous signal and filtered by an SVR with wavelet kernel function. The results show that the method proposed here reduces the radar speckle noise effectively while maintaining edge features and details well.
文摘A method of applying support vector machine (SVM) in speech recognition was proposed, and a speech recognition system for mandarin digits was built up by SVMs. In the system, vectors were linearly extracted from speech feature sequence to make up time-aligned input patterns for SVM, and the decisions of several 2-class SVM classifiers were employed for constructing an N-class classifier. Four kinds of SVM kernel functions were compared in the experiments of speaker-independent speech recognition of mandarin digits. And the kernel of radial basis function has the highest accurate rate of 99.33%, which is better than that of the baseline system based on hidden Markov models (HMM) (97.08%). And the experiments also show that SVM can outperform HMM especially when the samples for learning were very limited.
文摘Support Vector Machine(SVM) was demonstrated as a potentially useful tool to integrate multi-variables and to produce a predictive map for mineral deposits. The e 1071,a free R package,was used to construct a SVM with radial kernel function to integrate four evidence layers and to map prospectivity for Gangdese porphyry copper deposits.The results demonstrate that the predicted prospective target area for Cu occupies 20.5%of the total study area and contains 52.4%of the total number of known porphyry copper deposits.The results obtained
基金supported by the National Natural Science Foundation of China under Grant No.61966011.
文摘While malicious samples are widely found in many application fields of machine learning,suitable countermeasures have been investigated in the field of adversarial machine learning.Due to the importance and popularity of Support Vector Machines(SVMs),we first describe the evasion attack against SVM classification and then propose a defense strategy in this paper.The evasion attack utilizes the classification surface of SVM to iteratively find the minimal perturbations that mislead the nonlinear classifier.Specially,we propose what is called a vulnerability function to measure the vulnerability of the SVM classifiers.Utilizing this vulnerability function,we put forward an effective defense strategy based on the kernel optimization of SVMs with Gaussian kernel against the evasion attack.Our defense method is verified to be very effective on the benchmark datasets,and the SVM classifier becomes more robust after using our kernel optimization scheme.
文摘In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.
基金Supported by National Natural Science Foundation of China（ No. 50705030）.
文摘The principle of the support vector regression machine（SVR） is first analysed. Then the new data-dependent kernel function is constructed from information geometry perspective. The current waveforms change regularly in accordance with the different horizontal offset when the rotational frequency of the high speed rotational arc sensor is in the range from 15 Hz to 30 Hz. The welding current data is pretreated by wavelet filtering, mean filtering and normalization treatment. The SVR model is constructed by making use of the evolvement laws, the decision function can be achieved by training the SVR and the seam offset can be identified. The experimental results show that the precision of the offset identification can be greatly improved by modifying the SVR and applying mean filteringfrom the longitudinal direction.
基金supported by the National Natural Science Foundation of China(Nos.12026602,12071157,12271108)the Natural Science Foundation of Guangdong Provience(No.2024A1515012288)+1 种基金the Science and Technology Commission of Shanghai Municipality(No.23JC1400501)the Ministry of Science and Technology of China(No.G2023132005L).
文摘In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of mul-tipliers.Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function,the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subana-lytic.Through several numerical examples,they illustrate the effectiveness of the proposed splitting algorithm.
基金Support by China 973 Project (No. 2002CB312200).
文摘A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
文摘Support vector machines are recognized as a powerful tool for supervised analysis and classification in different fields,particularly geophysics.In summary,SVMs are binary classifiers.Thus,for the multiclass study,the problem is divided into a series of binary classifications.At the end,all the results obtained from these binary classifications are combined into a one-to-one or one-to-all comparison.In this article,the strategy consists of classifying soils using their chemical composition as characteristics specific to a soil.The prediction consists of 5 classes,which are:White Clay,Red Clay,Black Clay,Granite,and Sand.The dataset is composed of basic oxides,which contribute to increasing soil salinity,acidic oxides such as silica,which do not influence soil fertility,and amphoteric oxides.These data are divided into training,test,and validation data.The one-vs-all strategy was used.The results obtained showed the strength of the one-vs-all associated with SVM on all classification metrics.The selection of the kernel as well as hyperparameters also played an important role in the prediction score.From the results obtained,the one-vs-all associated with SVM can be used for classification problems.For further studies,geolocation can be introduced to have knowledge of the evolution according to the different sectors of the same region.
