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Modified possibilistic clustering model based on kernel methods

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Journal of Shanghai University(English Edition) 2008年第2期12卷 136-140页

作者：武小红周建江 College of Information Science and Technology Nanjing University of Aeronautics and Astronautics

A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.

关键词： fuzzy clustering kernel methods possibilistic c-means (PCM) kernel modified possibilistic c-means (KMPCM).

kernel feature extraction methods observed from the viewpoint of generating-kernels

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Frontiers of Electrical and Electronic Engineering in China 2011年第1期6卷 43-55页

作者： Jian YANG School of Computer Science and Technology Nanjing University of Science and TechnologyNanjing 210094China

This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the *** on this idea,we present two nonlinear feature extraction methods:generating kernel principal component analysis(GKPCA)and generating kernel Fisher discriminant(GKFD).These two methods are shown to be equivalent to the function-mapping-space PCA(FMS-PCA)and the function-mapping-space linear discriminant analysis(FMS-LDA)methods,*** equivalence reveals that the generating kernel is actually determined by the corresponding function *** the generating kernel point of view,we can classify the current kernel Fisher discriminant(KFD)algorithms into two categories:KPCA+LDA based algorithms and straightforward KFD(SKFD)*** KPCA+LDA based algorithms directly work on the given kernel and are not suitable for non-kernel functions,while the SKFD algorithms essentially work on the generating kernel from a given symmetric function and are therefore suitable for non-kernels as well as ***,we outline the tensor-based feature extraction methods and discuss ways of extending tensor-based methods to their generating kernel versions.

关键词： kernel methods feature extraction principal component analysis(PCA) Fisher linear discriminant analysis(FLD or LDA) tensor-based methods

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

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Chinese Physics B 2014年第3期23卷 159-164页

作者： Bilal Shoaib Ijaz Mansoor Qureshi Ihsanulhaq Shafqatullah Department of Electronic Engineering Faculty of Engineering and Technology International Islamic University Department of Electrical Engineering AIR University School of Engineering and Applied Sciences ISRA University

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

关键词： fractional least mean square kernel methods Reimann-Lioville derivative Mackey glass timeseries

Revisiting Total Model Errors and Model Validation

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Journal of Systems Science & Complexity 2021年第5期34卷 1598-1603页

作者： LJUNG Lennart Linkoping University Sweden

The paper contains a discussion of earlier work on Total Model Errors and Model *** is maintained that the recent change of paradigm to kernel based system identification has also affected the basis for(and interest i... 详细信息

关键词： Bias kernel methods model errors regularization system identification variance

kernel-Based State-Space Kriging for Predictive Control

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IEEE/CAA Journal of Automatica Sinica 2023年第5期10卷 1263-1275页

作者： A.Daniel Carnerero Daniel R.Ramirez Daniel Limon Teodoro Alamo the Department of System Engineering and Automation University of SevilleSevilla 41020Spain the School of Engineering Tokyo Institute of TechnologyTokyo 152-8552Japan Department of System Engineering and Automation University of SevilleSevilla 41020Spain

In this paper, we extend the state-space kriging(SSK) modeling technique presented in a previous work by the authors in order to consider non-autonomous systems. SSK is a data-driven method that computes predictions as linear combinations of past outputs. To model the nonlinear dynamics of the system, we propose the kernel-based state-space kriging(K-SSK), a new version of the SSK where kernel functions are used instead of resorting to considerations about the locality of the data. Also, a Kalman filter can be used to improve the predictions at each time step in the case of noisy measurements. A constrained tracking nonlinear model predictive control(NMPC) scheme using the black-box input-output model obtained by means of the K-SSK prediction method is proposed. Finally, a simulation example and a real experiment are provided in order to assess the performance of the proposed controller.

关键词： Data-driven methods model identification kernel methods predictive control

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

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Computers, Materials & Continua 2021年第5期67卷 1413-1427页

作者： Bilal Shoaib Yasir Javed Muhammad Adnan Khan Fahad Ahmad Rizwan Majeed Muhammad Saqib Nawaz Muhammad Adeel Ashraf Abid Iqbal Muhammad Idrees School of Computer Science Minhaj University LahoreLahore54000Pakistan Prince Sultan University Riyadh11586Saudi Arabia Department of Computer Science Riphah International University Lahore CampusLahore54000Pakistan Department of Basic Sciences Deanship of Common First YearJouf UniversitySakakaAljouf72341Saudi Arabia Directorate of IT The Islamia University of BahawalpurBahawalpur63100Pakistan Department of Computer Science University of Management and TechnologyLahore54770Pakistan PUCIT University of the PunjabLahore54000Pakistan

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this *** proposed algorithm lends itself towards the parallel implementation as in the FPGA *** the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is *** computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this *** proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its *** the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than *** new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input *** experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

关键词： kernel methods square root adaptive filtering givens rotation mackey glass time series prediction recursive least squares kernel recursive least squares extended kernel recursive least squares square root extended kernel recursive least squares algorithm

Multi-instance learning for software quality estimation in object-oriented systems:a case study

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Journal of Zhejiang University-Science C(Computers and Electronics) 2010年第2期11卷 130-138页

作者： Peng HUANG Jie ZHU Department of Electronic Engineering Shanghai Jiao Tong University Shanghai 200240 China

We investigate a problem of object-oriented (OO) software quality estimation from a multi-instance (MI) perspective. In detail,each set of classes that have an inheritance relation,named 'class hierarchy',is regarded as a bag,while each class in the set is regarded as an instance. The learning task in this study is to estimate the label of unseen bags,i.e.,the fault-proneness of untested class hierarchies. A fault-prone class hierarchy contains at least one fault-prone (negative) class,while a non-fault-prone (positive) one has no negative class. Based on the modification records (MRs) of the previous project releases and OO software metrics,the fault-proneness of an untested class hierarchy can be predicted. Several selected MI learning algorithms were evalu-ated on five datasets collected from an industrial software project. Among the MI learning algorithms investigated in the ex-periments,the kernel method using a dedicated MI-kernel was better than the others in accurately and correctly predicting the fault-proneness of the class hierarchies. In addition,when compared to a supervised support vector machine (SVM) algorithm,the MI-kernel method still had a competitive performance with much less cost.

关键词： Object-oriented (OO) software Multi-instance (MI) learning Software quality estimation kernel methods

kernel selection with spectral perturbation stability of kernel matrix

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Science China(Information Sciences) 2014年第11期57卷 47-56页

作者： LIU Yong LIAO ShiZhong School of Computer Science and Technology Tianjin University

kernel selection is one of the key issues both in recent research and application of kernel *** is usually done by minimizing either an estimate of generalization error or some other related performance measure. Use of notions of stability to estimate the generalization error has attracted much attention in recent years. Unfortunately, the existing notions of stability, proposed to derive the theoretical generalization error bounds, are difficult to be used for kernel selection in practice. It is well known that the kernel matrix contains most of the information needed by kernel methods, and the eigenvalues play an important role in the kernel matrix. Therefore, we aim at introducing a new notion of stability, called the spectral perturbation stability,to study the kernel selection problem. This proposed stability quantifies the spectral perturbation of the kernel matrix with respect to the changes in the training set. We establish the connection between the spectral perturbation stability and the generalization error. By minimizing the derived generalization error bound, we propose a new kernel selection criterion that can guarantee good generalization properties. In our criterion,the perturbation of the eigenvalues of the kernel matrix is efficiently computed by solving the derivative of a newly defined generalized kernel matrix. Both theoretical analysis and experimental results demonstrate that our criterion is sound and effective.

关键词： kernel methods kernel selection stability spectral perturbation stability generalization error bound

Soft sensor modeling based on Gaussian processes

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Journal of Central South University of Technology 2005年第4期12卷 469-471页

作者：熊志化黄国宏邵惠鹤 Institute of Automation Shanghai Jiaotong University Shanghai 200030 China Institute

In order to meet the demand of online optimal running, a novel soft sensor modeling approach based on Gaussian processes was proposed. The approach is moderately simple to implement and use without loss of performance. It is trained by optimizing the hyperparameters using the scaled conjugate gradient algorithm with the squared exponential covariance function employed. Experimental simulations show that the soft sensor modeling approach has the advantage via a real-world example in a refinery. Meanwhile, the method opens new possibilities for application of kernel methods to potential fields.

关键词： Gaussian processes soft sensor modeling kernel methods