Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the propo...Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.展开更多
Multiblock kernel principal component analysis (MBKPCA) has been proposed to isolate the faults and avoid the high computation cost. However, MBKPCA is not available for dynamic processes. To solve this problem, recur...Multiblock kernel principal component analysis (MBKPCA) has been proposed to isolate the faults and avoid the high computation cost. However, MBKPCA is not available for dynamic processes. To solve this problem, recursive MBKPCA is proposed for monitoring large scale processes. In this paper, we present a new recursive MBKPCA (RMBKPCA) algorithm, where the adaptive technique is adopted for dynamic characteristics. The proposed algorithm reduces the high computation cost, and is suitable for online model updating in the feature space. The proposed algorithm was applied to an industrial process for adaptive monitoring and found to efficiently capture the time-varying and nonlinear relationship in the process variables.展开更多
The paper analyzes the problem of blind source separation （BSS） based on the nonlinear principal component analysis （NPCA） criterion. An adaptive strong tracking filter （STF） based algorithm was developed, which...The paper analyzes the problem of blind source separation （BSS） based on the nonlinear principal component analysis （NPCA） criterion. An adaptive strong tracking filter （STF） based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.展开更多
By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squa...By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covari- ance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resis- tance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhi- bition model (APEX) and least mean square error reconstruction (LMSER) algorithms.展开更多
提出一种改进的基于数据块更新的递归主元分析(recursive principal component analysis,RPCA)方法,对具有慢时变和多变量等特性的某型舰空导弹武器雷达发射机工作过程进行自适应监测。该方法在协方差矩阵的特征值分解中引入低秩奇异值...提出一种改进的基于数据块更新的递归主元分析(recursive principal component analysis,RPCA)方法,对具有慢时变和多变量等特性的某型舰空导弹武器雷达发射机工作过程进行自适应监测。该方法在协方差矩阵的特征值分解中引入低秩奇异值分解递归方法,实现负荷矩阵和特征值矩阵的递归计算;制定了均值、方差的更新策略;给出一种基于指数加权的控制限递归算法以提高RPCA的健壮性。实验证明该方法能自适应地跟踪过程时变并实时监测故障,同时有效地降低误警率。展开更多
基金Supported by the National Natural Science Foundation of Chinathe Science foundation of Guangxi Educational Administration
文摘Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.
基金Project supported by the National Basic Research Program (973) of China (No. 2009CB320600) the National Natural Science Foun-dation of China (No. 60974057)
文摘Multiblock kernel principal component analysis (MBKPCA) has been proposed to isolate the faults and avoid the high computation cost. However, MBKPCA is not available for dynamic processes. To solve this problem, recursive MBKPCA is proposed for monitoring large scale processes. In this paper, we present a new recursive MBKPCA (RMBKPCA) algorithm, where the adaptive technique is adopted for dynamic characteristics. The proposed algorithm reduces the high computation cost, and is suitable for online model updating in the feature space. The proposed algorithm was applied to an industrial process for adaptive monitoring and found to efficiently capture the time-varying and nonlinear relationship in the process variables.
基金Supported by the Basic Research Foundation of Tsinghua National Laboratory for Information Science and Technology (TNList) the National Natural Science Foundation of China (No. 60675002)
文摘The paper analyzes the problem of blind source separation （BSS） based on the nonlinear principal component analysis （NPCA） criterion. An adaptive strong tracking filter （STF） based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.60172011 and 69831040)Guangxi Natural Science Foundation(Grant No.gzk0007011)the Science Foundation of Guangxi Education Bureau,China
文摘By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covari- ance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resis- tance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhi- bition model (APEX) and least mean square error reconstruction (LMSER) algorithms.
文摘提出一种改进的基于数据块更新的递归主元分析(recursive principal component analysis,RPCA)方法,对具有慢时变和多变量等特性的某型舰空导弹武器雷达发射机工作过程进行自适应监测。该方法在协方差矩阵的特征值分解中引入低秩奇异值分解递归方法,实现负荷矩阵和特征值矩阵的递归计算;制定了均值、方差的更新策略;给出一种基于指数加权的控制限递归算法以提高RPCA的健壮性。实验证明该方法能自适应地跟踪过程时变并实时监测故障,同时有效地降低误警率。
