Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Anal...Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.展开更多
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
The spaceborne synthetic aperture radar(SAR)sparse flight 3-D imaging technology through multiple observations of the cross-track direction is designed to form the cross-track equivalent aperture,and achieve the third...The spaceborne synthetic aperture radar(SAR)sparse flight 3-D imaging technology through multiple observations of the cross-track direction is designed to form the cross-track equivalent aperture,and achieve the third dimensionality recognition.In this paper,combined with the actual triple star orbits,a sparse flight spaceborne SAR 3-D imaging method based on the sparse spectrum of interferometry and the principal component analysis(PCA)is presented.Firstly,interferometric processing is utilized to reach an effective sparse representation of radar images in the frequency domain.Secondly,as a method with simple principle and fast calculation,the PCA is introduced to extract the main features of the image spectrum according to its principal characteristics.Finally,the 3-D image can be obtained by inverse transformation of the reconstructed spectrum by the PCA.The simulation results of 4.84 km equivalent cross-track aperture and corresponding 1.78 m cross-track resolution verify the effective suppression of this method on high-frequency sidelobe noise introduced by sparse flight with a sparsity of 49%and random noise introduced by the receiver.Meanwhile,due to the influence of orbit distribution of the actual triple star orbits,the simulation results of the sparse flight with the 7-bit Barker code orbits are given as a comparison and reference to illuminate the significance of orbit distribution for this reconstruction results.This method has prospects for sparse flight 3-D imaging in high latitude areas for its short revisit period.展开更多
Signals can be sampled by compressive sensing theory with a much less rate than those by traditional Nyquist sampling theorem,and reconstructed with high probability,only when signals are sparse in the time domain or ...Signals can be sampled by compressive sensing theory with a much less rate than those by traditional Nyquist sampling theorem,and reconstructed with high probability,only when signals are sparse in the time domain or a transform domain.Most signals are not sparse in real world,but can be expressed in sparse form by some kind of sparse transformation.Commonly used sparse transformations will lose some information,because their transform bases are generally fixed.In this paper,we use principal component analysis for data reduction,and select new variable with low dimension and linearly correlated to the original variable,instead of the original variable with high dimension,thus the useful data of the original signals can be included in the sparse signals after dimensionality reduction with maximize portability.Therefore,the loss of data can be reduced as much as possible,and the efficiency of signal reconstruction can be improved.Finally,the composite material plate is used for the experimental verification.The experimental result shows that the sparse representation of signals based on principal component analysis can reduce signal distortion and improve signal reconstruction efficiency.展开更多
Adding colors to monochrome thermal infrared images can help observers understand the scenery better. A nonlinear color estimation method for single-band thermal infrared imagery based on kernel principal component an...Adding colors to monochrome thermal infrared images can help observers understand the scenery better. A nonlinear color estimation method for single-band thermal infrared imagery based on kernel principal component analysis (KPCA) and sparse representation was proposed. Nonlinear features of infrared image were extracted using KPCA. The relationship between image features and chromatic values was learned using sparse representation and a color estimation model was obtained. The thermal infrared images can be rendered automatically using the color estimation model. The experimental results show that the proposed method can render infrared image with an accurate color appearance. The proposed idea can also be used in other color estimation problem.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
文摘Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.
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This work was supported by the General Design Department,China Academy of Space Technology(10377).
文摘The spaceborne synthetic aperture radar(SAR)sparse flight 3-D imaging technology through multiple observations of the cross-track direction is designed to form the cross-track equivalent aperture,and achieve the third dimensionality recognition.In this paper,combined with the actual triple star orbits,a sparse flight spaceborne SAR 3-D imaging method based on the sparse spectrum of interferometry and the principal component analysis(PCA)is presented.Firstly,interferometric processing is utilized to reach an effective sparse representation of radar images in the frequency domain.Secondly,as a method with simple principle and fast calculation,the PCA is introduced to extract the main features of the image spectrum according to its principal characteristics.Finally,the 3-D image can be obtained by inverse transformation of the reconstructed spectrum by the PCA.The simulation results of 4.84 km equivalent cross-track aperture and corresponding 1.78 m cross-track resolution verify the effective suppression of this method on high-frequency sidelobe noise introduced by sparse flight with a sparsity of 49%and random noise introduced by the receiver.Meanwhile,due to the influence of orbit distribution of the actual triple star orbits,the simulation results of the sparse flight with the 7-bit Barker code orbits are given as a comparison and reference to illuminate the significance of orbit distribution for this reconstruction results.This method has prospects for sparse flight 3-D imaging in high latitude areas for its short revisit period.
基金supported by the National Natural Science Foundation of China(Nos.51405241,61672290)the Jiangsu Government Scholarship for Overseas Studies and the PAPD Fund
文摘Signals can be sampled by compressive sensing theory with a much less rate than those by traditional Nyquist sampling theorem,and reconstructed with high probability,only when signals are sparse in the time domain or a transform domain.Most signals are not sparse in real world,but can be expressed in sparse form by some kind of sparse transformation.Commonly used sparse transformations will lose some information,because their transform bases are generally fixed.In this paper,we use principal component analysis for data reduction,and select new variable with low dimension and linearly correlated to the original variable,instead of the original variable with high dimension,thus the useful data of the original signals can be included in the sparse signals after dimensionality reduction with maximize portability.Therefore,the loss of data can be reduced as much as possible,and the efficiency of signal reconstruction can be improved.Finally,the composite material plate is used for the experimental verification.The experimental result shows that the sparse representation of signals based on principal component analysis can reduce signal distortion and improve signal reconstruction efficiency.
基金National Natural Science Foundation of China(No. 61072090)the Fundamental Research Funds for the Central Universities,China+2 种基金Shanghai Pujiang Program,China(No. 12PJ1402200)China Postdoctoral Science Foundation Funded Project(No. 2012M511058)Shanghai Postdoctoral Sustentation Fund,China(No. 12R21412500)
文摘Adding colors to monochrome thermal infrared images can help observers understand the scenery better. A nonlinear color estimation method for single-band thermal infrared imagery based on kernel principal component analysis (KPCA) and sparse representation was proposed. Nonlinear features of infrared image were extracted using KPCA. The relationship between image features and chromatic values was learned using sparse representation and a color estimation model was obtained. The thermal infrared images can be rendered automatically using the color estimation model. The experimental results show that the proposed method can render infrared image with an accurate color appearance. The proposed idea can also be used in other color estimation problem.
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.
