卷积鲁棒主成分分析

鲁棒主成分分析(RPCA)是一种经典的高维数据分析方法,可从带噪声的观测样本中恢复出原始数据.但是,RPCA能工作的前提是目标数据拥有低秩矩阵结构,不能有效处理实际应用中广泛存在的非低秩数据.研究发现,虽然图像、视频等数据矩阵本身可能不是低秩的,但它们的卷积矩阵通常是低秩的.根据这一原理,提出一种称为卷积鲁棒主成分分析...     

Diagonal principal component analysis for face recognition

In this paper, a novel subspace method called diagonal principal component analysis (DiaPCA) is proposed for face recognition. In contrast to standard PCA, DiaPCA directly seeks the optimal projective vectors from diagonal face images without image-to-vector transformation. While in contrast to 2DPCA, DiaPCA reserves the correlations between variations of rows and those of columns of images. Experiments show that DiaPCA is much more accurate than both PCA and 2DPCA. Furthermore, it is shown that the accuracy can be further improved by combining DiaPCA with 2DPCA.     

鲁棒主元分析在掌纹识别中的应用

为了对存在异常值的图像构建低维线性子空间的描述,提出用鲁棒主元分析(RPCA)的新方法进行掌纹识别。运用图像下抽样方法降低掌纹空间的维数,在低维图像上应用RPCA提取低维的投影向量,然后将训练图像和待识别图像向投影向量上投影得到鲁棒主元特征,计算特征向量间的余弦距离进行掌纹匹配。运用PolyU掌纹图像库进行测试,结果表明,与主元分析(PCA)、独立元分析(ICA)和核主元分析(KPCA)相比,RPCA算法的识别率最高为99%,特征提取和匹配总时间0.032 s,满足了实时系统的要求。     

On Bayesian principal component analysis

A complete Bayesian framework for principal component analysis (PCA) is proposed. Previous model-based approaches to PCA were often based upon a factor analysis model with isotropic Gaussian noise. In contrast to PCA, these approaches do not impose orthogonality constraints. A new model with orthogonality restrictions is proposed. Its approximate Bayesian solution using the variational approximation and results from directional statistics is developed. The Bayesian solution provides two notable results in relation to PCA. The first is uncertainty bounds on principal components (PCs), and the second is an explicit distribution on the number of relevant PCs. The posterior distribution of the PCs is found to be of the von-Mises-Fisher type. This distribution and its associated hypergeometric function, , are studied. Numerical reductions are revealed, leading to a stable and efficient orthogonal variational PCA (OVPCA) algorithm. OVPCA provides the required inferences. Its performance is illustrated in simulation, and for a sequence of medical scintigraphic images.     

牛顿-软阈值迭代鲁棒主成分分析算法

针对鲁棒主成分分析（RPCA）问题，为了降低RPCA算法的时间复杂度，提出了牛顿-软阈值迭代（NSTI）算法。首先，使用低秩矩阵的Frobenius范数与稀疏矩阵的l₁-范数的和来构造NSTI算法的模型；其次，同时使用两种不同的优化方式求解模型的不同部分，即用牛顿法快速计算出低秩矩阵，用软阈值迭代算法快速计算出稀疏矩阵，交替使用这两种方法计算出原数据的低秩矩阵和稀疏矩阵的分解；最后，得到原始数据的低秩特征。在数据规模为5 000×5 000，低秩矩阵的秩为20的情况下，NSTI算法和梯度下降（GD）算法、低秩矩阵拟合（LMaFit）算法相比，时间效率分别提高了24.6%、45.5%。对180帧的视频前景背景进行分离，NSTI耗时3.63 s，时间效率比GD算法、LMaFit算法分别高78.7%、82.1%。图像降噪实验中，NSTI算法耗时0.244 s，所得到的降噪后的图像与原始图像的残差为0.381 3，与GD算法、LMaFit算法相比，时间效率和精确度分别提高了64.3%和45.3%。实验结果证明，NSTI算法能够有效解决RPCA问题并提升RPCA算法的时间效率。     

Two-stage image denoising by principal component analysis with local pixel grouping

This paper presents an efficient image denoising scheme by using principal component analysis (PCA) with local pixel grouping (LPG). For a better preservation of image local structures, a pixel and its nearest neighbors are modeled as a vector variable, whose training samples are selected from the local window by using block matching based LPG. Such an LPG procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for PCA transform estimation, so that the image local features can be well preserved after coefficient shrinkage in the PCA domain to remove the noise. The LPG-PCA denoising procedure is iterated one more time to further improve the denoising performance, and the noise level is adaptively adjusted in the second stage. Experimental results on benchmark test images demonstrate that the LPG-PCA method achieves very competitive denoising performance, especially in image fine structure preservation, compared with state-of-the-art denoising algorithms.     

Robust multi-scale principal components analysis with applications to process monitoring

Robust multi-scale principal component analysis (RMSPCA) improves multi-scale principal components analysis (MSPCA) techniques by incorporating the uncertainty of signal noise distributions and eliminating/down-weighting the effects of abnormal data in the training set. The novelty of the approach is to integrate MSPCA with the robustness to the typical normality assumption of noisy data. By using an M-estimator based on the generalized T distribution, RMSPCA adaptively transforms the data in the score space at each scale in order to eliminate/down-weight the effects of the outliers in the original data. The robust estimation of the covariance or correlation matrix at each scale is obtained by the proposed approach so that accurate MSPCA models can be obtained for process monitoring purposes. The performance of the proposed approach in process fault detection is illustrated and compared with that of the conventional MSPCA approach through a pilot-scale setting.     

牛顿-软阈值迭代鲁棒主成分分析算法

针对鲁棒主成分分析（RPCA）问题,为了降低RPCA算法的时间复杂度,提出了牛顿-软阈值迭代（NSTI）算法。首先,使用低秩矩阵的Frobenius范数与稀疏矩阵的l₁-范数的和来构造NSTI算法的模型;其次,同时使用两种不同的优化方式求解模型的不同部分,即用牛顿法快速计算出低秩矩阵,用软阈值迭代算法快速计算出稀疏矩阵,交替使用这两种方法计算出原数据的低秩矩阵和稀疏矩阵的分解;最后,得到原始数据的低秩特征。在数据规模为5 000×5 000,低秩矩阵的秩为20的情况下,NSTI算法和梯度下降（GD）算法、低秩矩阵拟合（LMaFit）算法相比,时间效率分别提高了24.6%、45.5%。对180帧的视频前景背景进行分离,NSTI耗时3.63 s,时间效率比GD算法、LMaFit算法分别高78.7%、82.1%。图像降噪实验中,NSTI算法耗时0.244 s,所得到的降噪后的图像与原始图像的残差为0.381 3,与GD算法、LMaFit算法相比,时间效率和精确度分别提高了64.3%和45.3%。实验结果证明,NSTI算法能够有效解决RPCA问题并提升RPCA算法的时间效率。     

A robust strategy for real-time process monitoring

An operator support system (OSS) is proposed to reliably retain salient information in a high dimensional and correlated database, to uncover linear and nonlinear correlations among variables, to reconstruct failed/unavailable sensors, and to assess process-operating performance in the presence of noise and outliers. The proposed strategy carries out the task in three steps. In the first step, a robust tandem filter is used to suppress noise and reject any outlying observations. Next, an orthogonal nonlinear principal component analysis network is utilized to optimally retain a parsimonious representation of the system. In the final step, the process status is checked against the normal operating region defined by kernel density estimation, and failed/unavailable sensors are reconstructed via constrained optimization and the trained network. The strategy is demonstrated in real-time using a pilot-scale distillation column.     

基于鲁棒主成分分析的智能电网虚假数据注入攻击

基于主成分分析（PCA）的盲攻击策略仅对具有高斯噪声的测量数据有效,在存在异常值的情况下,上述攻击策略将被传统的坏数据检测模块检测。针对异常值存在的问题,提出一种基于鲁棒主成分分析（RPCA）的盲攻击策略。首先,攻击者收集含有异常值的测量数据;然后,通过基于交替方向法（ADM）的稀疏优化技术从含有异常值的测量数据中分离出异常值和真实的测量数据;其次,对真实测量数据进行PCA,得到系统的相关信息;最后,利用获得的系统信息构造攻击向量,并根据得到的攻击向量注入虚假数据。该攻击策略在IEEE 14-bus系统上进行了测试,实验结果表明,在异常值存在的情况下,传统的基于PCA的攻击方法将被坏数据检测模块检测,而所提方法基于鲁棒PCA的攻击策略能够躲避坏数据检测模块的检测。该策略使得在异常值存在的情况下虚假数据注入攻击（FDIA）仍然能够成功实施。     

An iterative algorithm for robust kernel principal component analysis

We introduce a technique to improve iterative kernel principal component analysis (KPCA) robust to outliers due to undesirable artifacts such as noises, alignment errors, or occlusion. The proposed iterative robust KPCA (rKPCA) links the iterative updating and robust estimation of principal directions. It inherits good properties from these two ideas for reducing the time complexity, space complexity, and the influence of these outliers on estimating the principal directions. In the asymptotic stability analysis, we also show that our iterative rKPCA converges to the weighted kernel principal kernel components from the batch rKPCA. Experimental results are presented to confirm that our iterative rKPCA achieves the robustness as well as time saving better than batch KPCA.     

Weighted preliminary-summation-based principal component analysis for non-Gaussian processes

For industrial chemical process, preliminary-summation-based principal component analysis (PS-PCA), an amended PCA method was recently provided for coping with both Gaussian and non-Gaussian characteristics. By summing the training and monitoring data respectively, PS-PCA is capable of resolving the issue of non-Gaussian processes and achieves higher fault detection rate than the traditional PCA. However, in the PS-PCA summation operation, all data samples are regarded as the same weight, which results in the fault information of newly-samples may be diluted, leading to significant detection delays. To address this challenge, in this paper, we propose a novel weighted PS-PCA (WPS-PCA) method that employs an exponential weighting scheme to put more emphasis on recent information. Subsequently, a mathematical argument demonstrates that when the number of variables is enough plentiful, the obtained summation combined with the generalized central limit theorem conforms to approximately a Gaussian distribution. The kurtosis relationships indicate this conversion will bring out well-pleasing feasibility for conventional PCA. Ultimately, the proposed technique verifies detection performance using the Tennessee Eastman process, which is compared with the existing PCA and PS-PCA schemes, in terms of the fault detection time and fault detection rate. The simulation studies reveal that the proposed method is efficient and superior.     

Parallel quality-related dynamic principal component regression method for chemical process monitoring

Traditional quality-related process monitoring mainly focuses on the magnitude change of the quality variables caused by additive faults. However, the abnormal fluctuations in the quality variables caused by multiplicative faults are often overlooked. In this paper, a novel parallel dynamic principal component regression (P-DPCR) algorithm is proposed to monitor the changes in the magnitude and fluctuation of the quality variables simultaneously. Firstly, in order to eliminate the interference of quality-unrelated variables, the quality-related process variables are selected on the basis of correlation analysis. Secondly, the dynamic extension and moving window are carried out for process variables and quality variables, in which the dynamic variables space (called X-space/Y-space) and the variance space (called VX-space/VY-space) are constructed. Afterwards, double quality-related statistics based on the regression model of these four spaces are given, and the comprehensive monitoring decision can be obtained. Finally, two numerical cases and the Tennessee Eastman process are used to show the effectiveness of the proposed method.     

A novel design of wafer yield model for semiconductor using a GMDH polynomial and principal component analysis

According to previous studies, the Poisson model and negative binomial model could not accurately estimate the wafer yield. Numerous mathematical models proposed in past years were very complicated. Furthermore, other neural networks models can not provide a certain equation for managers to use. Thus, a novel design of this paper is to construct a new wafer yield model with a handy polynomial by using group method of data handling (GMDH). In addition to defect cluster index (CI_M), 12 critical electrical test parameters are also considered simultaneously. Because the number of input variables for GMDH is inadvisable to be too many, principal component analysis (PCA) is used to reduce the dimensions of 12 critical electrical test parameters to a manageable few without much loss of information. The proposed approach is validated by a case obtained in a DRAM company in Taiwan.     

多特征稳健主成分分析的视频运动目标分割

提出一种多特征稳健主成分分析(MFRPCA)算法,该算法融合多种视觉特征进行视频运动目标分割,分割的目的即将运动目标从静止信息中提取出来,分割的主要过程是将多特征视频矩阵分解为低秩矩阵和稀疏矩阵.矩阵分解过程是求解一个带受限条件的核范数与L2,1范数组合的最小化问题,此最小化问题可以通过增广拉格朗日乘子法(ALM)有效求解.与其他算法相比,本文算法融合了图像的颜色、边缘和纹理特征等多个特征,通过对变化检测基准数据集进行检测,本文算法获得的查全率为0.486 0和F度量为0.559 7,实验结果表明,本文算法的稳健性和可靠性均优于其他算法.     

一种增量PCA算法及其在人脸识别中的应用

主成分分析（PCA）是模式识别领域一种重要的方法,现在已被广泛地应用于人脸识别算法中,但基于PCA人脸识别系统在应用中面临着一个重要障碍：增量学习问题。针对这个问题,提出了一种适用于成批增量数据的IPCA算法,该算法在原始PCA分解的基础上,利用空间投影变换,使得可以在一个低维空间求解整体PCA,从而降低了求解的复杂度,在此基础上对该增量算法进行了核化,并在ORL人脸数据库上验证了算法的有效性。     

Volcanic ash cloud detection from remote sensing images using principal component analysis

Thermal infrared remote sensing can quickly and accurately detect the volcanic ash cloud. However, remote sensing data have pretty strong inter-band correlation and data redundancy, both of which have decreased to a certain degree the detecting accuracy of volcanic ash cloud. Principal component analysis (PCA) can compress a large number of complex information into a few principal components and overcome the correlation and redundancy. Taking the Eyjafjallajokull volcanic ash cloud formed on April 19, 2010 for example, in this paper, the PCA is used to detect the volcanic ash cloud based on moderate resolution imaging spectroradiometer (MODIS) remote sensing image. The results show that: the PCA can successfully acquire the volcanic ash cloud from MODIS image; the detected volcanic ash cloud has a good consistency with the spatial distribution, SO₂ concentration and volcanic absorbing aerosol index (AAI).     

基于ICA-PCA的化工流程仪表故障诊断

传统的多元统计过程控制(MSPC)的故障诊断方法要求观测变量数据服从高斯分布,然而实际化工流程中的仪表数据中难以满足这一要求。针对这一问题,提出在仪表数据中提取分离出非高斯信息和高斯信息,并分别利用独立元分析法和主元分析法建立不同的故障诊断模型。在检测到发生故障后,通过改进的贡献度算法定位出发生故障的仪表。通过对Tennessee Eastman(TE)过程数据进行仿真研究,验证了ICA-PCA故障诊断法在化工流程仪表不同故障诊断中的有效性。     

Process identification based on last principal component analysis

A simple linear identification algorithm is presented in this paper. The last principal component (LPC), the eigenvector corresponding to the smallest eigenvalue of a non-negative symmetric matrix, contains an optimal linear relation of the column vectors of the data matrix. This traditional, well-known principal component analysis is extended to the generalized last principal component analysis (GLPC). For processes with colored measurement noise or disturbances, consistency of the GLPC estimator is achieved without involving iteration or non-linear numerical optimization. The proposed algorithm is illustrated by a simulated example and application to a pilot-scale process.     

Ensemble model of wastewater treatment plant based on rich diversity of principal component determining by genetic algorithm for status monitoring

Wastewater treatment plants (WWTPs) is a complex process, effective process monitoring can make it stable and prevent the destruction of the ecological environment. Principal component analysis (PCA) has been widely used in process monitoring. However, most PCA-based methods construct a single PCA model using several principal components (PCs), causing loss of information on some faults and less generalization ability of the PCA model. Thus, this study proposed a novel ensemble process monitoring method based on genetic algorithm (GA) for selective diversity of PCs. GA is used to determine a set of principal component subspaces with the greatest diversity as the base models. Bayesian inference is adopted to combine the results of base models into a probability index. Cases study on TE benchmark process and an actual WWTP show the excellent performance of the proposed method compared with several PCA-based methods and the strong generalization ability of the ensemble model.