Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

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.

Kernel principal component analysis network for image classification

In order to classify nonlinear features with a linear classifier and improve the classification accuracy, a deep learning network named kernel principal component analysis network（ KPCANet） is proposed. First, the data is mapped into a higher-dimensional space with kernel principal component analysis to make the data linearly separable. Then a two-layer KPCANet is built to obtain the principal components of the image. Finally, the principal components are classified with a linear classifier. Experimental results showthat the proposed KPCANet is effective in face recognition, object recognition and handwritten digit recognition. It also outperforms principal component analysis network（ PCANet） generally. Besides, KPCANet is invariant to illumination and stable to occlusion and slight deformation.

NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS

In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.

Kernel Generalization of Multi-Rate Probabilistic Principal Component Analysis for Fault Detection in Nonlinear Process

In practical process industries,a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes,which indicates that the measurements coming from different sources are collected at different sampling rates.To build a complete process monitoring strategy,all these multi-rate measurements should be considered for data-based modeling and monitoring.In this paper,a novel kernel multi-rate probabilistic principal component analysis(K-MPPCA)model is proposed to extract the nonlinear correlations among different sampling rates.In the proposed model,the model parameters are calibrated using the kernel trick and the expectation-maximum(EM)algorithm.Also,the corresponding fault detection methods based on the nonlinear features are developed.Finally,a simulated nonlinear case and an actual pre-decarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL-BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.

Sparse flight spotlight mode 3-D imaging of spaceborne SAR based on sparse spectrum and principal component analysis

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.

Compressive Sensing Sparse Sampling Method for Composite Material Based on Principal Component Analysis

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.

Application of Particle Swarm Optimization to Fault Condition Recognition Based on Kernel Principal Component Analysis

Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.

基于SMOTE-IKPCA-SeNet深度迁移学习的小批量生产质量预测研究

随着智能制造技术的发展和客户个性化需求的增加,多品种小批量生产方式逐渐成为制造业的主流。面向大批量生产、以统计过程控制为核心的质量管理方式并不适用于小批量生产。针对复杂生产过程存在参数多、非线性和交互作用的问题,提出利用深度迁移学习的方式将历史生产数据作为源域迁移至小样本目标产品数据进行质量预测。首先,通过合成少数类过采样技术(synthetic minority over-sampling technique,SMOTE)和改进的核主成分分析(improved kernel principal component analysis,IKPCA)算法筛选源域和目标域的可迁移特征,这不仅兼顾了特征重要性和可迁移性,还减少了“负迁移”,提高了模型泛化能力;然后,采用结合通道注意力机制的卷积神经网络SeNet构建基于深度迁移学习的质量预测模型。仿真结果表明,随着目标域样本的增加,所提方法的预测准确性明显优于广泛采用的支持向量机建模方法。同时,所提可迁移特征筛选方法显著提高了深度迁移学习的质量预测效果,为复杂的小批量生产过程质量保证提供了新方法。

Statistical Monitoring of Chemical Processes Based on Sensitive Kernel Principal Components

The kernel principal component analysis （KPCA） method employs the first several kernel principal components （KPCs）, which indicate the most variance information of normal observations for process monitoring, but may not reflect the fault information. In this study, sensitive kernel principal component analysis （SKPCA） is proposed to improve process monitoring performance, i.e., to deal with the discordance of T2 statistic and squared prediction error SVE statistic and reduce missed detection rates. T2 statistic can be used to measure the variation di rectly along each KPC and analyze the detection performance as well as capture the most useful information in a process. With the calculation of the change rate of T2 statistic along each KPC, SKPCA selects the sensitive kernel principal components for process monitoring. A simulated simple system and Tennessee Eastman process are employed to demonstrate the efficiency of SKPCA on online monitoring. The results indicate that the monitoring performance is improved significantly.

Comparison of Kernel Entropy Component Analysis with Several Dimensionality Reduction Methods

Dimensionality reduction techniques play an important role in data mining. Kernel entropy component analysis( KECA) is a newly developed method for data transformation and dimensionality reduction. This paper conducted a comparative study of KECA with other five dimensionality reduction methods,principal component analysis( PCA),kernel PCA( KPCA),locally linear embedding( LLE),laplacian eigenmaps( LAE) and diffusion maps( DM). Three quality assessment criteria, local continuity meta-criterion( LCMC),trustworthiness and continuity measure(T&C),and mean relative rank error( MRRE) are applied as direct performance indexes to assess those dimensionality reduction methods. Moreover,the clustering accuracy is used as an indirect performance index to evaluate the quality of the representative data gotten by those methods. The comparisons are performed on six datasets and the results are analyzed by Friedman test with the corresponding post-hoc tests. The results indicate that KECA shows an excellent performance in both quality assessment criteria and clustering accuracy assessing.

A deep kernel method for lithofacies identification using conventional well logs

How to fit a properly nonlinear classification model from conventional well logs to lithofacies is a key problem for machine learning methods.Kernel methods(e.g.,KFD,SVM,MSVM)are effective attempts to solve this issue due to abilities of handling nonlinear features by kernel functions.Deep mining of log features indicating lithofacies still needs to be improved for kernel methods.Hence,this work employs deep neural networks to enhance the kernel principal component analysis(KPCA)method and proposes a deep kernel method(DKM)for lithofacies identification using well logs.DKM includes a feature extractor and a classifier.The feature extractor consists of a series of KPCA models arranged according to residual network structure.A gradient-free optimization method is introduced to automatically optimize parameters and structure in DKM,which can avoid complex tuning of parameters in models.To test the validation of the proposed DKM for lithofacies identification,an open-sourced dataset with seven con-ventional logs(GR,CAL,AC,DEN,CNL,LLD,and LLS)and lithofacies labels from the Daniudi Gas Field in China is used.There are eight lithofacies,namely clastic rocks(pebbly,coarse,medium,and fine sand-stone,siltstone,mudstone),coal,and carbonate rocks.The comparisons between DKM and three commonly used kernel methods(KFD,SVM,MSVM)show that(1)DKM(85.7%)outperforms SVM(77%),KFD(79.5%),and MSVM(82.8%)in accuracy of lithofacies identification;(2)DKM is about twice faster than the multi-kernel method(MSVM)with good accuracy.The blind well test in Well D13 indicates that compared with the other three methods DKM improves about 24%in accuracy,35%in precision,41%in recall,and 40%in F1 score,respectively.In general,DKM is an effective method for complex lithofacies identification.This work also discussed the optimal structure and classifier for DKM.Experimental re-sults show that(m_(1),m_(2),O)is the optimal model structure and linear svM is the optimal classifier.(m_(1),m_(2),O)means there are m KPCAs,and then m2 residual units.A workflow to determine an optimal classifier in DKM for lithofacies identification is proposed,too.

Kernel Factor Analysis Algorithm with Varimax

Kernal factor analysis （KFA） with vafimax was proposed by using Mercer kernel function which can map the data in the original space to a high-dimensional feature space, and was compared with the kernel principle component analysis （KPCA）. The results show that the best error rate in handwritten digit recognition by kernel factor analysis with vadmax （4.2%） was superior to KPCA （4.4%）. The KFA with varimax could more accurately image handwritten digit recognition.

Color Estimation for Thermal Infrared Imagery Based on Kernel PCA and Sparse Representation

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.

基于KPCA-CNN-DBiGRU模型的短期负荷预测方法

本文针对已有神经网络模型在短期负荷预测中输入维度过高、预测误差较大等问题,提出了一种结合核主成分分析、卷积神经网络和深度双向门控循环单元的短期负荷预测方法。先运用核主成分分析法对原始高维输入变量进行降维,再通过卷积深度双向门控循环单元网络模型进行负荷预测。以第九届全国电工数学建模竞赛试题A题中的负荷数据作为实际算例,结果表明所提方法较降维之前预测误差大大降低,与已有预测方法相比也有大幅的误差降低。

基于KPCA-PSO-ELM算法的地表水化学需氧量紫外-可见吸收光谱检测研究

化学需氧量(COD)是水质检测重要指标之一,反映水体有机物含量。传统的COD化学检测方法存在操作繁琐,等待时间长,二次污染等缺点。紫外-可见吸收光谱法是目前水体化学需氧量检测中应用最为广泛的方法之一,具有检测快速、无污染等特点。为了满足地表水化学需氧量快速、实时、在线监测等要求,采用紫外-可见吸收光谱进行测量,提出了内核主成分分析(KPCA)结合粒子群优化极限学习机(PSO-ELM)预测模型,满足当前对地表水化学需氧量快速、实时监测的要求。对光谱进行Savitzky-Golay(SG)滤波以降低随机噪声的影响;用积分光谱代替原光谱,以降低信号波动带来的影响;再将得到的光谱信息归一化,消除不同光谱数据量纲的影响。将预处理后的数据利用KPCA算法将全光谱数据压缩为5个特征,有效解决光谱信息冗余的问题;采用PSO算法对ELM的权重和偏置进行优化极大提高了模型的精度。对217个河流、长江及支流、湖库等地表水样本按照7∶3随机划分成训练集和测试集,并进行建模测试,其中训练集拟合优度(R2)为0.930 2、均方根误差(RMSE)为0.363 0 mg·L^(-1)、测试集拟合优度R2为0.931 9、均方根误差(RMSE)为0.400 7 mg·L^(-1)。为了验证提出的基于KPCA全光谱数据压缩方法对预测模型的提升效果,分别对比了主成分分析(PCA)、连续投影算法(SPA)、套索回归(LASSO)等特征处理算法。PCA-PSO-ELM模型的RMSE为0.715 1 mg·L^(-1)、 SPA-PSO-ELM模型的RMSE为0.473 7 mg·L^(-1)、 LASSO-PSO-ELM模型的RMSE为0.412 6 mg·L^(-1), KPCA-PSO-ELM模型较上述三种模型,RMSE分别降低了78.46%、 18.22%、 2.97%,结果表明KPCA是一种高效的光谱降维算法,能够有效消除光谱冗余信息,提升模型预测精度。基于KPCA-PSO-ELM预测模型结合紫外-可见吸收光谱可以实现对地表水COD快速、实时检测,为在线COD检测场景提供方法支撑。

多策略改进黏菌算法阶段优化HSVM变压器故障辨识

为解决变压器故障诊断精度较低的问题,提出了一种多策略改进黏菌算法(ISMA)阶段优化混合核支持向量机(HSVM)的变压器故障诊断新方法。首先,利用主成分分析(PCA)来消除变量之间的信息冗余并降低数据集维度。其次,引入黏菌算法(SMA),并结合Logistic混沌映射、二次插值、自适应权重多策略改进SMA,以提高SMA算法收敛速度和局部搜索能力;然后,与原始SMA、WHO和GWO算法进行寻优测试,对比验证改进后SMA算法的优越性;最后,使用改进SMA算法分阶段对混合核支持向量机参数寻优,构建ISMA-HSVM变压器故障诊断模型。将降维后的特征数据输入HSVM模型与BPPN、ELM和SVM进行比较,HSVM模型的诊断准确性分别提高了5.55%、8.89%、5.55%。使用ISMA优化HSVM模型参数,与WHO、GWO、SMA算法优化效果比较,结果准确性提高了13.33%、12.22%、5.55%。其中,ISMA-HSVM模型的诊断精度为93.33%。实验结果表明,所提模型有效提升故障诊断分类性能,且具有较高的故障诊断精度。

基于KPCA与KLPP及Wilks统计量的留兰香三维荧光数据特征提取与鉴别分析

为实现留兰香产地的快速鉴别,该研究提出了一种核主成分分析(kernel principal component analysis,KPCA)与核局部保持投影(kernel locality preserving projections,KLPP)及WilksΛ统计量序贯融合的特征波长提取策略,在此基础上鉴别5个产地的留兰香。首先,在采集5个产地300个留兰香样本的三维荧光数据后,运用三角形内插值法去除原始光谱中的瑞利散射和拉曼散射,并运用SG(Savitzky-Golay)对数据进行平滑预处理。然后,对预处理后的荧光光谱数据分别利用KPCA、KPCA+KLPP、KPCA+WilksΛ统计量、 KPCA+KLPP+WilksΛ统计量4种方法提取特征激发波长和特征发射波长。接着,按特征激发波长从小到大顺序将其对应的特征发射波长光谱值首尾相连转换成行向量;4种方法从300个样本中各得到1个300行的特征波长光谱值矩阵。再者,运用Fisher判别分析(fisher discriminant analysis,FDA)对特征波长光谱值矩阵进行数据可分性融合,生成可分性FD(fisher discriminant)变量。选取前4个累计判别能力达到99%的FD变量作为鉴别模型的输入向量。最后,用支持向量机(support vector machine,SVM)算法分析4个FD变量,分别得到对应于4种特征提取波长方法的FDA+SVM鉴别结果,其正确率分别为92.00%、96.00%、94.67%、100%。结果表明,所提出的KPCA+KLPP+WilksΛ统计量序贯融合的特征波长提取策略能够有效减少三维荧光光谱数据的冗余,并能表征原始荧光数据的信息特征,实现了5种留兰香产地的正确鉴别。该研究可为后续利用三维荧光光谱开展留兰香重要组分量化分析提供一定的基础。

流程生产安全数智化监测系统传感器故障诊断研究

为保障流程生产安全监测数据的准确性,提出1种结合核主元分析和累积残差贡献率法的故障诊断方法。首先提出“感知-汇聚-决策”的多层级数智化监控系统架构;针对感知层传感器,基于核主元分析构建故障检测模型并通过累积残差贡献率法定位故障传感器;以DYTG转炉厂连铸作业区进行实证分析。研究结果表明:该故障诊断方法在SPE指标上的平均检测率和平均误检率分别为95.28%和2.61%,在T^(2)指标上的平均检测率和平均误检率分别为84.36%和1.71%,且针对4种故障形式均能精准定位故障传感器。研究结果有助于降低监测系统的维护成本,提升流程生产安全管控水平。