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.

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.

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.

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.

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.

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.

Multivariate Cluster and Principle Component Analyses of Selected Yield Traits in Uzbek Bread Wheat Cultivars

Investigation of genetic diversity of geographically distant wheat genotypes is a useful approach in wheat breeding providing efficient crop varieties. This article presents multivariate cluster and principal component analyses (PCA) of some yield traits of wheat, such as thousand-kernel weight (TKW), grain number, grain yield and plant height. Based on the results, an evaluation of economically valuable attributes by eigenvalues made it possible to determine the components that significantly contribute to the yield of common wheat genotypes. Twenty-five genotypes were grouped into four clusters on the basis of average linkage. The PCA showed four principal components (PC) with eigenvalues > 1, explaining approximately 90.8% of the total variability. According to PC analysis, the variance in the eigenvalues was the greatest (4.33) for PC-1, PC-2 (1.86) and PC-3 (1.01). The cluster analysis revealed the classification of 25 accessions into four diverse groups. Averages, standard deviations and variances for clusters based on morpho-physiological traits showed that the maximum average values for grain yield (742.2), biomass (1756.7), grains square meter (18,373.7), and grains per spike (45.3) were higher in cluster C compared to other clusters. Cluster D exhibited the maximum thousand-kernel weight (TKW) (46.6).

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.

Robust Recommendation Algorithm Based on Kernel Principal Component Analysis and Fuzzy C-means Clustering

The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy c-means clustering. Firstly, we use kernel principal component analysis method to reduce the dimensionality of the original rating matrix, which can extract the effective features of users and items. Then, according to the dimension-reduced rating matrix and the high correlation characteristic between attack profiles, we use fuzzy c-means clustering method to cluster user profiles, which can realize the effective separation of genuine profiles and attack profiles. Finally, we construct an indicator function based on the attack detection results to decrease the influence of attack profiles on the recommendation, and incorporate it into the matrix factorization technology to design the corresponding robust recommendation algorithm. Experiment results indicate that the proposed algorithm is superior to the existing methods in both recommendation accuracy and robustness.

Adaptive multiblock kernel principal component analysis for monitoring complex industrial processes

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.

Multi-response optimization of Ti-6A1-4V turning operations using Taguchi-based grey relational analysis coupled with kernel principal component analysis

Ti-6A1-4V has a wide range of applications, especially in the aerospace field;however, it is a difficultto- cut material. In order to achieve sustainable machining of Ti?6A1-4V, multiple objectives considering not only economic and technical requirements but also the environmental requirement need to be optimized simultaneously. In this work, the optimization design of process parameters such as type of inserts, feed rate, and depth of cut for Ti-6A1-4V turning under dry condition was investigated experimentally. The major performance indexes chosen to evaluate this sustainable process were radial thrust, cutting power, and coefficient of friction at the toolchip interface. Considering the nonlinearity between the various objectives, grey relational analysis (GRA) was first performed to transform these indexes into the corresponding grey relational coefficients, and then kernel principal component analysis (KPCA) was applied to extract the kernel principal components and determine the corresponding weights which showed their relative importance. Eventually, kernel grey relational grade (KGRG) was proposed as the optimization criterion to identify the optimal combination of process parameters. The results of the range analysis show that the depth of cut has the most significant effect, followed by the feed rate and type of inserts. Confirmation tests clearly show that the modified method combining GRA with KPCA outperforms the traditional GRA method with equal weights and the hybrid method based on GRA and PCA.

基于String Kernel和KPCA的负实例语法特征提取算法

提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特征索引表设计了一个分类器,待检查的句子通过此分类器被分配到某个负实例特征表里进行匹配搜索,而此特征表的特征属性数和记录数要远远小于原始负实例数据库中的相应数目,从而大大提高了检查的速度,同时不影响语法检查的精度。通过比较测试,可看出提出的方法在保证语法检查精确度的同时有更快的速度。

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。

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。

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。

基于KPCA特征量降维的风电并网系统暂态电压稳定性评估

针对电力系统暂态电压稳定性评估中所需特征量数据庞大,影响模型训练时间,降低计算效率等问题,提出了一种基于核主成分分析方法KPCA和CPSO-BP组合的风电并网系统暂态电压稳定性评估方法.首先根据输入特征采集原始特征集,采用核主成分分析算法对特征量进行非线性数据处理,提取出最优的特征集.然后将降维后的特征集作为CPSO-BP神经网络输入量进行监督学习,将得到的模型按照临界故障切除时间裕度值的大小进行分类,将分类后的样本进行风电并网系统的暂态电压稳定性评估和临界故障切除时间裕度值预测.仿真分析结果表明,对输入特征进行降维,保留重要输入特征量,剔除冗余特征量,不仅简化了模型,还提高了网络评估的准确性和计算效率.