概率核主成分分析及其应用

主成分分析（PCA）、核主成分分析（KPCA）和概率主成分分析（PPCA）是已经取得广泛应用的特征提取方法。提出一种基于概率核主成分分析（PKPCA）的检测液晶屏幕亮点的方法。作为对PPCA的一种非线性扩展,PKPCA在PPCA的基础上引入了核函数方法,因而其捕获模式非线性特征的能力更强。在KPCA和PPCA的基础上推导了PKPCA过程公式,并在检测液晶屏幕亮点的应用中将PKPCA、PPCA、PCA算法进行比较。实验结果表明,PKPCA的检测率和局部信噪比优于其他两者。     

基于GMM的间歇过程故障检测

对间歇过程的多操作阶段进行划分时,往往会被离群点和噪声干扰,影响建模的精确性,针对此问题提出一种新的方法:主元分析--多方向高斯混合模型(Principal component analysis-multiple Gaussian mixture model, PCA-MGMM)建模方法.首先用最短长度法对数据进行等长处理,融合不同展开方法相结合的处理方式消除数据预估问题;利用主元分析方法将数据转换到对故障较为敏感的低维子空间中,得到主元的同时消除了离群点和噪声的干扰;通过改进的高斯混合模型(Gaussian mixture model, GMM)算法对各阶段主元进行聚类,减少了运算量的同时自动得到最佳高斯成分和对应的统计分布参数;最后将局部指标融合为全局概率监控指标,实现了连续的在线监控.通过一个实际的半导体制造过程的仿真研究验证了所提方法的有效性.     

基于动态概率主元分析的统计过程监测

概率主元分析(PPCA)已广泛应用于工业过程监测.然而,PPCA法仅构造了生产过程的静态线性关系,处理具有较强动态特性的实际工业生产过程效果较差.为此提出动态概率主元分析(DPPCA)法,对经过时谱扩展后的变量数据阵,通过期望最大化(EM)算法建立生成模型,从而将静态PPCA推广到动态多变量过程.最后将此法应用于TE过程的仿真研究,结果表明该法有效.     

改进PCA在发酵过程监测与故障诊断中的应用

提出一种改进的主元分析(PCA)法．利用主元相关变量残差统计量代替平方预测误差Q统计量,并采用累积方差贡献率及复相关系数确定PCA模型的主元数．将改进的主元分析法应用于粘菌素发酵过程监测和故障诊断中,仿真结果表明改进的PCA方法避免了Q统计量的保守性,并保证了主元子空间中的信忠存量．与一种基于特征子空间的系统性能监控方法相比较,改进的PCA方法具有更强的有效性．     

基于概率PCA过程监控中遗失数据的重构

在实际工业过程中,PCA常常被用于数据重构。但是相比于概率PCA(PPCA),PCA无论在建模上还是在统计监控指标上都存在一些缺陷。基于此,本文提出一种基于PPCA的遗失数据重构方法。通过使样本数据点与其在PPCA模型上的投影点之问的距离最小,该方法能够有效地进行数据重构。此外,还分析了使样本数据白化值最小的数据重构方法。在田纳西-伊斯曼过程中的应用验证了其有效性。     

基于PCA算法的人脸识别

介绍了隐马尔可夫特征脸模型（HMEM）,由概率性主成分分析方法（PPCA）与离散空间马尔可夫模型法（SL-HMM）整合而成,具有PPCA和SL-HMM的双重特性。利用ORL数据库进行人脸识别实验,结果说明该模型在性能上表现出较大的优势。     

基于分段主元分析的变负荷过程监控方法

针对变负荷的多工况过程,提出了一种基于分段主元分析的监控方法。对于稳态工况,直接利用历史数据建立不同负荷下的主元监控模型。对于工况之间的过渡过程,根据先验知识可将其划分为跟踪时段和调节时段。在两大时段内分别将训练数据细分为多个子时段,进而在每一子时段内设定参考轨迹,利用训练数据与参考轨迹的残差建立主元监控模型,并采用改进的层次聚类算法合并特性相近的时段。在线监控时,根据负荷设定信息判断过程所处的工况,再选择相应的主元模型进行监控。在Alstom气化炉中的应用结果表明,该算法不仅能够避免传统多模型监控方法在工况过渡时出现的大量误警,也能在过渡过程中实现准确的故障检测。     

基于特征样本的KPCA在故障诊断中的应用

核函数主元分析（KPCA）可用于非线性过程监控.建立KPCA模型首先要计算核矩阵K,K的维数等于训练样本的数量,对于大样本集,计算K很困难.对此提出一种基于特征样本的KPCA（SKPCA）,其基本思想是,首先利用非线性映射函数将输入空间映射到特征子空间,然后在特征子空间中计算主元.将SKPCA应用于监控Tennessee Eastman过程,并与基于全体样本的KPCA作比较,仿真结果显示,二者诊断结果基本相同,然而特征样本只是训练样本中的一小部分,因此减少了K的维数,解决了K的计算问题.     

基于KPCA-PNN的复杂工业过程集成故障辨识方法

针对核主元分析方法在复杂工业在线监控过程中易出现的核矩阵KKK难以计算和初始故障源难以辨识的问题,提出了一种基于核主元分析和概率神经网络的集成故障辨识方法．首先通过特征样本提取方法预处理工业数据集,然后采用核函数主元分析的Hotelling统计量T2和SPE方法检测故障,采用核函数梯度算法定义了两个新的统计量CT2和CSPE,计算了每个监控变量对统计量T2和SPE的贡献程度,并提取了故障特征．最后,利用概率神经网络技术进一步从关联故障特征中辨识出初始故障源．将上述故障诊断方法应用到TennesseeEastman（TE）化工过程;多种故障模式下的仿真结果显示,该方法能够有效地检测并辨识出多种故障类型．     

基于稀疏主元分析的过程监控研究

主元分析（principal component analysis）是一种多元统计技术,在过程监控和故障诊断中具有广泛的应用。针对过程监控中数据量大的特点,提出一种稀疏主元分析（sparse principal component analysis）方法,通过引入lasso约束函数,构建稀疏主元分析的框架,将PCA降维问题转化为回归最优化问题,从而求解得到稀疏化的主元,并提高了主元模型的抗干扰能力。由于稀疏后主元相关的数据量减少,利用数据建立过程监控模型,减少了计算量,并缩短了计算时间,进而提高了监控的实时性。利用田纳西伊斯特曼过程（TE processes）进行实验仿真,并与传统的主元分析方法进行对比研究。结果表明,新提出的稀疏主元分析方法在计算效率和监控实时性上均优于传统的主元分析方法。     

Probabilistic contribution analysis for statistical process monitoring: A missing variable approach

Probabilistic models, including probabilistic principal component analysis (PPCA) and PPCA mixture models, have been successfully applied to statistical process monitoring. This paper reviews these two models and discusses some implementation issues that provide alternative perspective on their application to process monitoring. Then a probabilistic contribution analysis method, based on the concept of missing variable, is proposed to facilitate the diagnosis of the source behind the detected process faults. The contribution analysis technique is demonstrated through its application to both PPCA and PPCA mixture models for the monitoring of two industrial processes. The results suggest that the proposed method in conjunction with PPCA model can reduce the ambiguity with regard to identifying the process variables that contribute to process faults. More importantly it provides a fault identification approach for PPCA mixture model where conventional contribution analysis is not applicable.     

Automatic Model Selection by Cross-Validation for Probabilistic PCA

The Mixture of Probabilistic Principal Components Analyzers (MPPCA) is a multivariate analysis technique which defines a Gaussian probabilistic model at each unit. The numbers of units and principal directions in each unit are not learned in the original approach. Variational Bayesian approaches have been proposed for this purpose, which rely on assumptions on the probability distributions of the MPPCA parameters. Here we present a different way to solve this problem, where cross-validation and simulated annealing are combined to guide the search for an optimal model selection, providing a structured strategy to escape from suboptimal configurations. This allows to learn the model architecture without the need of any assumptions other than those of the basic PPCA framework. Experimental results are presented, which show the probability density estimation and missing value imputation features of the proposal.     

Probabilistic PCA Self-Organizing Maps

In this paper, we present a probabilistic neural model, which extends Kohonen's self-organizing map (SOM) by performing a probabilistic principal component analysis (PPCA) at each neuron. Several SOMs have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model while it has a low complexity on the dimensionality of the input space. This allows to process very high-dimensional data to obtain reliable estimations of the probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high-dimensional data, and its potential in image and video compression applications.     

Spatio-temporal context for robust multitarget tracking

In multitarget tracking, the main challenge is to maintain the correct identity of targets even under occlusions or when differences between the targets are small. The paper proposes a new approach to this problem by incorporating the context information. The context of a target in an image sequence has two components: the spatial context including the local background and nearby targets and the temporal context including all appearances of the targets that have been seen previously. The paper considers both aspects. We propose a new model for multitarget tracking based on the classification of each target against its spatial context. The tracker searches a region similar to the target while avoiding nearby targets. The temporal context is included by integrating the entire history of target appearance based on probabilistic principal component analysis (PPCA). We have developed a new incremental scheme that can learn the full set of PPCA parameters accurately online. The experiments show robust tracking performance under the condition of severe clutter, occlusions, and pose changes     

Robust monitoring and fault reconstruction based on variational inference component analysis

Probabilistic models such as probabilistic principal component analysis (PPCA) have recently caught much attention in the process monitoring area. An important issue of the PPCA method is how to determine the dimensionality of the latent variable space. In the present paper, one of the most popular Bayesian type chemometric methods, Bayesian PCA (BPCA) is introduced for process monitoring purpose, which is based on the recent developed variational inference algorithm. In this monitoring framework, the effectiveness of each extracted latent variable can be well reflected by a hyperparameter, upon which the dimensionality of the latent variable space can be automatically determined. Meanwhile, for practical consideration, the developed BPCA-based monitoring method is robust to missing data and can also give satisfactory performance under limited data samples. Another contribution of this paper is due to the proposal of a new fault reconstruction method under the BPCA model structure. Two case studies are provided to evaluate the performance of the proposed method.     

A low-cost variational-Bayes technique for merging mixtures of probabilistic principal component analyzers

Mixtures of probabilistic principal component analyzers (MPPCA) have shown effective for modeling high-dimensional data sets living on non-linear manifolds. Briefly stated, they conduct mixture model estimation and dimensionality reduction through a single process. This paper makes two contributions: first, we disclose a Bayesian technique for estimating such mixture models. Then, assuming several MPPCA models are available, we address the problem of aggregating them into a single MPPCA model, which should be as parsimonious as possible. We disclose in detail how this can be achieved in a cost-effective way, without sampling nor access to data, but solely requiring mixture parameters. The proposed approach is based on a novel variational-Bayes scheme operating over model parameters. Numerous experimental results and discussion are provided.     

Reconstruction-based multivariate contribution analysis for fault isolation: A branch and bound approach

Identification of faulty variables is an important component of multivariate statistical process monitoring (MSPM); it provides crucial information for further analysis of the root cause of the detected fault. The main challenge is the large number of combinations of process variables under consideration, usually resulting in a combinatorial optimization problem. This paper develops a generic reconstruction based multivariate contribution analysis (RBMCA) framework to identify the variables that are the most responsible for the fault. A branch and bound (BAB) algorithm is proposed to efficiently solve the combinatorial optimization problem. The formulation of the RBMCA does not depend on a specific model, which allows it to be applicable to any MSPM model. We demonstrate the application of the RBMCA to a specific model: the mixture of probabilistic principal component analysis (PPCA mixture) model. Finally, we illustrate the effectiveness and computational efficiency of the proposed methodology through a numerical example and the benchmark simulation of the Tennessee Eastman process.     

A new image representation algorithm inspired by image submodality models, redundancy reduction, and learning in biological vision

We develop a new biologically motivated algorithm for representing natural images using successive projections into complementary subspaces. An image is first projected into an edge subspace spanned using an ICA basis adapted to natural images which captures the sharp features of an image like edges and curves. The residual image obtained after extraction of the sharp image features is approximated using a mixture of probabilistic principal component analyzers (MPPCA) model. The model is consistent with cellular, functional, information theoretic, and learning paradigms in visual pathway modeling. We demonstrate the efficiency of our model for representing different attributes of natural images like color and luminance. We compare the performance of our model in terms of quality of representation against commonly used basis, like the discrete cosine transform (DCT), independent component analysis (ICA), and principal components analysis (PCA), based on their entropies. Chrominance and luminance components of images are represented using codes having lower entropy than DCT, ICA, or PCA for similar visual quality. The model attains considerable simplification for learning from images by using a sparse independent code for representing edges and explicitly evaluating probabilities in the residual subspace.     

A probabilistic principal component analysis-based approach in process monitoring and fault diagnosis with application in wastewater treatment plant

Probabilistic principal component analysis (PPCA) based approaches have been widely used in the field of process monitoring. However, the traditional PPCA approach is still limited to linear dimensionality reduction. Although the nonlinear projection model of PPCA can be obtained by Gaussian process mapping, the model still lacks robustness and is susceptible to process noise. Therefore, this paper proposes a new nonlinear process monitoring and fault diagnosis approach based on the Bayesian Gaussian latent variable model (Bay-GPLVM). Bay-GPLVM can obtain the posterior distribution rather than point estimation for latent variables, so the model is more robust. Two monitoring statistics corresponding to latent space and residual space are constructed for PM-FD purpose. Further, the cause of fault is analyzed by calculating the gradient value of the variable at the fault point. Compared with several PPCA-based monitoring approaches in theory and practical application, the Bay-GPLVM-based process monitoring approach can better deal with nonlinear processes and show high efficiency in process monitoring.     

Dimensionality reduction for multivariate time-series data mining

A multivariate time series is one of the most important objects of research in data mining. Time and variables are two of its distinctive characteristics that add the complication of the algorithms applied to data mining. Reduction in the dimensionality is often regarded as an effective way to address these issues. In this paper, we propose a method based on principal component analysis (PCA) to effectively reduce the dimensionality. We call it “piecewise representation based on PCA” (PPCA), which segments multivariate time series into several sequences, calculates the covariance matrix for each of them in terms of the variables, and employs PCA to obtain the principal components in an average covariance matrix. The results of the experiments, including retained information analysis, classification, and a comparison of the central processing unit time consumption, demonstrate that the PPCA method used to reduce the dimensionality in multivariate time series is superior to the prior methods.