Local Principal Component Analysis Models Research Articles

Data fusion of Raman spectra in MSPC for fault detection and diagnosis in pharmaceutical manufacturing

This study investigates the use of Raman spectroscopy fused with other types of data (e.g., pH, temperature and turbidity) for multivariate statistical process control of two pharmaceutical case studies: one simulated industrial-scale fed-batch process for the production of penicillin and one real lab-scale crystallization process. The monitoring schemes are built on local principal component analysis models and hyper-parameters are tuned with regards to highest accuracy in fault detection. Accuracies above 90% are obtained for all types of data and level of DF. Furthermore, for the first case study the model built solely on spectra achieves higher fault detection rates, when only considering faults that also result in off-specification quality. This is supported by the fact that the fault is not necessarily detected when it occurs, but rather when it starts to affect quality variables as measured by the spectra.

GMM and optimal principal components-based Bayesian method for multimode fault diagnosis

Principal component analysis (PCA) serves as the most fundamental technique in multivariate statistical process monitoring. However, other than determining contributions to a fault from each variable based on the pre-selected major principal components (PCs), the PCA-based fault diagnosis with an optimal selection of PCs is seldom investigated. This paper presents a novel Gaussian mixture model (GMM) and optimal principal components (OPCs)-based Bayesian method for efficient multimode fault diagnosis. First, the GMM and Bayesian inference is utilized to identify the operating mode, and then local PCA model is established in each mode. Second, given that the various principal components (PCs) may contain distinct fault signatures, the behavior of each PC in local PCA is examined and the OPCs are selected through stochastic optimization algorithm. Based on the OPCs, a Bayesian diagnosis system is then formulated to identify the fault statuses in a probability manner. Performance of GMM–OPC Bayesian diagnosis is examined through a numerical example and the Tennessee Eastman challenge process. The efficiency and feasibility are demonstrated.

Field-Based near Infrared Spectroscopy for Analysis of Scandinavian Stone Age Rock Paintings

During the early autumn of 2014 a field-based near infrared (NIR) spectroscopy study was carried out at Swedish and Norwegian Stone Age rock painting sites. This article presents results from one of them, namely Flatruet, Härjedalen, Sweden. Here, field-based NIR measurements were conducted using the 908–1676 nm wavelength range to gather 479 spectra: 427 of rock paintings and 52 of local lithology background. The whole dataset was analysed using principal component analysis (PCA) and four principal components were extracted explaining 98.5% (PC1), 1.4% (PC2), 0.06% (PC3) and 0.04% (PC4). The PCA results showed that there was a large spread in the spectra of both background and red paint objects, but also some evidence of clustering could be seen where background and paintings could be separated. An improvement in separation was achieved with partial least squares discriminant analysis (PLS-DA) using the background and paint as categorical variables. The most important components of the PLS-DA model showed a better separation in the score plot. A small test set of 10 paint and 10 background samples showed that one of the paint samples and two of the background samples were misclassified. One conclusion is that there is a large spread in background due to varying precipitation of secondary iron oxides. It was also decided to look deeper into local models of painted elks and their pigments alone. This was done using local PCA models and soft independent modelling of class analogies showing that some painted elks could be separated from each other while others were quite similar, which is important for answering questions about origin, age and weathering.

Leukemia and small round blue-cell tumor cancer detection using microarray gene expression data set: Combining data dimension reduction and variable selection technique

Using gene expression data in cancer classification plays an important role for solving the fundamental problems relating to cancer diagnosis. Because of high throughput of gene expression data for healthy and patient samples, a variable selection method can be applied to reduce complexity of the model and improve the classification performance. Since variable selection procedures pose a risk of over-fitting, when a large number of variables with respect to sample are used, we have proposed a method for coupling data dimension reduction and variable selection in the present study. This approach uses the concept of variable clustering for the original data set. Significant components of local principal component analysis models have just been retained from all clusters. Then, the variable selection algorithm is performed on these locally derived principal component variables. The proposed algorithm has been evaluated on two gene expression data sets; namely, acute Leukemia and small round blue-cell tumor (SRBCT). Our results confirmed that the classification models achieved on the reduced data were better than those obtained on the entire microarray gene expression profile.

Local matrix adaptation in topographic neural maps

The self-organizing map (SOM) and neural gas (NG) and generalizations thereof such as the generative topographic map constitute popular algorithms to represent data by means of prototypes arranged on a (hopefully) topology representing map. Most standard methods rely on the Euclidean metric, hence the resulting clusters tend to have isotropic form and they cannot account for local distortions or correlations of data. For this reason, several proposals exist in the literature which extend prototype-based clustering towards more general models which, for example, incorporate local principal directions into the winner computation. This allows to represent data faithfully using less prototypes. In this contribution, we establish a link of models which rely on local principal components (PCA), matrix learning, and a formal cost function of NG and SOM which allows to show convergence of the algorithm. For this purpose, we consider an extension of prototype-based clustering algorithms such as NG and SOM towards a more general metric which is given by a full adaptive matrix such that ellipsoidal clusters are accounted for. The approach is derived from a natural extension of the standard cost functions of NG and SOM (in the form of Heskes). We obtain batch optimization learning rules for prototype and matrix adaptation based on these generalized cost functions and we show convergence of the algorithm. The batch optimization schemes can be interpreted as local principal component analysis (PCA) and the local eigenvectors correspond to the main axes of the ellipsoidal clusters. Thus, this approach provides a cost function associated to proposals in the literature which combine SOM or NG with local PCA models. We demonstrate the behavior of matrix NG and SOM in several benchmark examples and in an application to image compression.

Classification of GC‐MS measurements of wines by combining data dimension reduction and variable selection techniques

AbstractDifferent classification methods (Partial Least Squares Discriminant Analysis, Extended Canonical Variates Analysis and Linear Discriminant Analysis), in combination with variable selection approaches (Forward Selection and Genetic Algorithms), were compared, evaluating their capabilities in the geographical discrimination of wine samples. Sixty‐two samples were analysed by means of dynamic headspace gas chromatography mass spectrometry (HS‐GC‐MS) and the entire chromatographic profile was considered to build the dataset. Since variable selection techniques pose a risk of overfitting when a large number of variables is used, a method for coupling data dimension reduction and variable selection was proposed. This approach compresses windows of the original data by retaining only significant components of local Principal Component Analysis models. The subsequent variable selection is then performed on these locally derived score variables. The results confirmed that the classification models achieved on the reduced data were better than those obtained on the entire chromatographic profile, with the exception of Extended Canonical Variates Analysis, which gave acceptable models in both cases. Copyright © 2008 John Wiley & Sons, Ltd.

Fault Detection Based on a Maximum-Likelihood Principal Component Analysis (PCA) Mixture

Multivariate statistical process control (MSPC) that is based on principal component analysis (PCA) has been applied to many industrial processes. Such an approach assumes that the process signals are normally distributed and exhibit stationary behavior. These assumptions significantly limit the range of applicability of the methodology. In this paper, a monitoring scheme based on a maximum-likelihood PCA (MLPCA) mixture is proposed. The main idea behind the approach is that complex data patterns obtained from a process can be described by several local models. A learning algorithm that helps determine model structure, i.e., the number of local PCA models to be constructed and the number of principal components to be included in each local model, is proposed, resulting in the efficient determination of a MLPCA mixture model. Two monitoring statistics used in the MLPCA-based monitoring scheme are then derived and a two-step fault detection method is proposed. Several mathematical models that describe different process features, including multiple steady states, nonlinearity, and process dynamics, are used to demonstrate the potential of the proposed method. The approach is compared with previous approaches, including nonlinear PCA and dynamic PCA, and it is confirmed that the developed methodology is a good alternative. Finally, the method is applied for fault detection on a continuously stirred tank reactor process, and its performance for detecting six types of faults, in terms of false alarm rate, missed alarm rate, and detection delay, is shown to outperform current approaches.

ファジィクラスタリングを用いた主成分分析における変量選択とデータマイニングへの応用

Knowledge discovery in databases (KDD) or data mining involves fitting models to or determining patterns from high dimensional data sets, and extraction of correlation rules plays an important role. This paper proposes a new approach to knowledge discovery with linear model estimation, in which principal component analysis (PCA) is performed by selecting variables. The proposed algorithm is a hybrid of fuzzy clustering and PCA based on lower rank approximation of data matrix, in which the relative responsibilities of the variables are estimated by using possibilistic constraint for memberships. The proposed algorithm is also enhanced to a local PCA model that can be used for data mining by performing both of linear model estimation and stratified sampling.

Integrated methodology for forensic oil spill identification.

A new integrated methodology for forensic oil spill identification is presented. It consists of GC-MS analysis, chromatographic data processing, variable-outlier detection, multivariate data analysis, estimation of uncertainties, and statistical evaluation. The methodology was tested on four groups of diagnostic ratios composed of petroleum biomarkers and ratios within homologous PAH categories. Principal component analysis (PCA) was employed and enabled the simultaneous analysis of many diagnostic ratios. Weathering was taken into account by considering the sampling uncertainties estimated from replicate spill samples. Statistical evaluation ensured an objective matching of oil spill samples with suspected source oils as well as classification into positive match, probable match, and nonmatch. The data analysis is further refined if two or more source oils are classified as probable match by using weighted least squares fitting of the principal components, local PCA models, and additional information relevant to the spill case. The methodology correctly identified the source of two spill samples (i.e., crude oils from Oseberg East and Oseberg Field Centre) and distinguished them from closely related source oils.

Topological local principal component analysis

In help of the Kohonen's self-organizing maps we present a topological local principal component analysis model which is capable of exploiting both the global topological structure and each local cluster structure. A newly proposed self-organizing strategy that can enhance the learning speed is introduced to train the model.

Improved system for object detection and star/galaxy classification via local subspace analysis

The two traditional tasks of object detection and star/galaxy classification in astronomy can be automated by neural networks because the nature of the problems is that of pattern recognition. A typical existing system can be further improved by using one of the local Principal Component Analysis (PCA) models. Our analysis in the context of object detection and star/galaxy classification reveals that local PCA is not only superior to global PCA in feature extraction, but is also superior to gaussian mixture in clustering analysis. Unlike global PCA which performs PCA for the whole data set, local PCA applies PCA individually to each cluster of data. As a result, local PCA often outperforms global PCA for data of multi-modes. Moreover, since local PCA can effectively avoid the trouble of having to specify a large number of free elements of each covariance matrix of gaussian mixture, it can give a better description of local subspace structures of each cluster when applied on high dimensional data with small sample size. In this paper, the local PCA model proposed by Xu [IEEE Trans. Neural Networks 12 (2001) 822] under the general framework of Bayesian Ying Yang (BYY) normalization learning will be adopted. Endowed with the automatic model selection ability of BYY learning, the BYY normalization learning-based local PCA model can cope with those object detection and star/galaxy classification tasks with unknown model complexity. A detailed algorithm for implementation of the local PCA model will be proposed, and experimental results using both synthetic and real astronomical data will be demonstrated.