Principal Component Analysis Mixture Research Articles

Unsupervised Fault Detection for Building Air Handling Unit Systems Using Deep Variational Mixture of Principal Component Analyzers

Unsupervised Fault Detection for Building Air Handling Unit Systems Using Deep Variational Mixture of Principal Component Analyzers

Urinary Concentrations of Phthalate Metabolite Mixtures in Relation to Serum Biomarkers of Thyroid Function and Autoimmunity among Women from a Fertility Center.

Background:Although previous epidemiological studies have explored associations of phthalate metabolites with thyroid function, no studies to date have assessed associations of mixtures with thyroid function and autoimmunity among potentially susceptible subgroups such as subfertile women.Objective:We aimed to explore associations of mixtures of urinary phthalate metabolites with serum markers of thyroid function and autoimmunity.Methods:This cross-sectional study included 558 women attending a fertility center who provided one spot urine and one blood sample at enrollment (2005–2015). We quantified urinary concentrations of eight phthalate metabolites using mass spectrometry, and biomarkers of thyroid function [thyroid-stimulating hormone (TSH), free and total thyroxine (, ) and triiodothyronine (, ), and autoimmunity [thyroid peroxidase and thyroglobulin antibodies (TPOAb and TgAb, respectively)] in serum using electrochemiluminescence assays. We applied principal component analysis (PCA) and Bayesian kernel machine regression (BKMR) to identify the main patterns of urinary phthalate metabolites. We used linear mixed models to assess the association between PCA-derived factor scores in quintiles and serum thyroid function and autoimmunity, adjusting for age, body mass index (BMI), specific gravity (SG), and, for the PCA, other factor scores.Results:We observed two factors using PCA, one representing the di(2-ethylhexyl) (DEHP) and another non-DEHP metabolites. Compared to women in the lowest quintile of the DEHP factor scores, women in the highest quintile had significantly lower serum concentrations of , , , and [absolute difference: ; 95% confidence interval (CI): , ; ; absolute difference: ; 95% CI: , ; ; absolute difference: ; 95% CI: 0.54, ; ; and absolute difference: ; 95% CI: , ; , respectively]. Using BKMR, we observed that mono(2-ethyl-5-hydroxyhexyl) phthalate (MEHHP) was the primary contributor to these negative associations. DEHP and non-DEHP factor scores were not associated with serum TSH, TgAb, or TPOAb.Conclusions:Mixtures of urinary DEHP metabolites were inversely associated with serum biomarkers of thyroid function but not with autoimmunity, which were within normal ranges for healthy adult women. https://doi.org/10.1289/EHP6740

Mixture decompositions and lithofacies clustering from wireline logs

Finite mixture models provide useful methods for modeling a wide variety of natural phenomena. Decomposing a mixture of distributions, however, has many difficulties, including separability of the component distributions, determination of the number of components, predictability of the clusters with realistic spatial patterns, and linkages between the component density functions and underlying physical processes. In this article, we use principal component analysis (PCA) to synthesize multiple wireline logs and decompose mixture populations for lithofacies clustering. The principal components of these logs characterize the rock physics; some of them contain essential information of lithofacies while others represent less relevant information or noise. In many cases, clustering based on one component is effective for decomposing the mixture and classifying lithofacies, although rotating principal components is often necessary to improve the lithofacies discrimination. In more complicated cases, PCA and direct mixture decomposition using histogram can be cascaded to decompose finite mixture models of a rock property. The proposed methodology combines the delicacy of probability theory and simplicity of linear transforms to classify lithofacies. • We present multivariate analysis of wireline logs. • Lithofacies are classified using wireline logs. • Principal component analysis is used to synthesize multiple logs and characterize rock physics of the resource formation. • Probabilistic method of histogram decomposition of rock properties is performed using principal component analysis. • We demonstrate the lithofacies classification and mixture decomposition using wireline logs with a number of examples.

MLiT: mixtures of Gaussians under linear transformations

The curse of dimensionality hinders the effectiveness of density estimation in high dimensional spaces. Many techniques have been proposed in the past to discover embedded, locally linear manifolds of lower dimensionality, including the mixture of principal component analyzers, the mixture of probabilistic principal component analyzers and the mixture of factor analyzers. In this paper, we propose a novel mixture model for reducing dimensionality based on a linear transformation which is not restricted to be orthogonal nor aligned along the principal directions. For experimental validation, we have used the proposed model for classification of five “hard” data sets and compared its accuracy with that of other popular classifiers. The performance of the proposed method has outperformed that of the mixture of probabilistic principal component analyzers on four out of the five compared data sets with improvements ranging from 0.5 to 3.2%. Moreover, on all data sets, the accuracy achieved by the proposed method outperformed that of the Gaussian mixture model with improvements ranging from 0.2 to 3.4%.

A mixture neural methodology for computing rice consumptive water requirements in Fada N’Gourma Region, Eastern Burkina Faso

Crop consumptive water requirement (Crop-ET) is a key variable for developing management plans to optimize the efficiency of water use for crop production particularly in semiarid zone. In Burkina Faso, the unfavorable climatic conditions characterized by the low and unevenly distribution of rainfall have pushed water resources management to the forefront of the crop production issue. Crop-ET is extremely required in rainwater effective management for mitigating the impact of water deficit on the crops. Basically, Crop-ET determination involves reference evapotranspiration (ETo) and crop coefficient (Kc) which required complete climatic data and specific site crop information, respectively. ETo estimation with the recommended FAO56 Penman–Monteith (PM) equation is limited in Burkina Faso due to the numerous meteorological data required which are not always available in many production sites. In such circumstances, research to compute directly Crop-ET as an alternative to the two-step approach of calculating ETo and determining site specific Kc, seems desirable. Therefore, this study aims to evaluate the performance of a mixture principal component analysis neural network (PCANN) model for computing rice Crop-ET directly from temperatures data in Fada N’Gourma region located in Eastern Burkina Faso, Africa. From the statistical results, rice Crop-ET can be successfully computed by using PCANN methodology, when only temperatures data are available in this African semiarid environment. Thus, in poor data situation, Crop-ET direct computation can be rapidly addressed through PCANN model for agricultural water management in African semiarid regions.

Handling of incomplete data sets using ICA and SOM in data mining

Based on independent component analysis (ICA) and self-organizing maps (SOM), this paper proposes an ISOM-DH model for the incomplete data’s handling in data mining. Under these circumstances the data remain dependent and non-Gaussian, this model can make full use of the information of the given data to estimate the missing data and can visualize the handled high-dimensional data. Compared with mixture of principal component analyzers (MPCA), mean method and standard SOM-based fuzzy map model, ISOM-DH model can be applied to more cases, thus performing its superiority. Meanwhile, the correctness and reasonableness of ISOM-DH model is also validated by the experiment carried out in this paper.

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.

Almost autonomous training of mixtures of principal component analyzers

In recent years, a number of mixtures of local PCA models have been proposed. Most of these models require the user to set the number of submodels (local models) in the mixture and the dimensionality of the submodels (i.e., number of PC's) as well. To make the model free of these parameters, we propose a greedy expectation-maximization algorithm to find a suboptimal number of submodels. For a given retained variance ratio, the proposed algorithm estimates for each submodel the dimensionality that retains this given variability ratio. We test the proposed method on two different classification problems: handwritten digit recognition and 2-class ionosphere data classification. The results show that the proposed method has a good performance.

Variational Bayes method for Mixture of Principal Component Analyzers

AbstractWhen dealing with high‐dimensional data, it is proper to construct an appropriate feature space consisting of relevant features extracted from given data. Mixture of Principal Component Analyzers (MPCA) is a feature extracting tool in which clustering in the data space and principal component analysis in each cluster are simultaneously done. A probabilistic model of MPCA and its maximum likelihood (ML) inference were presented by Tipping and Bishop (1999). Although the probabilistic formulation can be satisfactorily advantageous within Bayesian inference instead of ML inference, Bayesian inference often requires difficult integrations. Such difficulty comes to be overcome by the variational Bayes (VB) approximation that has recently been developed. In this paper, we present a VB inference algorithm for MPCA, and its application to a recognition problem of handwritten digit images. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(11): 55–66, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10394

Face recognition using the mixture-of-eigenfaces method

This paper deals with face recognition using the mixture-of-eigenfaces method. The well-known eigenface method uses one set of holistic facial features obtained by principal component analysis (PCA). However, a single set of eigenfaces is not enough to represent face images with large variations. To overcome this weakness, we propose the mixture-of-eigenfaces method, which uses more than one set of eigenfaces obtained from the expection maximization learning in the PCA mixture model. In this method, several sets of eigenfaces are obtained from all face images, and each template face image is represented by an appropriate set of eigenfaces. Recognition was performed using the distance between the input image and the labelled template image stored in the face database, where the distance is the difference of the feature values that are obtained from the set of eigenfaces indicated by the labelled template image. Simulation results show that the proposed mixture-of-eigenfaces method outperforms the eigenface method in terms of recognition accuracy for face images with pose and illumination variations.

A numeral character recognition using the PCA mixture model

This paper proposes a method for recognizing the numeral characters based on the PCA (Principal Component Analysis) mixture model. The proposed method is motivated by the idea that the classification accuracy is improved by modeling each class into a mixture of several components and by performing the classification in the compact and decorrelated feature space. For realizing the idea, each numeral class is partitioned into several clusters and each cluster's density is estimated by a Gaussian distribution function in the PCA transformed space. The parameter estimation is performed by an iterative EM (Expectation Maximization) algorithm, and model order is selected by a fast sub-optimal validation scheme. The proposed method is also computation-effective because the optimal feature components for a cluster are determined by a sequential elimination of insignificant feature due to the ordering property of the significance among the feature components in the PCA transformed space. Simulation results shows that the proposed recognition method outperforms other methods such as the k-NN (Nearest Neighbor) method, a single PCA model, or the ICA (Independent Component Analysis) mixture model in terms of recognition accuracy.

Using Mixture Principal Component Analysis Networks To Extract Fuzzy Rules from Data

In this paper, an innovative method of advanced data preprocessing for rule extraction using mixture principal component analysis (PCA) models is proposed to build the fault diagnosis system. The experimental data are properly transformed and classified by heuristic smoothing clustering (HSC) and PCA. HSC is a very good method for smoothing measurement observations and characterizing the local variations of the observations. This heuristic building rule is able to derive fuzzy rules quickly from a set of local regions. Then, the expectation-maximization algorithm is used to tune the corresponding rule parameters for estimating maximum likelihood parameters of PCA models without solving the highly nonlinear coupled equations. The fuzzy rules are constructed by hyperellipsoids of the PCA model whose principal axes are parallel to the major directions of system data distribution. This research is to create an alternative knowledge acquisition methodology based on the mathematical type to describe the elicited knowledge. Results obtained using the new method present the capability of determining the set of conditions for the artificially created data and the well-known reactor system.

Mixture Principal Component Analysis Models for Process Monitoring

A mixture principal component analysis (MixPCA) model detector is proposed. The detector creates each cluster by aggregating input exemplars. The number of clusters in the data set is automatically determined by a Gaussian filter technique called heuristic smoothing clustering. The structure building contains two stages: (1) sizing each cluster on the basis of the clustering analysis and (2) setting up the multivariable statistic confidence levels for each cluster. After the clusters are identified, MixPCA, which is a group of PCA models, will then be created. If any input pattern is under normal operation, it would fall into the accepted region whose criteria are set on the basis of the principal component analysis (PCA), T2 and Q charts. In addition, the techniques of similarity measuring and merging between clusters are also developed for the new correlation structure of the process variables when new data sets are included. The proposed model development procedure is favorable because of its simplici...