Principal Component Projection Research Articles

Self-consistency and a generalized principal subspace theorem

Principal subspace theorems deal with the problem of finding subspaces supporting optimal approximations of multivariate distributions. The optimality criterion considered in this paper is the minimization of the mean squared distance between the given distribution and an approximating distribution, subject to some constraints. Statistical applications include, but are not limited to, cluster analysis, principal components analysis and projection pursuit. Most principal subspace theorems deal with elliptical distributions or with mixtures of spherical distributions. We generalize these results using the notion of self-consistency. We also show their connections with the skew-normal distribution and projection pursuit techniques. We also discuss their implications, with special focus on principal points and self-consistent points. Finally, we access the practical relevance of the theoretical results by means of several simulation studies.

Convergence and reproducibility in molecular dynamics simulations of the DNA duplex d(GCACGAACGAACGAACGC)

BackgroundThe structure and dynamics of DNA are critically related to its function. Molecular dynamics simulations augment experiment by providing detailed information about the atomic motions. However, to date the simulations have not been long enough for convergence of the dynamics and structural properties of DNA. MethodsMolecular dynamics simulations performed with AMBER using the ff99SB force field with the parmbsc0 modifications, including ensembles of independent simulations, were compared to long timescale molecular dynamics performed with the specialized Anton MD engine on the B-DNA structure d(GCACGAACGAACGAACGC). To assess convergence, the decay of the average RMSD values over longer and longer time intervals was evaluated in addition to assessing convergence of the dynamics via the Kullback–Leibler divergence of principal component projection histograms. ResultsThese molecular dynamics simulations—including one of the longest simulations of DNA published to date at ~44μs—surprisingly suggest that the structure and dynamics of the DNA helix, neglecting the terminal base pairs, are essentially fully converged on the ~1–5μs timescale. ConclusionsWe can now reproducibly converge the structure and dynamics of B-DNA helices, omitting the terminal base pairs, on the μs time scale with both the AMBER and CHARMM C36 nucleic acid force fields. Results from independent ensembles of simulations starting from different initial conditions, when aggregated, match the results from long timescale simulations on the specialized Anton MD engine. General significanceWith access to large-scale GPU resources or the specialized MD engine “Anton” it is possible for a variety of molecular systems to reproducibly and reliably converge the conformational ensemble of sampled structures. This article is part of a Special Issue entitled: Recent developments of molecular dynamics.

Consistency of a numerical approximation to the first principal component projection pursuit estimator

We generalize to functional data, the approach given by Croux and Ruiz-Gazen (1996) to compute robust projection-pursuit principal direction estimators, allowing also for smoothness in the estimators. Consistency of the approximated first principal direction estimator is derived.

On Objective Estimation Algorithm Based on PCA Image Sparse

Since it is usually unknown the over-sampling and under-sampling of image sparse in image compression, thereby can not verify the merits of sampling and reconstruction algorithm. Therefore it studies the signal sparse K estimation method of compressive sensing and proposes the objective estimation algorithm based on PCA image sparse which combined forward projection transformation theory and principal component transformation (PCA) method. In this paper, it creates image sparse and a linear relationship between the variance of coefficient function through the elaboration of compressive sensing theory to PCA and under the assumption that the principal component transform coefficient is approximately normal function. Experimental results show that: the proposed algorithm possess advantages of fast, low complexity and so on

Headspace-gas chromatographic fingerprints to discriminate and classify counterfeit medicines.

Counterfeit medicines are a global threat to public health. These pharmaceuticals are not subjected to quality control and therefore their safety, quality and efficacy cannot be guaranteed. Today, the safety evaluation of counterfeit medicines is mainly based on the identification and quantification of the active substances present. However, the analysis of potential toxic secondary components, like residual solvents, becomes more important. Assessment of residual solvent content and chemometric analysis of fingerprints might be useful in the discrimination between genuine and counterfeit pharmaceuticals. Moreover, the fingerprint approach might also contribute in the evaluation of the health risks different types of counterfeit medicines pose. In this study a number of genuine and counterfeit Viagra(®) and Cialis(®) samples were analyzed for residual solvent content using headspace-GC-MS. The obtained chromatograms were used as fingerprints and analyzed using different chemometric techniques: Principal Component Analysis, Projection Pursuit, Classification and Regression Trees and Soft Independent Modelling of Class Analogy. It was tested whether these techniques can distinguish genuine pharmaceuticals from counterfeit ones and if distinct types of counterfeits could be differentiated based on health risks. This chemometric analysis showed that for both data sets PCA clearly discriminated between genuine and counterfeit drugs, and SIMCA generated the best predictive models. This technique not only resulted in a 100% correct classification rate for the discrimination between genuine and counterfeit medicines, the classification of the counterfeit samples was also superior compared to CART. This study shows that chemometric analysis of headspace-GC impurity fingerprints allows to distinguish between genuine and counterfeit medicines and to differentiate between groups of counterfeit products based on the public health risks they pose.

A structural damage detection indicator based on principal component analysis and statistical hypothesis testing

A comprehensive statistical analysis is performed for structural health monitoring (SHM). The analysis starts by obtaining the baseline principal component analysis (PCA) model and projections using measurements from the healthy or undamaged structure. PCA is used in this framework as a way to compress and extract information from the sensor-data stored for the structure which summarizes most of the variance in a few (new) variables into the baseline model space. When the structure needs to be inspected, new experiments are performed and they are projected into the baseline PCA model. Each experiment is considered as a random process and, consequently, each projection into the PCA model is treated as a random variable. Then, using a random sample of a limited number of experiments on the healthy structure, it can be inferred using the χ2 test that the population or baseline projection is normally distributed with mean μh and standard deviation σh. The objective is then to analyse whether the distribution of samples that come from the current structure (healthy or not) is related to the healthy one. More precisely, a test for the equality of population means is performed with a random sample, that is, the equality of the sample mean μs and the population mean μh is tested. The results of the test can determine that the hypothesis is rejected (μh ≠ μc and the structure is damaged) or that there is no evidence to suggest that the two means are different, so the structure can be considered as healthy. The results indicate that the test is able to accurately classify random samples as healthy or not.

Metabolomics research on time-selected combination of Liuwei Dihuang and Jinkui Shenqi pills in treating kidney deficiency and aging by chemometric methods

Jinkui Shenqi pill (JKSQ) and Liuwei Dihuang (LWDH) pills are ancient traditional Chinese medicines (TCMs), which are usually used for the treatment of kidney deficiency for thousands of years in China. Time-selected combination of LWDH and JKSQ pills in treating kidney deficiency and aging is one of the features of traditional Chinese medicines (TCMs). However, the molecular mechanisms of time-selected combination remain unclear. In this work, UHPLC–QTOF/MS based metabolomics research was conducted to evaluate the therapeutic effect of LWDH, JKSQ pills and their combinations on kidney deficiency in Sprague–Dawley rats induced by d-galactose and Dexamethasone. Based on peak areas of serum extracts, analysis of variance (ANOVA) and graphical index of separation (GIOS) were employed to select the significant variables for kidney deficiency and aging and principal component projection (PCP) was subsequently applied to evaluate the influence of drugs on endogenous metabolites. 10 endogenous metabolites from 22 important ions were identified via database search. The score plot of PCA shows that nourishing Yang–nourishing Yin group shows the strongest rehabilitation for metabolic disorder induced by kidney deficiency and aging, which is consistent with the classic theories of traditional Chinese medicine. Moreover, metabolic pathway function analysis indicates that kidney deficiency and aging might possess closed relationships with lipid metabolism and energy metabolism. In this work, the change trends of potential biomarkers after administration provide molecular evidence for combined administration of Jinkui Shenqi pill in the morning and Liuwei Dihuang pill at night for the patients with kidney deficiency. The method proposed in this study may provide inspiration for evaluation of the therapeutic effect of Chinese medicines by comparing the rehabilitation of potential biomarkers.

A Novel Feature Selection Method for Process Fault Diagnosis

To increase fault classification performance and reduce computational complexity,the feature selection process has been used for fault diagnosis.In this paper, we proposed a sparse representation based feature selection method and gave detailed procedure of the algorithm. Traditional selecting methods based on wavelet package decomposition and Bhattacharyya distance methods,and sparse methods, including sparse representation classifier, sparsity preserving projection and sparse principal component analysis,were compared to the proposed method.Simulations showed the proposed selecting method gave better performance on fault diagnosis with Tennessee Eastman Process data.

Steady State Power Quality Assessment Based on Principal Component Projection Method

Limitations exist when individual indexes of power quality are adopted to reflect the comprehensive level of power quality in practice. In this paper, a comprehensive analysis of the individual indexes is made to get the only parameter that can show the overall specific characterization of the power quality level. The weight values of the indexes can be calculated by combining the subjective and objective weighting methods. Combined with the principal component projection method, the projection values of the border data and the data waiting for evaluating to the ideal evaluation vector can be easily obtained. Then with the projection values, it is easy to determine the grade range where the power quality data set locates. Simulation results show that this method is effective.

Separating Smoking-Related Diseases Using NMR-Based Metabolomics of Exhaled Breath Condensate

Nuclear magnetic resonance (NMR)-based metabolomics separates exhaled breath condensate (EBC) profiles of patients affected by pulmonary disease from those of healthy subjects. Here we show the discriminatory ability of NMR-based metabolomics in separating patients exposed to the same risk factor, namely, smoking habit in smoking-related diseases. Fifty duplicated EBC samples from a cohort of current smokers without chronic obstructive pulmonary disease (COPD, henceforth HS), COPD smokers, and subjects with established pulmonary Langerhans cell histiocytosis (PLCH) were analyzed by means of NMR spectroscopy followed by principal component analysis (PCA) and projection to latent structures discriminant analysis (PLS-DA). Clusterization of EBC spectra was disease-specific. COPD and PLCH samples present a profile different from that of HS, showing acetate increase and 1-methylimidazole reduction. An inverse behavior of 2-propanol and isobutyrate characterized COPD with respect to PLCH (high/low in COPD, low/high in PLCH). Both the 2-component and the 3-component PLS-DA models showed a 96% cross-validated accuracy, presenting R(2) and Q(2) values in the ranges of 0.97-0.87 and 0.91-0.78, respectively, and R(2) = 0.87 and Q(2) = 0.78, indicating that data variation is well explained by each model (R(2)), with a good predictivity (Q(2)). NMR spectra of EBC discriminate COPD and PLCH patients from HS and between them, with well-defined metabolic profiles for each class. The specificity of EBC profiles suggests that disease itself drives metabolic separation overwhelming the "common background" due to smoking habit. EBC-NMR investigation offers a powerful tool for assessing the evolution of airway diseases even in the presence of a strong common factor.

Classification and Reconstruction From Random Projections for Hyperspectral Imagery

There is increasing interest in dimensionality reduction through random projections due in part to the emerging paradigm of compressed sensing. It is anticipated that signal acquisition with random projections will decrease signal-sensing costs significantly; moreover, it has been demonstrated that both supervised and unsupervised statistical learning algorithms work reliably within randomly projected subspaces. Capitalizing on this latter development, several class-dependent strategies are proposed for the reconstruction of hyperspectral imagery from random projections. In this approach, each hyperspectral pixel is first classified into one of several pixel groups using either a conventional supervised classifier or an unsupervised clustering algorithm. After the grouping procedure, a suitable reconstruction method, such as compressive projection principal component analysis, is employed independently within each group. Experimental results confirm that such class-dependent reconstruction, which employs statistics pertinent to each class as opposed to the global statistics estimated over the entire data set, results in more accurate reconstructions of hyperspectral pixels from random projections.

Structural Damage Detection in a Truss Bridge Model Using Fuzzy Clustering and Measured FRF Data Reduced by Principal Component Projection

This study deals with vibration-based damage detection in a truss bridge model and suggests a novel methodology based on fuzzy clustering and measured frequency response function (FRF) data reduced by principal component projection. A six-bay truss bridge model is designed and fabricated in laboratory, various connection damages are simulated by loosening the end connecter bolts, and the environmental effects are taken into account by changing in excitation force levels of a shaker. The FRFs of the healthy and the damaged structure are used as initial data. The FRF data normalization is performed for eliminating the effects caused by the environmental and operational variability. Two data projection algorithms, namely principal component analysis (PCA) and kernel principal component analysis (KPCA) are adopted for data compression and the median values of principal components are defined for damage feature extraction. The fuzzy c-means (FCM) clustering algorithm is used to categorize these features for structural damage detection. The illustrated results show that the proposed method can effectively identify the bridge damages simulated by loosening the bolted joints of the truss bridge structure. It is sensitive to the structural damage but it is non-sensitive to the effect of the environmental and operational variations. This makes it quite generic and permits its potential development for real and complex truss bridges in site.

Chemometric Analysis of Croatian Extra Virgin Olive Oils from Central Dalmatia Region

Extra virgin olive oil samples were collected from different geographical areas of Central Dalmatia region in Croatia including locations both on the coast and islands. This set included 41 oils of cul-tivar Oblica, 1 per cultivars Coratina and Leccino, and 5 of mixed cultivars Lastovka and Oblica. Attenuated total reflectance (ATR) spectra of non-treated samples were recorded and principal component analysis (PCA) was carried out on a set of obtained spectra, as well as their first and second derivatives. The quality of PCA models was assessed using leave-one-out cross-validation and optimal number of principal components was determined. In the case of ATR spectra, the first principal component accounted for 42.92 % of the total variance among the samples and the optimal number of components was 6, whereas in the case of second derivatives the first principal component accounted for 95.76 % of the total variance and the optimal number of components was 3. Classification of olive oils on the basis of geographical origin was proposed and underlying spectral differences among the spectra were determined by investigating principal component loadings. These differences arise as a result of variations in fatty acid composition. It was found out that ATR in combination with PCA could easily distinguish between samples collected from the coastal area and those from the islands. Classification results were further confirmed by using spherical principal components procedure, projection pursuit and robust PCA, as well as hierarchical cluster analysis.

MiR-20b, miR-98, miR-125b-1*, and let-7e* as new potential diagnostic biomarkers in ulcerative colitis

To use microarray-based miRNA profiling of colonic mucosal biopsies from patients with ulcerative colitis (UC), Crohn's disease (CD), and controls in order to identify new potential miRNA biomarkers in inflammatory bowel disease. Colonic mucosal pinch biopsies from the descending part were obtained endoscopically from patients with active UC or CD, quiescent UC or CD, as well as healthy controls. Total RNA was isolated and miRNA expression assessed using the miRNA microarray Geniom Biochip miRNA Homo sapiens (Febit GmbH, Heidelberg, Germany). Data analysis was carried out by principal component analysis and projection to latent structure-discriminant analysis using the SIMCA-P+12 software package (Umetrics, Umea, Sweden). The microarray data were subsequently validated by quantitative real-time polymerase chain reaction (qPCR) performed on colonic tissue samples from active UC patients (n = 20), patients with quiescent UC (n = 19), and healthy controls (n = 20). The qPCR results were analyzed with Mann-Whitney U test. In silico prediction analysis were performed to identify potential miRNA target genes and the predicted miRNA targets were then compared with all UC associated susceptibility genes reported in the literature. The colonic mucosal miRNA transcriptome differs significantly between UC and controls, UC and CD, as well as between UC patients with mucosal inflammation and those without. However, no clear differences in the transcriptome of patients with CD and controls were found. The miRNAs with the strongest differential power were identified (miR-20b, miR-99a, miR-203, miR-26b, and miR-98) and found to be up-regulated more than a 10-fold in active UC as compared to quiescent UC, CD, and controls. Two miRNAs, miR-125b-1* and let-7e*, were up-regulated more than 5-fold in quiescent UC compared to active UC, CD, and controls. Four of the seven miRNAs (miR-20b, miR-98, miR-125b-1*, and let-7e*) were validated by qPCR and found to be specifically upregulated in patients with UC. Using in silico analysis we found several predicted pro-inflammatory target genes involved in various pathways, such as mitogen-activated protein kinase and cytokine signaling, which are both key signaling pathways in UC. The present study provides the first evidence that miR-20b, miR-98, miR-125b-1*, and let-7e* are deregulated in patients with UC. The level of these miRNAs may serve as new potential biomarkers for this chronic disease.

Non-invasive characterization of polymeric materials in relation to art conservation using unilateral NMR combined with multivariate data analysis

This article shows how to interpret data obtained by unilateral NMR for the characterization of works of art using multivariate analysis. Transverse 1H relaxation decays acquired by a Carr–Purcell–Meiboom–Gill pulse sequence are directly treated by Principal Component Analysis (PCA) and projection to latent structure by partial least square (PLS). The advantage of this procedure is the avoidance of any ambiguity in the model. The NMR signal is formed by a number of different hydrogen spins rendering the resulting relaxation decays multi-exponential. Therefore conventional approaches of fitting call for the use of mono-, bi-, or multi-exponential models yielding results depending on the choice of the model function. We demonstrate the technique on three examples: characterization of a set of resins representative for modern materials in art and design artefacts, mapping the state of degradation of an art work made of latex, and the analysis of a depth profile of an aged urethane rubber sample. In situ measurements often result in low signal-to-noise ratio data and the suggested technique does not only allow an unambiguous model-free approach, but is also robust against such low sensitivity data.

Validation of Gene Expression Profiles in Genomic Data through Complementary Use of Cluster Analysis and PCA-Related Biplots

High-throughput genomic assays are used in molecular biology to explore patterns of joint expression of thousands of genes. These methodologies had relevant developments in the last decade, and concurrently there was a need for appropriate methods for analyzing the massive data generated. Identifying sets of genes and samples characterized by similar values of expression and validating these results are two critical issues related to these investigations because of their clinical implication. From a statistical perspective, unsupervised class discovery methods like Cluster Analysis are generally adopted. However, the use of Cluster Analysis mainly relies on the use of hierarchical techniques without considering possible use of other methods. This is partially due to software availability and to easiness of representation of results through a heatmap, which allows to simultaneously visualize clusterization of genes and samples on the same graphical device. One drawback of this strategy is that clusters’ stability is often neglected, thus leading to over-interpretation of results. Moreover, validation of results using external datasets is still subject of discussion, since it is well known that batch effects may condition gene expression results even after normalization. In this paper we compared several clustering algorithms (hierarchical, k-means, model-based, Affinity Propagation) and stability indices to discover common patterns of expression and to assess clustering reliability, and propose a rank-based passive projection of Principal Components for validation purposes. Results from a study involving 23 tumor cell lines and 76 genes related to a specific biological pathway and derived from a publicly available dataset, are presented.

Research on the Classification of Coupling Relationship among the Ecological Environment, Natural Disasters and Regional Poverty in Inner Mongolia Autonomous Region

This paper first built the evaluation index system for the eco-environmental vulnerability, natural disaster, and regional poverty in Inner Mongolia, and then adopted the principal component projection analysis to obtain vulnerability degree of eco-environment, risk degree of natural disaster and regional poverty degree. Then the classification for them was conducted, coupled with the analysis of their own characteristics. Moreover, the coupling analysis was utilized to carry out classification and research for the coupling relationship between them, aiming to provide scientific theoretical basis for the ecological protection and construction, the disaster prevention and mitigation as well as the poverty alleviation and development in Inner Mongolia.

Utilities for quantifying separation in PCA/PLS-DA scores plots

Metabolic fingerprinting studies rely on interpretations drawn from low-dimensional representations of spectral data generated by methods of multivariate analysis such as principal components analysis and projection to latent structures discriminant analysis. The growth of metabolic fingerprinting and chemometric analyses involving these low-dimensional scores plots necessitates the use of quantitative statistical measures to describe significant differences between experimental groups. Our updated version of the PCAtoTree software provides methods to reliably visualize and quantify separations in scores plots through dendrograms employing both nonparametric and parametric hypothesis testing to assess node significance, as well as scores plots identifying 95% confidence ellipsoids for all experimental groups.

Multivariate Image Analysis (MIA) for Industrial Flare Combustion Control

A new approach for flare monitoring is proposed so that flare combustion efficiency can be predicted online in industrial plants. Multivariate image analysis (MIA), which is based on principal component analysis (PCA) and projection to latent structures (PLS), has been applied to flare combustion systems in order to predict their resulting combustion efficiencies, as a function of the crosswind velocity, using simulated results, and as a function of steam or air flow rates, using experimental tests of a full-size flare. The results show that a multivariate regression model based on flare color images can be used to predict the flare performance over a range of operating conditions for steam-assisted flares. Therefore, simple two-dimensional color images of industrial flares may be a fast, accurate, and inexpensive approach for online monitoring of these industrial combustion systems. This would allow for developing effective flare control and mitigation strategies.

Population structure of Hispanics in the United States: the multi-ethnic study of atherosclerosis.

Using ∼60,000 SNPs selected for minimal linkage disequilibrium, we perform population structure analysis of 1,374 unrelated Hispanic individuals from the Multi-Ethnic Study of Atherosclerosis (MESA), with self-identification corresponding to Central America (n = 93), Cuba (n = 50), the Dominican Republic (n = 203), Mexico (n = 708), Puerto Rico (n = 192), and South America (n = 111). By projection of principal components (PCs) of ancestry to samples from the HapMap phase III and the Human Genome Diversity Panel (HGDP), we show the first two PCs quantify the Caucasian, African, and Native American origins, while the third and fourth PCs bring out an axis that aligns with known South-to-North geographic location of HGDP Native American samples and further separates MESA Mexican versus Central/South American samples along the same axis. Using k-means clustering computed from the first four PCs, we define four subgroups of the MESA Hispanic cohort that show close agreement with self-identification, labeling the clusters as primarily Dominican/Cuban, Mexican, Central/South American, and Puerto Rican. To demonstrate our recommendations for genetic analysis in the MESA Hispanic cohort, we present pooled and stratified association analysis of triglycerides for selected SNPs in the LPL and TRIB1 gene regions, previously reported in GWAS of triglycerides in Caucasians but as yet unconfirmed in Hispanic populations. We report statistically significant evidence for genetic association in both genes, and we further demonstrate the importance of considering population substructure and genetic heterogeneity in genetic association studies performed in the United States Hispanic population.