Interval Principal Component Analysis Research Articles

Generalized Gaussian Distribution-Based Interval Principal Component Analysis (GGD-IPCA) for Anomaly Detection of Processes With Uncertainty

Generalized Gaussian Distribution-Based Interval Principal Component Analysis (GGD-IPCA) for Anomaly Detection of Processes With Uncertainty

Theoretical derivation of interval principal component analysis

Principal Component Analysis is a well-known method that can be used for dimensionality reduction, a useful technique in the Big Data era. There have been a series of proposed adaptations of the Principal Component Analysis method for interval-valued symbolic data, all of which have the downside of having intermediate steps that deal with conventional data. In this work, we put forward an interval Principal Component Analysis that only deals with symbolic data by developing a theoretical framework that allows for the definition of symbolic principal components. This framework provides the mathematical tools needed to use the symbolic principal components to transform the original data in a way that is mathematically coherent with the remainder of the framework and defines the principal components as solutions to maximisation problems, similarly to what is done in conventional Principal Component Analysis. After the theoretical foundations are laid down, we explore real-world data from the telecommunications sector, in an attempt to detect Internet redirection attacks in real-time. In particular, we use our symbolic method to improve and simplify an anomaly detection method that has been proposed in the literature for conventional data.

Rapid and low-cost liquid biopsy with ATR-FTIR spectroscopy to discriminate the molecular subtypes of breast cancer

Breast cancer (BC) is the most prevalent cancer worldwide. The prognosis and survival of these patients are directly related to the diagnostic stage. Even so, the gold standard screening method (mammography) has a long waiting period, high rates of false positives, anxiety for patients, and consequently delays the diagnosis by core needle biopsy (invasive method). Alternatively, the Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) spectroscopy is a noninvasive, low-cost, rapid, and reagent-free technique that generates the spectral metabolomic profile of biomolecules. This makes it possible to assess systemic repercussions, such as the BC carcinogenesis process. Blood plasma samples (n = 56 BC and n = 18 controls) were analyzed in the spectrophotometer in the ATR-FTIR mode. For the exploratory analysis of the data, interval Principal Component Analysis (iPCA) was used, and for predictive chemometric modeling, the Orthogonal Partial Least Squares Discriminant Analysis (OPLS-DA) algorithm with validation by leave-one-out cross-validation. iPCA in the region of 1118–1052 cm−1 (predominantly DNA/RNA bands) showed significant clustering of molecular subtypes and control. The OPLS-DA model achieved 100% accuracy with only 1 latent variable and Root Mean Square Error of Cross-Validation (RMSECV) < 0.005 for all molecular subtypes and control. The wavenumbers (cm−1) with the highest iPCA peaks (loadings: 1117, 1089, 1081, 1075, 1057, and 1052) were used as input to MANOVA (Wilks' Lambda, p < 0.001 between molecular subtypes and control). The rapid and low-cost detection of BC molecular subtypes by ATR-FTIR spectroscopy would plausibly allow initial screening and clinical management, improving prognosis, reducing mortality and costs for the health system.

Spectral radius-based interval principal component analysis (SR-IPCA) for fault detection in industrial processes with imprecise data

Data-driven process monitoring approaches like principal component analysis (PCA) have been widely used in many industrial processes, most of which assume that the data are precise and reliable. However, the data collected from actual processes are usually contaminated with uncertainties due to measurement noise, severe working scenarios and other reasons. Aiming at fault detection in the complex industrial processes with imprecise measurement data, a spectral radius-based interval PCA (SR-IPCA) method is proposed in this work. First, kernel density estimation (KDE)-based measurement error estimation strategy is presented to transform imprecise single-valued data into interval-valued data. Then, a spectral radius based eigen-decomposition method for interval matrix is developed to extract the process features by projecting high-dimensional interval data to low-dimensional space. Moreover, four monitoring statistics are defined to analyze process status and identify the fault. The proposed SR-IPCA method can effectively tackle the uncertainties by defining an interval domain and extract correlation structure with relative low computation complexity. The simulation results on the synthetic data sets and the Tennessee Eastman process (TEP) reveal that SR-IPCA significantly reduces the false alarm rate and the missed detection rate compared with PCA, vertices PCA (V-PCA) and centers PCA (C-PCA).

Portable Raman spectroscopy applied to the study of drugs of abuse.

The use of drugs of abuse has grown significantly in recent decades. In forensic chemistry, methods of identifying and characterizing illicit drugs contribute to the interests of researchers, experts, and public security authorities. Among existing methods, portable Raman spectroscopy is notable for performing rapid, non-destructive, and highly selective analysis in the laboratory or on-site. When the resulting spectral data are paired with chemometric tools, methods of exploratory analysis and multivariate calibration can be developed. Thus, this work describes the application of Raman spectroscopy associated with principal component analysis (PCA) and interval principal component analysis (iPCA) to assessing trends in samples of cocaine (n= 40), crack (n= 33), and their main adulterants (n= 5) and diluents (n= 5), tablets of ecstasy (n= 14), designer drugs papers (n= 27), and alcoholic solutions adulterated with benzodiazepines (alprazolam and diazepam). In addition, competitive adaptive reweighted sampling (CARS) combined with partial least squares (PLS) regression (CARSPLS) was used to quantify adulterants (benzocaine, lidocaine, and procaine) in binary mixtures with crack (n= 21) and solutions of cachaça adulterated with bromazepam (n= 11).

Applying interval PCA and clustering to quantile estimates: empirical distributions of fertilizer cost estimates for yearly crops in European Countries

The decision to adopt one or another of the sustainable land management alternatives should not be based solely on their respective benefits in terms of climate change mitigation but also based on the performances of the productive systems used by farm holdings, assessing their environmental impacts through the cost of fertilizer resources used. This communication uses the symbolic clustering tools in order to analyze the conditional quantile estimates of the fertilizer costs of yearly crop productions in agriculture, as a replacement proxy for internal soil erosion costs. After recalling the conceptual framework of the estimation of agricultural production costs, we present the empirical data model, the quantile regression approach and the interval principal component analysis clustering tools used to obtain typologies of European countries on the basis of the conditional quantile distributions of fertilizer cost empirical estimates. The comparative analysis of econometric results for yearly crops between European countries illustrates the relevance of the typologies obtained for international comparisons to assess land management alternatives based on their impact on agricultural carbon sequestration in soils.

Interval-Valued Features Based Machine Learning Technique for Fault Detection and Diagnosis of Uncertain HVAC Systems

The operation of heating, ventilation, and air conditioning (HVAC) systems is usually disturbed by many uncertainties such as measurement errors, noise, as well as temperature. Thus, this paper proposes a new multiscale interval principal component analysis (MSIPCA)-based machine learning (ML) technique for fault detection and diagnosis (FDD) of uncertain HVAC systems. The main goal of the developed MSIPCA-ML approach is to enhance the diagnosis performance, improve the indoor environment quality, and minimize the energy consumption in uncertain building systems. The model uncertainty is addressed by considering the interval-valued data representation. The performance of the proposed FDD is investigated using sets of synthetic and emulated data extracted under different operating conditions. The presented results confirm the high-efficiency of the developed technique in monitoring uncertain HVAC systems due to the high diagnosis capabilities of the interval feature-based support vector machines and k-nearest neighbors and their ability to distinguish between the different operating modes of the HVAC system.

A new interval diagnosis method: Application to the spacecraft rendezvous phase of the Mars sample return mission

SummaryThis paper presents a new optimized interval principal component analysis applied to detect and isolate actuators faults of an autonomous spacecraft involved in the rendezvous phase of the Mars sample return mission. Based on the exploitation of various arithmetic and interval analysis properties, the new interval model is built by solving the interval eigenpairs problem via a resolution of a parametric linear programming problem. The detection and isolation phases are performed by extending the classic methods to interval‐valued data. The proposed method is applied to detect and isolate actuators faults that can occur on the spacecraft's thrusters. Based on data provided by a “high fidelity” industrial simulator developed by Thales Alenia Space, the obtained results proved the effectiveness of the proposed interval fault diagnosis method on detecting and isolating thrusters' faults.

Multivariate Analysis of Difference Raman Spectra of the Irradiated Nucleus and Cytoplasm Region of SH-SY5Y Human Neuroblastoma Cells.

Previous works showed that spatially resolved Raman spectra of cytoplasm and nucleus region of single cells exposed to X-rays evidence different features. The present work aims to introduce a new approach to profit from these differences to deeper investigate X-ray irradiation effects on single SH-SY5Y human neuroblastoma cells. For this aim, Raman micro-spectroscopy was performed in vitro on single cells after irradiation by graded X-ray doses (2, 4, 6, 8 Gy). Spectra from nucleus and cytoplasm regions were selectively acquired. The examination by interval Principal Component Analysis (i-PCA) of the difference spectra obtained by subtracting each cytoplasm-related spectrum from the corresponding one detected at the nucleus enabled us to reveal the subtle modifications of Raman features specific of different spatial cell regions. They were discussed in terms of effects induced by X-ray irradiation on DNA/RNA, lipids, and proteins. The proposed approach enabled us to evidence some features not outlined in previous investigations.

Multivariate fault detection and classification using interval principal component analysis

Principal component analysis (PCA) is a linear data analysis tool that aims to reduce the dimensionality of a dataset, while retaining most of the variation found in it. It transforms the variables of a dataset into a new set, called the principal components, using linear combinations of the original variables. PCA is a powerful statistical technique used in research for fault detection, classification and feature extraction. Interval principal component analysis (IPCA) is an extension to PCA designed to apply PCA to large datasets using interval data generated from single-valued samples. In this paper, three IPCA methods are compared: centers IPCA, midpoint-radii IPCA, and symbolic covariance IPCA, and methods for fault detection and classification using interval data are described. Fault detection and classification applications are respectively carried out through two examples, one using synthetic and the other using real data, and the results are compared to those of the classical PCA.The results show that IPCA methods have a higher detection rate than classical PCA, for the same false alarm rate. Moreover, IPCA methods are capable of differentiating the type of fault to a high degree of accuracy, unlike classical PCA. Interval centers were capable of detecting changes in mean, while interval radii were capable of detecting changes in variance. Furthermore, for data classification, the results show that MRIPCA had a higher classification precision than other IPCA methods and classical PCA.

Identification of anisodamine tablets by Raman and near-infrared spectroscopy with chemometrics

Vibrational spectroscopy including Raman and near-infrared (NIR) spectroscopy has become an attractive tool for pharmaceutical analysis. In this study, effective calibration models for the identification of anisodamine tablet and its counterfeit and the distinguishment of manufacturing plants, based on Raman and NIR spectroscopy, were built, respectively. Anisodamine counterfeit tablets were identified by Raman spectroscopy with correlation coefficient method, and the results showed that the predictive accuracy was 100%. The genuine anisodamine tablets from 5 different manufacturing plants were distinguished by NIR spectroscopy using partial least squares discriminant analysis (PLS-DA) models based on interval principal component analysis (iPCA) method. And the results showed the recognition rate and rejection rate were 100% respectively. In conclusion, Raman spectroscopy and NIR spectroscopy combined with chemometrics are feasible and potential tools for rapid pharmaceutical tablet discrimination.

Fourier Transform Infrared Spectroscopy (FTIR) and Multivariate Analysis for Identification of Different Vegetable Oils Used in Biodiesel Production

The main objective of this study was to use infrared spectroscopy to identify vegetable oils used as raw material for biodiesel production and apply multivariate analysis to the data. Six different vegetable oil sources—canola, cotton, corn, palm, sunflower and soybeans—were used to produce biodiesel batches. The spectra were acquired by Fourier transform infrared spectroscopy using a universal attenuated total reflectance sensor (FTIR-UATR). For the multivariate analysis principal component analysis (PCA), hierarchical cluster analysis (HCA), interval principal component analysis (iPCA) and soft independent modeling of class analogy (SIMCA) were used. The results indicate that is possible to develop a methodology to identify vegetable oils used as raw material in the production of biodiesel by FTIR-UATR applying multivariate analysis. It was also observed that the iPCA found the best spectral range for separation of biodiesel batches using FTIR-UATR data, and with this result, the SIMCA method classified 100% of the soybean biodiesel samples.

Adaptation of interval PCA to symbolic histogram variables

This paper is an adaptation of symbolic interval Principal Component Analysis (PCA) to histogram data. We proposed two methodologies. The first one involved three steps: the coding of bins of histogram, the ordinary PCA of means of variables and the representation of dispersion of symbolic observations we call concepts. For the representation of dispersion of these concepts we proposed the transformation of histograms into intervals. Then, we suggest the projection of the hypercubes or the interval lengths associated to each concept on the principal axes of the ordinary PCA of means. In the second methodology, we proposed the use of the three previous steps with the angular transformation.