Multivariate Exploratory Data Analysis Research Articles

Normalization of gene counts affects principal components-based exploratory analysis of RNA-sequencing data

Normalization of gene expression count data is an essential step of in the analysis of RNA-sequencing data. Its statistical analysis has been mostly addressed in the context of differential expression analysis, that is in the univariate setting. However, relationships among genes and samples are better explored and quantified using multivariate exploratory data analysis tools like Principal Component Analysis (PCA). In this study we investigate how normalization impacts the PCA model and its interpretation, considering twelve different widely used normalization methods that were applied on simulated and experimental data. Correlation patterns in the normalized data were explored using both summary statistics and Covariance Simultaneous Component Analysis. The impact of normalization on the PCA solution was assessed by exploring the model complexity, the quality of sample clustering in the low-dimensional PCA space and gene ranking in the model fit to normalized data. PCA models upon normalization were interpreted in the context gene enrichment pathway analysis. We found that although PCA score plots are often similar independently form the normalization used, biological interpretation of the models can depend heavily on the normalization method applied.

Multivariate data analysis for semen quality in two frog species

Despite the growing body of research on frog reproduction and semen quality, studies employing statistical methods and analyses are scarce. The present study aimed to examine the use of exploratory multivariate data analysis for evaluating the seminal quality of frogs, determining a possible hierarchy among frog species based on semen characteristics, and identifying the most effective clustering strategy. Data on the seminal quality of the butter frog (Leptodactylus ocellatus, native specie) were collected from seven samples, and for the bullfrog (Lithobates catesbeianus, exotic specie), five samples were used, all derived from a literature review. Four distinct clustering strategies were tested: Single Linkage, Unweighted Pair Group Method with Arithmetic Mean (UPGMA), Complete Linkage, and Ward’s method. Exploratory multivariate data analysis could effectively evaluate frog seminal quality, allowing the classification of frog species (both native and exotic) based on semen. Among the tested strategies, UPGMA emerged as the most suitable grouping method.

Monitoring settling of anaerobic digestates using low-field MRI profiling and NMR relaxometry measurements

Dewatering of anaerobic digestate from red meat processing was assessed using low field MRI profiling and NMR relaxometry. Samples were flocculated using a cationic flocculant (EM640CT) at dosing range (0 to 1.6% v/v) and monitored during the initial 30 min of settling via MRI profiling to assess changes in water fraction, settling time and initial settling velocity. The profiles showed decreasing settling time and increasing initial settling velocity with increased dosing, while sample porosity was observed to increase up to the optimal dosing point (0.8% v/v). Significant increases in sample variability were observed past this point due to flocculant overdosing. The samples were then analysed in terms of turbidity and NMR relaxometry. Increasing flocculant concentration caused turbidity to decrease from 210 to 13 NTU. The relaxation rate of free water showed a strong positive correlation with turbidity. T2 peaks observed before overdosing could be assigned to different water structures (free, interstitial, vicinal and hydration). An additional T2 population emerged in the T2 distributions at the optimal dosing point. Multivariate exploratory data analysis (MEDA) showed that this T2 population from the solids layer was strongly correlated with the total solids layer height and turbidity of the watery layer. This T2 peak formation may therefore be used to study opaque flocculated solids to monitor for water structures associated with flocculant overdosing. Further studies using this technique will aim to assess the potential of low field T2 relaxometry monitoring inline before mechanical dewatering, to monitor optimal flocculant dosing during continuous operations on systems with high solids concentration.

더블링 기법을 활용한 대응분석에 대한 민감도분석

Correspondence analysis is generally a data analysis technique that expresses a two-dimensional or higher contingency table in a low-dimensional space to see the combination of rows and columns. In general, a statistical analysis method applied to contingency table analysis uses a chi-square test, but the chi-square test has a limitation in that it cannot show the coupling pattern for rows and columns. As an alternative, correspondence analysis is used. In general, the row profiles of correspondence analysis sum to 1. For data evaluated on the Likert scale for various attributes of each entity, the sum of rows is different for each row, so general correspondence analysis cannot be performed. Correspondence analysis can be applied to such data by doubling the number of column categories by adding the positive and negative values of each attribute so that the sum is equal. This is called the doubling technique. As a result of exploratory multivariate data analysis that does not rely on normal distribution and statistical models for Likert data, a correspondence analysis study using a doubling technique was proposed (Han, 2019). By quantifying the examiners and subjects, and expressing the result using a graphic technique, it was easy to visually recognize and interpret geometrically clear meaning. However, for the method proposed by Han (2019), the stability evaluation for quantification analysis results has not yet been developed. Therefore, in order to develop a methodology for the stability evaluation of the materialistic method for Likert data analysis, which is often seen in real life such as public opinion surveys or consumer preference surveys, but lacks development of analysis methods, and to show its usefulness through case analysis do.

Behavioral Study of Software-Defined Network Parameters Using Exploratory Data Analysis and Regression-Based Sensitivity Analysis

To provide a low-cost methodical way for inference-driven insight into the assessment of SDN operations, a behavioral study of key network parameters that predicate the proper functioning and performance of software-defined networks (SDNs) is presented to characterize their alterations or variations, given various emulated SDN scenarios. It is standard practice to use simulation environments to investigate the performance characteristics of SDNs, quantitatively and qualitatively; hence, the use of emulated scenarios to typify the investigated SDN in this paper. The key parameters studied analytically are the jitter, response time and throughput of the SDN. These network parameters provide the most vital metrics in SDN operations according to literature, and they have been behaviorally studied in the following popular SDN states: normal operating condition without any incidents on the SDN, hypertext transfer protocol (HTTP) flooding, transmission control protocol (TCP) flooding, and user datagram protocol (UDP) flooding, when the SDN is subjected to a distributed denial-of-service (DDoS) attack. The behavioral study is implemented primarily via univariate and multivariate exploratory data analysis (EDA) to characterize and visualize the variations of the SDN parameters for each of the emulated scenarios, and linear regression-based analysis to draw inferences on the sensitivity of the SDN parameters to the emulated scenarios. Experimental results indicate that the SDN performance metrics (i.e., jitter, latency and throughput) vary as the SDN scenario changes given a DDoS attack on the SDN, and they are all sensitive to the respective attack scenarios with some level of interactions between them.

Measuring residential segregation in multi‐ethnic and unequal European cities

AbstractImmigration flows and social inequalities reflect increased social and multi‐ethnic segregation in contemporary urban Europe. For a better understanding of these processes, the present study investigates the main strengths of the multi‐group residential indices, testing sensitivity and reliability under different metropolitan contexts in five European countries. These indices focus on different research dimensions and approach multi‐group residential segregation conceptually and mathematically in a different way. A multivariate exploratory data analysis was adopted to classify the observed segregation patterns into a few homogeneous types and to delineate the multivariate relationship between the indices. The results of principal component analysis demonstrate that the indices assessing uniformity and disproportionality of the social groups analysed (H and D) contribute largely to the diversification in today's multi‐ethnic communities, clarifying the importance of the dimension of evenness. Our results highlight how segregation is more evident in economically disadvantaged metropolitan regions with high levels of social vulnerability.

QUIMIOMETRIA III – REVISITANDO A ANÁLISE EXPLORATÓRIA DOS DADOS MULTIVARIADOS

CHEMOMETRICS III – REVISITING THE EXPLORATORY ANALYSIS OF MULTIVARIATE DATA. In this work, three methods for pattern recognition, used as exploratory data analysis, are revisited. A brief review of principal component analysis, PCA, an unsupervised method, is provided. Next, the Mahalanobis distance and the confidence ellipses usually drawn around the scores samples are discussed. Fisher’s canonical variate analysis (a supervised methodology) is the second method revisited in this work. The third exploratory data analysis methodology addressed is ANOVA-PCA, which uses the analysis of variance to separate variations into main effects, interaction and noise followed by principal component analysis. Unlike the other two, ANOVA-PCA was proposed recently and is still not yet explored in all its capabilities. One advantage of this method is the possibility to calculate the variance of each of the effects involved in the experimental design. The mathematical bases of the three methods are discussed as well as examples are presented.

Robust Bilinear Probabilistic Principal Component Analysis

Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which assumes that the noise terms follow matrix variate Gaussian distributions, has been introduced to directly deal with two-dimensional (2-D) data for preserving the matrix structure of 2-D data, such as images, and avoiding the curse of dimensionality. However, Gaussian distributions are not always available in real-life applications which may contain outliers within data sets. In order to make BPPCA robust for outliers, in this paper, we propose a robust BPPCA model under the assumption of matrix variate t distributions for the noise terms. The alternating expectation conditional maximization (AECM) algorithm is used to estimate the model parameters. Numerical examples on several synthetic and publicly available data sets are presented to demonstrate the superiority of our proposed model in feature extraction, classification and outlier detection.

Exploratory analysis of multivariate data: Applications of parallel coordinates in ecology

Exploratory analysis of biological communities and their environmental factors requires specialized tools to identify associations among variables and generate hypotheses about their causal relationships. Despite the ubiquity of multivariate data in ecology, the visualization and interpretation of such data can be challenging. This study introduces the application of parallel coordinates to ecologists, illustrating the utility of this tool to visualize and explore different types of multivariate data. We demonstrate this tool with two case studies in Canada to (i) explore water-quality associations with benthic macroinvertebrate indicators of stream condition in the St. Lawrence drainage basin, and (ii) identify environmental conditions that contribute to invasive zebra mussel (Dreissena polymorpha) proliferation across inland lakes of Ontario. We offer a novel demonstration of how parallel coordinates provide a practical alternative to current tools in the ecologist's toolbox for visualizing and exploring multivariate data, identifying hypotheses about causal relationships, and communicating science via interactive, web-based applications.

Multivariate exploratory data analysis by PCA of the combined effect of film-forming composition, drying conditions, and UV-C irradiation on the functional properties of films based on chitosan and pectin

The technical features of biodegradable films depend on several manufacturing parameters. Exploiting these films on an industrial basis requires statistical models for the fast and effective evaluation of these parameters. This study analyses the impact of compositional and drying factors on the microstructural and functional properties of films based on chitosan and pectin through a multivariate approach. A total of 32 formulations were developed and the results were analysed through principal component analysis (PCA). Four formulations did not form films due to the photodegradation caused by prolonged UV-C irradiation. Films containing glycerol had a higher elasticity (1.5–39%) than those with propylene glycol or that were not plasticized (1.2–12%). Glycerol increased the thickness of pectin films (56–77 μm). Sodium trimethaphosphate (STMP) enhanced the UV mean absorbance of both pectin and chitosan films (0.7–1.7). In addition, STMP led to an increase of thickness (72–129 μm) and air permeability (38.6 × 103 to 9206.1 × 103 cm3/m2 × day × kPa) of the chitosan films, while CaCl2 led to a decrease of thickness (31–59 μm) and air permeability (23.9 × 103 to 46.8 × 103 cm3/m2 × day × kPa) of the pectin films.

Empirical development of a typology on residential long-term care units in Germany - results of an exploratory multivariate data analysis

BackgroundOrganizational health care research focuses on describing structures and processes in organizations and investigating their impact on the quality of health care. In the setting of residential long-term care, this effort includes the examination and description of structural differences among the organizations (e.g., nursing homes). The objective of the analysis is to develop an empirical typology of living units in nursing homes that differ in their structural characteristics.MethodsData from the DemenzMonitor Study were used. The DemenzMonitor is an observational study carried out in a convenience sample of 103 living units in 51 nursing homes spread over 11 German federal states. Characteristics of living units were measured by 19 variables related to staffing, work organization, building characteristics and meal preparation. Multiple correspondence analysis (MCA) and agglomerative hierarchical cluster analysis (AHC) are suitable to create a typology of living units. Both methods are multivariate and explorative. We present a comparison with a previous typology (created by a nonexplorative and nonmultivariate process) of the living units derived from the same data set.ResultsThe MCA revealed differences among the living units, which are defined in particular by the size of the living unit (number of beds), the additional qualifications of the head nurse, the living concept and the presence of additional financing through a separate benefit agreement. We identified three types of living units; these clusters occur significantly with a certain combination of characteristics. In terms of content, the three clusters can be defined as: “house community”, “dementia special care units” and “usual care”.ConclusionA typology is useful to gain a deeper understanding of the differences in the care structures of residential long-term care organizations. In addition, the study provides a practical recommendation on how to apply the results, enabling living units to be assigned to a certain type. The typology can be used as a reference for definitions.

Homogeneity assessment of reference materials for sensory analysis of liquid foodstuffs. The virgin olive oil as case study

Sensory properties are critical characteristics that determine quality and can be evaluated by trained tasting panels. The panels function as multi-sensor measuring instrument and need the use of reference materials (RMs) for training.The homogeneity between units packaged from a batch of RM can be evaluated by gas chromatography coupled to flame ionization detection (GC-FID), using this instrumental technique as an alternative to sensory analysis. For this purpose, the fingerprint methodology is applied, taking into account that the homogeneity assessment will be based on evaluating the similarity between the fingerprints of the fraction of volatile organic compounds acquired from samples representative of the batch.The proposed methodology is applied with good results to evaluate the homogeneity of several RMs for sensory analysis of virgin olive oil samples, using similarity indices, control charts and exploratory analysis of multivariate data to observe the grouping RM and fingerprint regions representative of each defect.

Using MetaboAnalyst 4.0 for Comprehensive and Integrative Metabolomics Data Analysis.

MetaboAnalyst (https://www.metaboanalyst.ca) is an easy-to-use web-based tool suite for comprehensive metabolomic data analysis, interpretation, and integration with other omics data. Since its first release in 2009, MetaboAnalyst has evolved significantly to meet the ever-expanding bioinformatics demands from the rapidly growing metabolomics community. In addition to providing a variety of data processing and normalization procedures, MetaboAnalyst supports a wide array of functions for statistical, functional, as well as data visualization tasks. Some of the most widely used approaches include PCA (principal component analysis), PLS-DA (partial least squares discriminant analysis), clustering analysis and visualization, MSEA (metabolite set enrichment analysis), MetPA (metabolic pathway analysis), biomarker selection via ROC (receiver operating characteristic) curve analysis, as well as time series and power analysis. The current version of MetaboAnalyst (4.0) features a complete overhaul of the user interface and significantly expanded underlying knowledge bases (compound database, pathway libraries, and metabolite sets). Three new modules have been added to support pathway activity prediction directly from mass peaks, biomarker meta-analysis, and network-based multi-omics data integration. To enable more transparent and reproducible analysis of metabolomic data, we have released a companion R package (MetaboAnalystR) to complement the web-based application. This article provides an overview of the main functional modules and the general workflow of MetaboAnalyst 4.0, followed by 12 detailed protocols: © 2019 by John Wiley & Sons, Inc. Basic Protocol 1: Data uploading, processing, and normalization Basic Protocol 2: Identification of significant variables Basic Protocol 3: Multivariate exploratory data analysis Basic Protocol 4: Functional interpretation of metabolomic data Basic Protocol 5: Biomarker analysis based on receiver operating characteristic (ROC) curves Basic Protocol 6: Time-series and two-factor data analysis Basic Protocol 7: Sample size estimation and power analysis Basic Protocol 8: Joint pathway analysis Basic Protocol 9: MS peaks to pathway activities Basic Protocol 10: Biomarker meta-analysis Basic Protocol 11: Knowledge-based network exploration of multi-omics data Basic Protocol 12: MetaboAnalystR introduction.

THE METHOD OF MULTIVARIATE STATISTICAL ANALYSIS OF THE TIME MULTIVARIATE CRITICAL QUALITY ATTRIBUTES OF MANUFACTURE PROCESS WITH THE DATA FACTORIZATION

Context. This paper presents a method for solving the problem of product’s quality assurance at the stage of the initial manufacture process design in accordance with the process-analytical technology for the design of modern certified manufacturing – QbD. The method uses the information technologies of multivariate statistical analysis (MSA) to evaluate the influence of time multivariate critical process parameters (CPPs) on the time product critical quality attributes (CQAs). Preparatory transformation of clusters of critical process (manufacture process) parameters into factors of product critical quality attributes was carried out. Objective. To disclose the method of multivariate statistical analysis for assessing the character and features of the influence of time multivariate critical process parameters on time multivariate critical quality attributes at the design stage of the manufacture process. Method. The method consistently uses: statistical procedures of exploratory multivariate data analysis; transformation the homogeneous observed values matrices of CPPs and product CQAs into data frame (table) with factorized data; construction the regression trees of multivariate CPPs with a multivariate responses (CQAs). The method is implemented the R language packages software. Results. Factorized time multivariate CPPs make it possible to use methods of multivariate statistical analysis for evaluating the influence of CPPs factors on the time multivariate CQAs. Conclusions. This method of statistical analysis, together with statistical multivariate canonical analysis, represents an up-to-date information technology for detailed estimation the influence of time multivariate CPPs objects and some CPPs components on CQAs.

Fused adjacency matrices to enhance information extraction: The beer benchmark

Multivariate exploratory data analysis allows revealing patterns and extracting information from complex multivariate data sets. However, highly complex data may not show evident groupings or trends in the principal component space, e.g. because the variation of the variables are not grouped but rather continuous. In these cases, classical exploratory methods may not provide satisfactory results when the aim is to find distinct groupings in the data.To enhance information extraction in such situations, we propose a novel approach inspired by the concept of combining weak classifiers, but in the unsupervised context. The approach is based on the fusion of several adjacency matrices obtained by different distance measures on data from different analytical platforms. This paper is intended to present and discuss the potential of the approach through a benchmark data set of beer samples. The beer data were acquired using three spectroscopic techniques: Visible, near-Infrared and Nuclear Magnetic Resonance.The results of fusing the three data sets via the proposed approach are compared with those from the single data blocks (Visible, NIR and NMR) and from a standard mid-level data fusion methodology. It is shown that, with the suggested approach, groupings related to beer style and other features are efficiently recovered, and generally more evident.

Multivariate exploratory data analysis for large databases: An application to modelling firms’ innovation using CIS data

This paper argues that, when using a large database, organizational researchers would benefit from the use of specific multivariate exploratory data analysis (MEDA) before performing statistical modelling. Issues such as the representativeness of the database across domains (countries or sectors), assessment of confounding among categorical covariates, missing data, dimension reduction to produce performance indicators and/or remedy multicollinearity problems are addressed by specific MEDA. The proposed MEDA is applied to data from the Community Innovation Survey (CIS), a large database commonly used to analyse firms’ innovation activities, prior to fitting ordered logit and Tobit regression models. A set of recommended practices involving MEDA are proposed throughout the paper.

Integrating parametric and non-parametric multivariate analysis of urban growth and commuting patterns in a European metropolitan area

Mono-centric regions have experienced a progressive transformation towards polycentric structures. Transition to discontinuous and dispersed spatial configurations was particularly evident in formerly compact and dense European cities, as a result of increasingly complex commuting patterns. Under the hypothesis that central locations have a balanced rate of resident population to internal workers and attract workers from neighbouring places, a multivariate analysis of commuting patterns may reveal latent transformations of compact, mono-centric cities towards polycentrism and settlement scattering. A more comprehensive understanding of the intimate nature and implications of urban transitions taking place in the last decades in Athens (Greece), a representative metropolitan region in southern Europe, was carried out using census data analyzed through a framework integrating descriptive statistics and mapping, multivariate exploratory data analysis, non-parametric inference and regression models. The analytical framework was proposed with the aim to assess commuting patterns vis a vis urban hierarchy in a context of (more or less) de-centralized growth. Empirical results for the study area indicate the persistence of a bi-centric spatial structure gravitating on the central cities of Athens and Piraeus, with early formation of employment sub-centres and local-scale alterations of the mono-centric scheme as a result of discontinuous urban expansion. Exurban development was associated with the formation of self-contained sub-centres with an increasing proportion of workers in total resident population.

Texture analysis in liver of common carp (Cyprinus carpio) sub-chronically exposed to perfluorooctanoic acid

An operator-neutral, objective method was implemented to comparatively assess liver pathology in 30 specimens of common carp (Cyprinus carpio): 20 after experimental flow-through exposure to two perfluorooctanoic acid (PFOA) dosages (10 fish exposed to 200ngl−1 and 10 fish exposed to 2mgl−1) for 56days and 10 unexposed (negative control). The method relies on texture analysis as a complementary approach to traditional histopathology and chemical dosage analysis performed previously on the same experimental material. Texture features data were analyzed by means of Redundancy Analysis (RDA), Linear Discriminant Analysis (LDA) and Canonical Variates Analysis (CVA). LDA resulted in the correct classification of 80% of cases (24 out of 30 cases) with a sensitivity of 83.3% and a specificity of 83.3. In particular, four male samples from the low dosage group (200ngl−1) were misclassified as unexposed fish and two female samples from the unexposed group were misclassified as low dosage exposed. Nevertheless, PFOA liver chemical dosage analysis results were the same both in unexposed and in low dosage group fish, all below the limit of detection. No sample from the high dosage group (2mgl−1) has ever been misclassified. Interestingly, texture features correlated with the PFOA concentrations detected in the liver of each sampled fish. In the present study the technique of texture analysis was combined with techniques of multivariate exploratory data analysis (RDA, LDA/CVA). This approach resulted in a robust, sufficiently sensitive and specific means to study PFOA-induced liver pathology. The new method can discriminate between unexposed and two PFOA exposed groups with better confidence and in a more affordable way, compared to chemical quantification of liver PFOA. The texture features correlated well with liver PFOA concentrations and objectively quantified degenerative liver morphology. In conclusion the overall approach may be a suitable candidate as a reliable and broad-ranging method for biomarker analysis of exposure and effect.

Discriminating Brazilian crude oils using comprehensive two-dimensional gas chromatography–mass spectrometry and multiway principal component analysis

The geochemical characterization of petroleum is an essential task to develop new strategies and technologies when analyzing the commercial potential of crude oils for exploitation. Due to the chemical complexity of these samples, the use of modern analytical techniques along with multivariate exploratory data analysis approaches is an interesting strategy to extract relevant geochemical characteristics about the oils. In this work, important geochemical information obtained from crude oils from different production basins were obtained analyzing the maltene fraction of the oils by comprehensive two-dimensional gas chromatography coupled to quadrupole mass spectrometry (GC×GC–QMS), and performing multiway principal component analysis (MPCA) of the chromatographic data. The results showed that four MPC explained 93.57% of the data variance, expressing mainly the differences on the profiles of the saturated hydrocarbon fraction of the oils (C13-C18 and C19-C30n-alkanes and the pristane/phytane ratio). The MPC1 grouped the samples severely biodegraded oils, while the type of the depositional paleoenvironments of the oils and its oxidation conditions (as well as their thermal maturity) could be inferred analysing others relevant MPC. Additionally, considerations about the source of the oil samples was also possible based on the overall distribution of relevant biomarkers such as the phenanthrene derivatives, tri-, tetra- and pentacyclic terpanes.

Multivariate approach to gill pathology in European sea bass after experimental exposure to cadmium and terbuthylazine

The combined use of guided quantitative expert analysis and of multivariate exploratory data analysis is reported as a robust, sensitive and sufficiently specific approach to study European sea bass gill secondary lamellar pathology after exposure to incremental doses of cadmium and terbuthylazine up to 48h. The following elementary pathological findings were considered: “epithelial lifting”, “epithelial shrinkage”, “epithelial swelling”, “pillar cells coarctation”, “pillar cells detachment”, “channels fusion”, “chloride cells swelling”, and “chloride cells invasion”. The relative spatial extension was determined according to exposure class and data were analyzed by means of canonical correspondence analysis (CCA), linear discriminant analysis (LDA) and canonical variates analysis (CVA). Histologically and ultrastructurally, cellular shrinkage/coarctation prevailed in cadmium exposed lamellae, whereas cellular swelling and epithelial lifting were predominant in terbuthylazine exposed lamellae compared to unexposed fish. Both CCA and CVA permit a good graphical data grouping according to exposure classes by means of the convex hull minimum polygons. This also reveals exposure dose and time gradients in CCA plot. Accordingly, epithelial swelling and epithelial shrinkage were comparatively associated to higher exposure time, whereas epithelial shrinkage and pillar cells coarctation were comparatively associated to higher exposure dose. LDA with only “epithelial shrinkage”, “epithelial swelling” and “pillar cells coarctation” in the model classified correctly 87.5% of the cross-validated cases. A possible pathogenetic relationship between the discriminant elementary lesions and the toxic mode of action at the cellular level of both cadmium and terbuthylazine is also discussed.