Multiple factor analysis (MFA, also called multiple factorial analysis) is an extension of principal component analysis (PCA) tailored to handle multiple data tables that measure sets of variables ...collected on the same observations, or, alternatively, (in dual‐MFA) multiple data tables where the same variables are measured on different sets of observations. MFA proceeds in two steps: First it computes a PCA of each data table and ‘normalizes’ each data table by dividing all its elements by the first singular value obtained from its PCA. Second, all the normalized data tables are aggregated into a grand data table that is analyzed via a (non‐normalized) PCA that gives a set of factor scores for the observations and loadings for the variables. In addition, MFA provides for each data table a set of partial factor scores for the observations that reflects the specific ‘view‐point’ of this data table. Interestingly, the common factor scores could be obtained by replacing the original normalized data tables by the normalized factor scores obtained from the PCA of each of these tables. In this article, we present MFA, review recent extensions, and illustrate it with a detailed example. WIREs Comput Stat 2013, 5:149–179. doi: 10.1002/wics.1246
This article is categorized under:
Data: Types and Structure > Categorical Data
Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
R-mode hierarchical cluster and principal component analysis (PCA) were simultaneously applied to surface water hydrochemical data from three different locations, Ankwaso, Dominase and Prestea, along ...the Ankobra Basin, Ghana, to extract principal factors corresponding to the different sources of variation in the hydrochemistry, with the objective of defining the main controls on the hydrochemistry at the basin scale. Using the Kaiser criterion, principal components (PC) were extracted from the data and rotated using varimax normalization, for each location. The varimax rotation ensured that variation in the data was maximized for easy interpretation of the results. The analysis reduced 30, 33 and 33 data points, respectively, for Ankwaso, Dominase and Prestea to four, three and four PC representing the sources of variation in the hydrochemistry at the three different locations. Though the PC analysis proved to be more robust at unveiling the sources of variation in the hydrochemistry than the
R-mode hierarchical cluster analysis (HCA), the combined use of both techniques resulted in more reliable interpretations of the hydrochemistry. On the basis of these analyses, the hydrochemistry of the basin is controlled largely by the weathering of minerals (silicates, carbonates, gypsum and apatite) from the underlying meta-sediments of the Birimian and Tarkwaian Systems, and the decay of organic matter from the heavily forested regions. Concentrations of the major chemical parameters are within naturally acceptable limits and do not pose threats to the local ecology and humans. There is no strong evidence of high anthropogenic impacts on the major anions and cations used for this research, though there are variations at the different locations studied. The hydrochemistry at Ankwaso is principally controlled by the weathering of silicate minerals, whereas those of Dominase and Prestea are, respectively, influenced by precipitation and domestic wastewaters, and the decay of organic matter.
Dietary composition and rearing regime largely determine the trace elemental composition of pigs, and consequently their concentration in animal products. The present study evaluates thirteen macro- ...and trace element concentrations in pork from organic and conventional farms. Conventional pigs were given a commercial feed with added minerals; organic pigs were given a feed based on organic feedstuffs. The content of macro-elements (Na, K, Mg and Ca) and some trace elements (Ni, Fe, Zn and Sr) in organic and conventional meat samples showed no significant differences (P>0.05). Several trace element concentrations in organic pork were significantly higher (P<0.05) compared to conventional pork: Cr (808 and 500μg/kg in organic and conventional pork, respectively), Mn (695 and 473μg/kg) and Cu (1.80 and 1.49mg/kg). The results showed considerable differences in mineral content between samples from pigs reared in organic and conventional systems. Our results also indicate that authentication of organic pork can be realized by applying multivariate chemometric methods such as discriminant analysis to this multi-element data.
: Rice bean, a less known and underutilized legume, has emerged as a potential legume because of its nutritional potential. The nutritional quality of rice bean is higher as compared to many other ...legumes of Vigna family. In the present study, 16 diverse rice bean genotypes were evaluated for major nutritional constituents viz; protein content, total lipids, dietary fiber, total carbohydrates, vitamins, minerals, protein fractions, amino acid, and fatty acid profile. The protein content to the extent of 25.57% was observed in the genotype BRS‐2 with in vitro digestibility of 54.23%. The fatty acid profile revealed the higher percentage of unsaturated fatty viz., linoleic and linolenic acid, which are nutritionally desirable in the diet. Albumins (6.13% to 7.47%) and globulins (13.11% to 15.56%) constituted the major portion of proteins. Anti‐nutritional factors were in the range of: total phenolics (1.63% to 1.82%), total tannins (1.37% to 1.55%), condensed tannins (0.75% to 0.80%), hydrolysable tannins (0.56% to 0.79%), trypsin inhibitor (24.55 to 37.23 mg/g), phytic acid (7.32 to 8.17 mg/g), lipoxygenase activity (703 to 950 units/mg), and saponin content (1.2 to 3.1 mg/100 g). The oligosaccharides associated with the production of flatulence viz., raffinose, stachyose, and verbascose were in the limits of 1.66% to 2.58%, 0.94% to 1.88%, and 0.85% to 1.23%, respectively. In vitro protein digestibility up to 55.57% was observed in rice bean genotypes. The present study has revealed that rice bean is a nutritionally rich legume as compared to many other legumes of the category. Among different genotypes BRS‐2 was observed superior and could be advocated for consumption as well as for inclusion in crop improvement programs.
Practical Application: Rice bean is nutritionally rich legume, but despite its nutritional excellence, it has been put in underutilized category. Because of this and several other reasons the people are not aware of its nutritional benefits. Moreover, the complete nutritional details are also not available on this pulse. The present study gives the vivid description of nutritional attributes of this legume for making people aware of its nutritional excellence and provoking improved work in rice bean.
We have developed a new mass spectrometry (MS) technology, the Single-probe MS, capable of real-time, in situ metabolomic analysis of individual living cells. The Single-probe is a miniaturized ...multifunctional sampling and ionization device that is directly coupled to the mass spectrometer. With a sampling tip smaller than individual eukaryotic cells (<10 μm), the Single-probe can be inserted into single cells to sample the intracellular compounds for real-time MS analysis. We have used the Single-probe to detect several cellular metabolites and the anticancer small molecules paclitaxel, doxorubicin, and OSW-1 in individual cervical cancer cells (HeLa). Single cell mass spectrometry (SCMS) is an emerging scientific technology that could reshape the analytical science of many research disciplines, and the Single-probe MS technology is a novel method for SCMS that, through its accessible fabrication protocols, can be broadly applied to different research areas.
Organic aerosols were studied at the molecular level in 14 coastal and inland mega-cities in China during winter and summer 2003. They are characterized by the abundant presence of n-alkanes (annual ...average, 340 ng m-3), fatty acids (769 ng m-3), sugars (412 ng m-3), and phthalates (387 ng m-3). In contrast, fatty alcohols, polyols/polyacids, lignin and resin products, sterols, polycyclic aromatic hydrocarbons (PAHs), and hopanes were detected as relatively minor components. n-Alkanes show a weak odd/even carbon predominance (CPI = 1.1) and PAHs show a predominance of benzo(b)fluoranthene, suggesting a serious contribution from fossil fuel (mainly coal) combustion. Their concentrations (except for phthalates and polyols/polyacids) were 2−15 times higher in winter than summer due to a significant usage of coal burning and an enhancement of atmospheric inversion layers. Phthalates were found to be more abundant in summer than winter, probably due to enhanced vaporization from plastics followed by adsorptive deposition on the pre-existing particles. Concentrations of total quantified compounds are extremely high (∼10 μg m-3) in the midwest (Chongqing and Xi'an) where active industrialization/urbanization is going on. This study shows that concentrations of the compounds detected are 1−3 orders of magnitude higher than those reported from developed countries.
The spatial distribution and transport characteristics of heavy metals in an antimony mine area (Xikuangshan, China) were systematically studied using a field survey and geostatistical analytical ...methods. In the study area, 52 soil and sediment samples were collected from bare land, grassland, woodland and river sediments covering a surface area of 20 km2. The soil properties and heavy metal concentrations were measured by wavelength dispersive X-ray fluorescence spectrometry and inductively coupled plasma-mass spectrometry, respectively. Correlation analysis and principal component analysis suggest that Cu, Zn, Cd, As, Pb and Sb can be attributed to anthropogenic inputs, whereas Cr, Mn and Ni are of natural origin. Distribution maps of heavy metals were generated using the Kriging interpolation method to identify their distribution trends. The results show the influence of wind, river, distance and vegetation on the spatial distribution. The results also revealed that windborne transport may play a significant role in the spreading of contaminants. In addition, the environmental risk of heavy metal pollution was evaluated using their geoaccumulation indexes in the whole region. All of the results indicate that the heavy metal distributions in the soils were consistent with the local prevailing wind direction. In addition, the environmental quality could be seriously threatened by heavy metal contaminants from the smelter and tailings.
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●As and Sb showed similar geochemical behavior on transport and deposition.●Lower concentrations for Cr, Mn and Ni may be controlled by natural factors.●Cu, Zn, Cd and Pb may be released from sulfide minerals.●Heavy metal distribution trends were associated with local wind direction.●The environment quality was obviously threatened by accumulation of Sb and Cd.
National-scale empirical models for air pollution can include hundreds of geographic variables. The impact of model parsimony (i.e., how model performance differs for a large versus small number of ...covariates) has not been systematically explored. We aim to (1) build annual-average integrated empirical geographic (IEG) regression models for the contiguous U.S. for six criteria pollutants during 1979-2015; (2) explore systematically the impact on model performance of the number of variables selected for inclusion in a model; and (3) provide publicly available model predictions. We compute annual-average concentrations from regulatory monitoring data for PM10, PM2.5, NO2, SO2, CO, and ozone at all monitoring sites for 1979-2015. We also use ~350 geographic characteristics at each location including measures of traffic, land use, land cover, and satellite-based estimates of air pollution. We then develop IEG models, employing universal kriging and summary factors estimated by partial least squares (PLS) of geographic variables. For all pollutants and years, we compare three approaches for choosing variables to include in the PLS model: (1) no variables, (2) a limited number of variables selected from the full set by forward selection, and (3) all variables. We evaluate model performance using 10-fold cross-validation (CV) using conventional and spatially-clustered test data. Models using 3 to 30 variables selected from the full set generally have the best performance across all pollutants and years (median R2 conventional clustered CV: 0.66 0.47) compared to models with no (0.37 0) or all variables (0.64 0.27). Concentration estimates for all Census Blocks reveal generally decreasing concentrations over several decades with local heterogeneity. Our findings suggest that national prediction models can be built by empirically selecting only a small number of important variables to provide robust concentration estimates. Model estimates are freely available online.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
•Essential oil composition and antioxidant activity of fourteen Thymus accessions were investigated.•Thymol, carvacrol, geraniol and p-cymene were the major constituents of essential oil.•Based on ...bioactive components, three groups were identified in studied plants.•T. vulgaris and T. fedtschenkoi-1 possessed the highest amount of flavonoids.•T. daenensis-3, T. vulgaris and T. fedtschenkoi-3 had the highest antioxidant activity.
In this study, the essential oil (EO) composition, flavonoid and phenolic contents, and antioxidant activities of fourteen Thymus accessions belonging to ten species were evaluated. Gas chromatography–mass spectrometry (GC–MS) analysis revealed the presence of 38 compounds with the major constituents including thymol (12.4–79.74%), carvacrol (4.37–42.14%), geraniol (0.3–22.44%), and p-cymene (0.8–12.86%). Cluster analysis identified three groups of high thymol, geraniol/linalool, and high carvacrol. The highest phenolic and flavonoid contents were detected in T. daenensis-1 (70.6mg tannic acid equivalents (TAE) g−1 DW) and T. vulgaris (8.55mg quercetin equivalents (QE) g−1 DW), respectively. The antioxidant activities of the samples were determined using 1,1-diphenyl-2-picrylhydrazyl (DPPH) and reducing power assay. The results demonstrated that T. daenensis-3 (IC50=273.36), T. vulgaris (IC50=289.3), and T. fedtschenkoi-3 (IC50=339.22) possessed higher antioxidant activities than the others. Finally, the Thymus species with high bioactive compounds may be recommended for further food applications.
•Vegetables prepared with EVOO contained phenols not identified in the raw forms.•The vegetables were enriched with EVOO phenols transferred from the oil.•The antioxidant capacity of the foodstuffs ...increased more when prepared only in oil.•Oil in cooking water does not increase the antioxidant capacity of the vegetable.
Potato, tomato, eggplant and pumpkin were deep fried, sautéed and boiled in Mediterranean extra virgin olive oil (EVOO), water, and a water/oil mixture (W/O). We determined the contents of fat, moisture, total phenols (TPC) and eighteen phenolic compounds, as well as antioxidant capacity in the raw vegetables and compared these with contents measured after cooking. Deep frying and sautéing led to increased fat contents and TPC, whereas both types of boiling (in water and W/O) reduced the same. The presence of EVOO in cooking increased the phenolics identified in the raw foods as oleuropein, pinoresinol, hydroxytyrosol and tyrosol, and the contents of vegetable phenolics such as chlorogenic acid and rutin. All the cooking methods conserved or increased the antioxidant capacity measured by DPPH, FRAP and ABTS. Multivariate analyses showed that each cooked vegetable developed specific phenolic and antioxidant activity profiles resulting from the characteristics of the raw vegetables and the cooking techniques.
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