Isometric Log Ratio Research Articles

Using isometric log-ratio in compositional data analysis for developing a groundwater pollution index

This study introduces a novel groundwater pollution index (GPI) formulated through compositional data analysis (CoDa) and robust principal component analysis (RPCA) to enhance groundwater quality assessment. Using groundwater quality monitoring data from sites impacted by the 2010–2011 foot-and-mouth disease outbreak in South Korea, CoDa uncovers critical hydrochemical differences between leachate-influenced and background groundwater. The GPI was developed by selecting key subcompositional parts (NH4+-N, Cl-, and NO3--N) using RPCA, performing the isometric log-ratio (ILR) transformation, and normalizing the results to environmental standards, thereby providing a more precise and accurate assessment of pollution. Validated against government criteria, the GPI has shown its potential as an alternative assessment tool, with its reliability confirmed by receiver operating characteristic curve analysis. This study highlights the essential role of CoDa, especially the ILR -transformation, in overcoming the limitations of traditional statistical methods that often neglect the relative nature of hydrochemical data. Our results emphasize the utility of the GPI in significantly advancing groundwater quality monitoring and management by addressing a methodological gap in the quantitative assessment of groundwater pollution.

Proportion-based normalizations outperform compositional data transformations in machine learning applications

BackgroundNormalization, as a pre-processing step, can significantly affect the resolution of machine learning analysis for microbiome studies. There are countless options for normalization scheme selection. In this study, we examined compositionally aware algorithms including the additive log ratio (alr), the centered log ratio (clr), and a recent evolution of the isometric log ratio (ilr) in the form of balance trees made with the PhILR R package. We also looked at compositionally naïve transformations such as raw counts tables and several transformations that are based on relative abundance, such as proportions, the Hellinger transformation, and a transformation based on the logarithm of proportions (which we call “lognorm”).ResultsIn our evaluation, we used 65 metadata variables culled from four publicly available datasets at the amplicon sequence variant (ASV) level with a random forest machine learning algorithm. We found that different common pre-processing steps in the creation of the balance trees made very little difference in overall performance. Overall, we found that the compositionally aware data transformations such as alr, clr, and ilr (PhILR) performed generally slightly worse or only as well as compositionally naïve transformations. However, relative abundance-based transformations outperformed most other transformations by a small but reliably statistically significant margin.ConclusionsOur results suggest that minimizing the complexity of transformations while correcting for read depth may be a generally preferable strategy in preparing data for machine learning compared to more sophisticated, but more complex, transformations that attempt to better correct for compositionality.DL26Qs8hz41d9wKrFGqt9FVideo

Mapping soil particle-size fractions based on compositional balances

Mapping of soil particle-size fractions (PSFs) combined with log-ratio transformation has been widely employed, particularly for isometric log-ratio (ILR). Regression kriging (RK), as a hybrid interpolator, represents a method to enhance prediction accuracy. However, different choices of ILR balance yield distinct transformed data. It remains unclear and lacks a comparison as to whether these results exhibit robustness when employing RK modeling. In this study, we compared the performance of four modelling approaches–generalized linear model (GLM), random forest (RF), and their hybrid models (i.e., GLMRK and RFRK). These models were applied to three ILR transformed datasets based on different balances, resulting in a total of 12 models, in the upper reaches of the Heihe River Basin, China. The results indicated that RF tended to provide more accurate predictions of soil PSFs, while GLM was better at producing predictions with less bias. The study recommends the use of RK, as it was found to broaden the value ranges of predictions, adjust bias, and enhance accuracy, especially when applied in conjunction with RF models. Furthermore, prediction maps generated from RK unveiled finer details of soil sampling points. The choices of ILR balance resulted in varying data distributions for the components of sand, silt, and clay. These components tended to cluster at approximately 120° in three groups, thereby indicating that even components with small content also exert significant influence on soil compositions. Rather than solely focusing on the relative abundance of components, this study suggests that the alignment of ILR components with a normal distribution is crucial for better model performance, especially for the first ILR component. Opting for the most abundant component as the first permutation may not always lead to optimal results for soil PSF mapping. This study provides insights into the role of data distribution and ILR balance selection in soil PSF mapping with transformed data.

Spatial Overlay Analysis of Geochemical Singularity Index α-Value of Porphyry Cu Deposit in Gangdese Metallogenic Belt, Tibet, Western China

The statistical modeling with ILR-RPCA-back CLR has two problems when dealing with the closure effect of geochemical data. Firstly, after performing isometric logratio (ilr) transformation, robust principal component analysis (RPCA) is employed for processing. The double-plot diagram illustrates that the element sequence transformation occurs in the first and second principal components, while the unique principal component remains unattainable. Secondly, by transforming both the score and load into the centered logratio (CLR) space using the U matrix, it is possible to obtain a score result that corresponds to the original order of elements according to the CLR = ILR·U formula. However, for obtaining a load result that corresponds to the original order of elements, an alternative formula “CLR = UT·ILR” must be used instead. In order to determine the optimal element assemblage for porphyry copper deposits, this study conducted statistical analysis on mineral assemblages from discovered deposits in the Gangdese metallogenic belt and identified Cu, Mo, Au, Ag, W, and Bi as key elements associated with porphyry copper deposits. Subsequently, by analyzing the singularities of the composite elements, the spatial overlay of the combined element is carried out, and concentration-area (C-A) fractal filtering is applied to identify the anomaly and background areas. To facilitate comparison, we conducted an analysis of various mineral and ore deposit types, revealing the following findings: (1) Combination elements exhibit superior recognition capability than single elements in porphyry copper deposits; (2) Skarn-type copper deposits unrelated to porphyry show a high degree of dissimilarity compared to those related to porphyry; (3) this method offers advantages over the single element method in evaluating porphyry gold deposits by reducing anomaly levels and initial investment during the evaluation stage for porphyry copper anomalies; (4) However, this method has limited ability in distinguishing between porphyry copper and molybdenum deposits.

Statistical depth for point process via the isometric log-ratio transformation

Statistical depth, a useful tool to measure the center-outward rank of multivariate and functional data, is still under-explored in temporal point processes. Recent studies on point process depth proposed a weighted product of two terms - one indicates the depth of the cardinality of the process, and the other characterizes the conditional depth of the temporal events given the cardinality. The second term is of great challenge because of the apparent nonlinear structure of event times, and so far only parametric representations such as Gaussian and Dirichlet densities have been adopted in the definitions. However, these parametric forms ignore the underlying distribution of the process events and are difficult to apply to complicated patterns. To deal with these problems, a novel distribution-based approach is proposed to the conditional depth via the well-known Isometric Log-Ratio (ILR) transformation on the inter-event times. Motivated by a uniform distribution on simplex, the new method, called the ILR depth, is formally defined for general point process via a Time Rescaling. The mathematical properties of the ILR depth are thoroughly examined and the new method is well illustrated by using Poisson and non-Poisson processes to demonstrate its superiority over previous methods. Finally, the ILR depth is applied in a real dataset and the result clearly shows its effectiveness in ranking.

Racial and genetic ancestry associations with gene expression patterns in a real-world cohort of colorectal cancer patients.

3541 Background: There is a growing incidence of colorectal cancer (CRC) among young adults and persistent disparities in outcomes by race/ethnicity across all ages. Gene expression signatures, as well as consensus molecular subtypes (CMS) derived from these, have been proposed to predict prognosis and therapy response in CRC. However, it is unclear whether gene expression or CMS are associated with racial disparities observed in CRC. We assessed whether race or genetic ancestry are associated with CMS or gene expression patterns in a deidentified cohort of 1,768 CRC patients. Methods: Patients tumors’ underwent tumor profiling with the Tempus xT NGS 648-gene assay as well as full-transcriptome RNA sequencing. We used a set of 654 ancestry-informative markers to infer genetic ancestry likelihoods for Africa (AFR), America (AMR), East Asia (EAS), Europe (EUR), and South Asia (SAS). Race/ethnicity labels, often missing in real-world data, were imputed using ancestry proportions from the literature and adjusted based on observed metadata. Gene expression data was used to assign CMS to all patients (CMS1, 2, 3, 4 and indeterminate) using CMScaller, and multinomial logistic regression was used to assess associations with race/ethnicity imputed labels and ancestry proportions. We then assessed differential expression (DE) in the MSigDB hallmark and C2 BioCarta gene sets using four separate workflows. The first two workflows used limma-voom followed by ROAST to assess DE among the imputed labels and then among the ancestry proportions (isometric log ratio transformed). The second two workflows used GSVA followed by limma. Results: Among 1,768 patients, 240 were imputed non-Hispanic (NH) Black, 94 NH Asian, 261 Hispanic/Latino/Native American (HLN), and 1,173 NH White. NH Black patients had higher odds of CMS3 vs CMS1 (OR = 2.66, p < 0.001) and HLN patients had higher odds of indeterminate CMS vs CMS1 (OR = 1.90, p = 0.020), compared to NH White. AFR ancestry was significantly associated with CMS3 (OR = 1.05 per doubling in AFR proportion, p = 0.047) and indeterminate CMS (OR = 1.07, p = 0.023). In the gene set analysis, NH Black race/ethnicity was associated with over-expression of the BioCarta WNT pathway gene set. Both AFR ancestry and NH Black race/ethnicity were associated with under-expression of the MSigDB hallmark coagulation and BioCarta alternative complement gene sets and over-expression of the PITX2 pathway gene set (all significant with both ROAST and GSVA). Conclusions: We found that NH Black patients and AFR ancestry were associated with higher rates of CMS3, which is associated with KRAS mutation and was previously reported to be more common among Black patients. Indeterminate CMS associations with AFR ancestry and HLN highlights the need to use diverse patient cohorts when training unsupervised learning models to improve prognosis prediction in non-White patients.

Quantifying soil properties relevant to soil organic carbon biogeochemical cycles by infrared spectroscopy: The importance of compositional data analysis

Oxyhydroxides, soil texture and soil organic carbon (SOC) fractions are key parameters determining organic carbon cycling in soils. Standard laboratory methods to determine these soil properties are, however, time–consuming and expensive. Visible near infrared (Vis–NIR) and mid infrared (MIR) spectroscopy have been recognized as a promising alternative, but previous studies have not explicitly considered the above–mentioned soil properties as compositional data. The fractional components in compositional data are interrelated but their sum should be unity – these features should be represented in the spectral modeling process to minimize the prediction bias. In this study, two unique datasets were used to test these premises. The first one consisted of 655 samples collected from agricultural terraces and lynchets across Europe, which were scanned to acquire MIR spectra, while in the second one 4516 samples from private gardens across Flanders, Belgium were used to acquire Vis–NIR spectra. Memory–based learning models were optimized using both raw data (conventional method) and transformed data of soil properties by additive log–ratio (alr), centered log–ratio (clr), and isometric log–ratio (ilr) transformation methods. Results showed that the log–ratio transformation methods produced predictions as accurate as the conventional method, whilst also added two significant benefits: (1) they ensured the predicted fractions added up to 100% and (2) they reduced the number of samples with extreme prediction errors. We found that for 11 out of 18 investigated soil properties, the three log–ratio transformation methods provided similar model performance, whilst ilr outperformed clr for the prediction of silt and sand content of garden soils, for coarse particulate SOC (>250 µm) and microaggregate–associated SOC (250–53 µm) of terrace soils. For the remaining three properties (Al oxyhydroxides) alr outperformed ilr. Fair to excellent predictive models (RPD from 1.4 to 4.3; R2 from 0.50 to 0.95) were achieved for soil oxyhydroxides (Fe, Al, Mn) and soil texture from MIR spectra. Our approach also enabled accurate predictions of silt and sand content of garden soils using Vis–NIR spectra (RPD = 1.9; R2 = 0.72), although accuracy for clay was lower (RPD = 1.3; R2 = 0.49). This study demonstrates that combining soil infrared spectroscopy with a compositional data analysis is a promising technique that enables cost-effective and reliable quantification of soil properties relevant to SOC stability, thus offering a practical opportunity to assess the role of SOC in global C cycling.

An exploration into the relationship between mineral elements (nitrogen and phosphorus) and nutritional quality in soil-watermelon (Citrullus lanatus) system

To fundamentally explore the correlation between crop nutritional quality and mineral elements, specific tests and accurate analysis were carried out on all organs and root soil of watermelon (Citrullus lanatus). The results showed that the distribution patterns of nitrogen and phosphorus at watermelon maturity were similar, and the average nitrogen and phosphorus contents were in the orders of leaf and seed > stem, peel, root > pulp > root soil, and peel > seed > root, stem, leaf > root soil > pulp, respectively. From the perspective of element geochemistry, biophile and lithophile elements had the strongest correlation with nitrogen and phosphorus, and watermelon did not antagonize soil nitrogen and phosphorus uptake. The prediction model of nitrogen translocation factor in watermelon organs to total acid was established by partial least squares with R2 = 0.81. Significantly, when the isometric log-ratio of nitrogen to phosphorus in watermelon leaves was 1.97 to 2.19, the watermelon pulp showed better quality with total acid > 0.5%, total sugar > 5% and soluble solids > 10%. Therefore, the characterization of nitrogen and phosphorus in watermelon leaves can serve as a non-destructive analysis to predict watermelon fruit quality.

Machine learning models for predicting soil particle size fractions from routine soil analyses in Quebec

AbstractSoil texture and particle size distribution are important soil properties for understanding and interpreting the multiple processes and interactions in soil agrosystems. However, soil particle size analysis is rarely included in routine soil laboratory analyses due to cost but can be derived from other soil physico‐chemical properties and from more powerful regressions using machine learning techniques. The performance of multiple linear regression and four machine learning algorithms (MLAs)—K‐nearest neighbor (KNN), Random Forest, extra‐gradient boosting (XGBoost), and multilayer neural network (NeuralNetwork)—was compared to predict particle size fractions of clay, sand, and silt using routine analyses of soil pH, cation exchange capacity, Mehlich‐3 extracted elements, and density of dried sieved soil from 8,364 soil samples distributed across Quebec. Particle size fractions were predicted as compositional data using isometric log ratio transformation. The XGBoost model performed best, with RMSE values of 7, 10, and 12% and R2 values of .77, .57, and .73 for the prediction of clay, silt, and sand fractions, respectively. Feature importance classification varied from one model to another, but the best predictors remained the same regardless of the model used. Sieved soil density measured in the laboratory and Mehlich‐3 Mg, K, Fe, and Zn ranked as better predictors of particle size fractions. Predicting soil particle sizes using routine soil physico‐chemical properties and MLAs appears an option for incomplete legacy datasets and a promising economic alternative to current methods carried out in commercial laboratories.

Proportional allocation with soil depth improved mapping soil organic carbon stocks

Soil organic carbon (SOC) is vital to the assessment of land quality, management of farmland and ecological environment, and carbon cycle. A more accurate spatial prediction of multilayer soil organic carbon density (SOCD) can contribute to a better interpretation of the changes in multilayer SOC stocks and carbon dynamics. However, previous mapping techniques still have limitations, such as ignoring the relationship of profile depths, not further taking advantage of vertical distribution and surface categorical information. In addition, it is unclear whether it is better to model each depth interval of SOC separately or to model the total layer and then allocate it. Here, we propose two new methods based on the proportional allocation of soil depth for multilayer mapping: vertical log-ratio method (VLR) of SOCD by applying the percentage of SOCD data and isometric log-ratio (ILR) transformation, and vertical distribution method (VD) of SOCD by considering different land-use types. We compared five methods, including the two new methods, the exponential and equal-area spline functions, and independent modeling without depth information. We combined these five methods with the generalized linear model (GLM) and random forest (RF) to produce predictions of the Sanjiang Plain, northeastern China. The results demonstrated that SOCD did not always decrease with increasing soil depth, and classification of SOCD vertical distribution features needs to be considered by combining with soil depths. For accuracy assessment, the exponential mode with both GLM and RF over-calculated the predicted values and performed poorly, indicating that the blind use of depth information increased the prediction error. The spline function prediction was scarcely better than that of independent modeling. The proportional allocation methods performed better than other separate modeling methods for accuracy and interpretability with GLM or RF, especially for the middle and surface layers. The GLM generated more aggregated predictions than the RF, losing the distribution pattern of the original data. Therefore, we recommend RF combined with proportional allocation methods for spatial SOCD prediction in large-scale study areas. We calculated the SOC stocks in the Sanjiang Plain using our new methods, which were more reasonable compared with those of previous studies and had the advantages of in-depth information, environmental variable selection, and model optimization. Our findings provide not only other perspectives for SOCD mapping, with more fully integrated depth information and more accurate assessment of multilayer SOC stocks, but also provide guidance for the evaluation of land quality, farmland, and ecological environmental management.

Approximation of a Microbiome Composition Shift by a Change in a Single Balance Between Two Groups of Taxa.

ABSTRACTLinking microbiome composition obtained from metagenomic or 16S rRNA sequencing to various factors poses a real challenge. The compositional approach to such data is well described: a so-called isometric log-ratio (ILR) transform provides correct treatment of relative abundances. Most existing compositional methods differ in the particular choice of the transform. Although this choice does not influence the prediction of a model, it determines the subset of balances between groups of microbial taxa subsequently used for interpreting the composition shifts. We propose a method to interpret these shifts independently of the initial choice of ILR coordinates by the nearest single-balance shift. We describe here application of the method to regression, classification, and principal balance analysis of compositional data. Analytical treatment and cross-validation show that the approach provides the least-squares estimate of a single-balance shift associated with a factor with possible adjustment for covariates. As for classification and principal balance analysis, the nearest balance method provides results comparable to other compositional tools. Its advantages are the absence of assumptions about the number of taxa included in the balance and its low computational cost. The method is implemented in the R package NearestBalance.IMPORTANCE The method proposed here extends the range of compositional methods providing interpretation of classical statistical tools applied to data converted to the ILR coordinates. It provides a strictly optimal solution in several special cases. The approach is universally applicable to compositional data of any nature, including microbiome data sets.

Rank-Based Mixture Models for Temporal Point Processes

Temporal point process, an important area in stochastic process, has been extensively studied in both theory and applications. The classical theory on point process focuses on time-based framework, where a conditional intensity function at each given time can fully describe the process. However, such a framework cannot directly capture important overall features/patterns in the process, for example, characterizing a center-outward rank or identifying outliers in a given sample. In this article, we propose a new, data-driven model for regular point process. Our study provides a probabilistic model using two factors: (1) the number of events in the process, and (2) the conditional distribution of these events given the number. The second factor is the key challenge. Based on the equivalent inter-event representation, we propose two frameworks on the inter-event times (IETs) to capture large variability in a given process—One is to model the IETs directly by a Dirichlet mixture, and the other is to model the isometric logratio transformed IETs by a classical Gaussian mixture. Both mixture models can be properly estimated using a Dirichlet process (for the number of components) and Expectation-Maximization algorithm (for parameters in the models). In particular, we thoroughly examine the new models on the commonly used Poisson processes. We finally demonstrate the effectiveness of the new framework using two simulations and one real experimental dataset.

A compositional approach to in-situ evaluation of polymetallic deposits. A case study at Sungun Cu−Mo deposit, NW Iran

Mineral reserve evaluation is based on compositional data, reporting in units such as percentages, mg/kg or ppm. The nature of such data implies that the values cannot vary independently and geostatistical modeling of their raw form could be misleading. In this study we propose a compositional approach —based on orthonormal isometric logratio (olr) coordinates— to simulate the in-situ value (in US Dollars) at Sungun Cu − Mo deposit in NW Iran. A dataset of 1422 surface samples, analyzed for Ag, As, Au, Cu, Mo, Sb, Pb and Zn is used. This surface covers the current mine pit and is sampled prior to extraction, as a detailed exploration phase. We assumed the sampling surface as an extraction mine bench and separated 34% of the original samples for validation. Comparing with a noncompositional approach, it is prominent that in all extraction categories and for all Cu and Mo cut-off grades, the compositional values are closer to the real ones. Comparison of in-situ value maps revealed that the compositional approach is better able to delineate intense local variability; especially in high grade parts of the deposit. This superiority is also evident in Euclidean and Aitchison distance-distance diagrams of the real and simulated values. It is concluded that, in contrast with known geostatistical methods, the proposed olr-based method delivers more accurate models and, consequently, an improved and more realistic vision of the deposit value is achieved.

Compositional Analysis of Conventional and Unconventional Permian Basin-Produced Waters: A Simple Tool for Predicting Major Ion Composition

Summary Treatment methods for produced water (PW) are significantly affected by a high concentration of total dissolved solids (TDS), a summation of dissolved organic and inorganic compositions. Understanding the constituents of TDS to eliminate or prevent chemical reactions is critical in the design optimization of the treatment processes. In this paper, two PW geochemical data sets generated from conventional and unconventional reservoirs in the Permian Basin were analyzed to correlate constituents with TDS. Compositional data sets from over 115,000 PW samples originally reported by the U.S. Geological Survey (USGS) and 45 oil and gas operations were analyzed. Data preprocessing, culling, systematized- and meta-analysis, and statistical techniques were adapted to associate the data. Subcompositional geochemical data were transformed into isometric log ratios and are presented in bivariate and multivariate plots. Results indicate that Na+ and Ca2+ were the dominant cations and Cl− was the dominant anion. No observable trend differences in the Na+, Cl−, Ca2+, Mg+, and SO42− concentrations between PW from conventional and unconventional wells were registered. Variations in the isometric log ratio of Na/Cl and Ca/SO4 with TDS revealed that Na/Cl was nearly constant over the range of TDS, suggesting mineral buffering or a lack of significant water/rock reactions involving Na and Cl, and that Ca/SO4 increased with TDS, indicating that low-salinity fluids may have dissolved anhydrite producing a value near zero, with Ca gain and/or SO4 loss with increasing salinity. In all 10 counties and 8 formations investigated in this work, the ln (Ca/SO4) denotes Ca gain/SO4 loss relative to their composition in anhydrite or Permian seawater. Likely mechanisms leading to elevated ln (Ca/SO4) include sulfate reduction, dolomitization of calcite, Na/Ca cation exchange, albitization, and anhydrite precipitation from Ca-rich fluids. Results from this work are important as it is revealed that Ca/SO4 and Na/Cl can potentially be predicted from PW TDS concentrations. This information was combined to create a reservoir or location-specific model to estimate Na, Cl, Ca, and SO4 concentrations in Permian Basin PW, a powerful tool to improve treatment and reuse options in areas with few direct data.

A new class of [formula omitted]-transformations for the spatial analysis of Compositional Data

Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of α-transformations, named the Isometric α-transformation (α-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. Similarly to other α-transformations existing in the literature, it is shown that the ILR is the limit case of the α-IT as α tends to 0 and that α=1 corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when α>0. Maximum likelihood estimation of the parameter α is established. Prediction using kriging on α-IT transformed data is validated on synthetic spatial compositional data, using prediction scores computed either in the geometry induced by the α-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the α-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplified as α decreases, entailing poor kriging performances both within the α-IT geometry and for metrics in the simplex.

Spatial interpolation of coal properties using geographic quantile regression forest

Inaccuracies in spatial modelling of coal properties can impact coal resource and reserve estimates. Geostatistical methods which account for compositional data have previously been recommended as a preferred method for modelling of coal properties. These methods can quantify uncertainty, can use auxiliary information to improve estimates, and ensure that compositional data (such as coal proximate analysis) is modelled in a mathematically consistent way. However, geostatistical methods have drawbacks in that have rigid statistical assumptions about the distribution and stationarity of the target variable and require variogram interpretation which can be onerous when then number of domains and target variables are numerous. Due to these drawback, inverse distance weighting (a simple deterministic method) remains the most popular method for modelling coal properties in Australian resource estimates. To address the drawbacks of geostatistical methods, a machine learning approach based on the quantile regression forest algorithm is proposed as an alternative method to spatially model coal properties. This newly proposed method, accounts for spatial arrangement of data, requires minimal pre-processing steps, can quantify uncertainty and can easily incorporate auxiliary information of various types. To evaluate the performance of this method, the accuracy of predictions of coal proximate analysis properties, and coal density are compared to the predictions of inverse distance weighting and regression kriging. All methods incorporate isometric log ratio transform and back-transform of data in order to account for the compositional nature of coal proximate analysis. Data from an active coal mine in the Bowen Basin, Queensland Australia was used as basis of the results. A unique feature of the mine site in this basin is the presence of intrusion which impacts coal quality properties to various degrees. Using evaluation metrics from leave-one-out cross-validation, this paper demonstrates that quantile regression forest has higher accuracy, lower bias and higher precision than inverses distance weighting across all coal properties. The paper also shows that results of the new method are very similar or better than regression kriging. It is also demonstrated that the prediction maps produced by quantile regression forest could be used to more accurately map out coal impacted by intrusion compared to inverse distance weighting, and that inverse distance weighting overestimates the impact of intrusion and intrusion extent. A drawback of the method compared to inverse distance weighting, is that it is more computationally demanding, less intuitive and is currently not available in existing geological packages.

Application of compositional data analysis in geochemical exploration for concealed deposits: A case study of Ashele copper-zinc deposit, Xinjiang, China

One of the top priorities of ore body exploration geochemistry is to effectively identifying “anomalies” and separating them from “background” in geochemical data analyses, during which an accurate understanding of geochemical distribution patterns of elements and anomaly separation has been the focus of ore body hunting. However, geochemical data are compositional data with closure effect and require necessary logratio transformation to open closed data for the following statistical analysis. The invested dataset of 13 elements derived from 2264 surface rock samples from the northwestern Ashele mining area was processed and respectively analyzed as the raw data, logarithmically-transformed data, and isometric logratio (ilr) transformed data with exploratory data analysis (EDA) technology. Of which, the ilr transformed data yields an ideal data structure and scale distribution. The data then was analyzed with principal component analysis (PCA) and robust principal component analysis (RPCA), along with the compositional biplots and the first principal component score maps to identify the spatial distribution of element assemblages. After that, a comparative study of the geochemical distribution patterns based on the raw data of mineralized elements and the principal component scores based on ilr transformation data is conducted to explore the connection with mineralization. As a result, four prospecting prediction targets of two types are delineated in the study area.

Hydrogeochemical, microbial and compositional analysis of data from surface and groundwater sources in Southeastern Nigeria

Surface and groundwaters are the major sources of drinking and irrigation water in most developing countries. Hydrogeochemical data, being compositional in nature require adequate statistical treatment in order to provide dependable information needed for decision making. In this study, water samples were collected from 100 groundwaters and 24 surface waters within the principal Benin and Bende-Ameki lithostratigraphic units in Southeastern Nigeria, and analyzed for major ions, microbiological and other physicochemical parameters using standard methods. An approach based on the isometric logratio (ilr) transformation, leading to the ostensible symmetric coordinates was applied for multivariate statistics. Source ‘fit for purpose’ for drinking and irrigation was assessed using a modified water quality index (WQI), TDS-pE graph, sodium hazard (SAR), magnesium hazard (MAR), and other ionic models. Most surface and groundwater sources were acidic with 84% and 98% of the samples respectively having pH below WHO permissible limit for drinking water. Compositional data (CoDa) analysis produced robust principal components (PCs) and clusters that were key in explaining important hydrogeochemical processes in the water sources, whereas heatmaps of the correlated variables clearly showed how spurious effects due to the constant sum constraint of compositional data could occur using non-CoDa statistical approaches. The first two PCs of surface and groundwater data explained 74.8% and 67.0% of the total variance respectively, which indicated relative dominance of SO42− and HCO3− respectively. Results showed that all surface water sources were suitable for irrigation by SAR, MAR, Mg:Ca, and Wilcox method, whereas some groundwater sources were unsuitable. TDS-pE graph and WQI classified water sources as “excellent”, with the former being simple and generic for instant monitoring of water quality. More so, minimal treatment is recommended to meet the microbial criteria for domestic use of the water sources.

Leading Enterovirus Genotypes Causing Hand, Foot, and Mouth Disease in Guangzhou, China: Relationship with Climate and Vaccination against EV71.

(1) Background: Assignment of pathogens to the correct genus, species, and type is vital for controlling infectious epidemics. However, the role of different enteroviruses during hand, foot, and mouth disease (HFMD) epidemics and the major contributing factors remain unknown. (2) Methods: HFMD cases from 2016 to 2018 in Guangzhou, China were collected. The relationship between HFMD cases and genotype frequency, as well as the association between genotype frequency and climate factors, were studied using general linear models. We transformed the genotype frequency to the isometric log-ratio (ILR) components included in the model. Additionally, vaccination rates were adjusted in the climate-driven models. (3) Results: We observed seasonal trends in HFMD cases, genotype frequency, and climate factors. The model regressing case numbers on genotype frequency revealed negative associations with both the ILRs of CAV16 (RR = 0.725, p < 0.001) and EV71 (RR = 0.421, p < 0.001). The model regressing genotype frequency on driven factors showed that the trends for EV71 proportions were inversely related to vaccination rate (%, β = −0.152, p = 0.098) and temperature (°C, β = −0.065, p = 0.004). Additionally, the trends for CVA16 proportions were inversely related to vaccination rate (%, β = −0.461, p = 0.004) and temperature (°C, β = −0.068, p = 0.031). The overall trends for genotype frequency showed that EV71 decreased significantly, while the trends for CVA16 increased annually. (4) Conclusions: Our findings suggest a potential pathway for climate factors, genotype frequency, and HFMD cases. Our study is practical and useful for targeted prevention and control, and provides environmental-based evidence.

Convex clustering method for compositional data via sparse group lasso

High-dimensional sparse clustering with compositional data is of great practical importance, as exemplified by applications in high-throughput gene expression profiles analysis. In this paper, we develop a compositional clustering framework based on convex clustering, which is a convex relaxation of hierarchical clustering that incorporates a fused penalty term on the cluster prototypes. To explicitly deal with the issue of high dimensionality and sparsity, we propose the Compositional Convex Clustering with Sparse Group Lasso (CCC-SGL). The isometric logratio (ilr) transformation is first applied to transform the composition in the simplex space to the standard Euclidean geometry. Then, a group lasso penalty and a lasso penalty are imposed on the cluster centers, which effectively selects informative features and promotes within-feature sparsity. The proposed convex clustering formulation is numerically and efficiently solved with the proximal gradient descent algorithm within the Alternating Direction Method of Multipliers (ADMM) framework. Simulation studies are carried out to evaluate the performance of the proposed methodology and also a real data set in microbiome sequencing is analyzed.