Biweight Midcorrelation Research Articles

Biweight midcorrelation-based CRITIC method: a case study for electrification of BIPV in Iran

Criteria weights are essential in various multi-criteria decision-making (MCDM) approaches. The amount of weight indicates the criterion's importance, and the performance of MCDM techniques depends on the correct estimation of criteria weights and criteria amount in the decision matrix. The distance correlation-based CRiteria Importance Through Inter-criteria Correlation (CRITIC) technique is a modified version of the CRITIC method. Since Pearson's correlation is sensitive to noisy and outlier data, this paper proposes using the biweight midcorrelation as a robust alternative to Pearson's correlation. The weights obtained from the proposed biweight midcorrelation method make using the full range of MCDM techniques possible. This study examined the performance of the proposed method in comparison with eight criteria weighting techniques on the electric supply for a Building-Integrated PhotoVoltaic (BIPV) problem. Results from three different tests (i.e. distance correlation, Spearman rank-order correlation, and symmetric mean absolute percentage error (sMAPE)) indicated that the proposed method could produce more valid criteria weights and ranks than other methods. The value of the sMAPE criterion for the proposed method is 0.1096. Sensitivity analysis also revealed that the proposed method provides more robust criteria weights and ranks with a larger decision matrix.

Biweight Midcorrelation Based Transmission Line Pilot Protection Algorithm

Biweight Midcorrelation Based Transmission Line Pilot Protection Algorithm

27. Cellular aging for risk stratification in adult deformity surgery: utilization of seven epigenetic clocks and two telomere length measurements in the analysis of comorbidity burden, frailty, disability and complications in adult deformity surgery

<h3>BACKGROUND CONTEXT</h3> Recent advances in risk stratification have led to improvements in our ability to predict complications, cost and outcomes. Chronological age is important in almost all risk calculators; however, genetic or biological age may be more informative. Several techniques exist to assess genetic age including DNA methylation patterns with epigenetic clocks, telomere length and analysis of both mitochondrial DNA and single nucleotide polymorphisms. Our lab recently demonstrated a novel association between telomere length and 90-day complications in adult deformity surgery. There are no current risk stratification tools that integrate markers of cellular aging or biophysiologic reserve. Determining the optimal aging biomarkers to include in risk assessment models will be critical to future work in preoperative risk assessment. <h3>PURPOSE</h3> To assess the utility of epigenetic clocks and telomere length in evaluating comorbidity burden, frailty, disability and postoperative complications. <h3>STUDY DESIGN/SETTING</h3> Prospective cohort of adult deformity patients performed at a single academic center. <h3>PATIENT SAMPLE</h3> Adult patients with spinal deformity undergoing elective surgery. <h3>OUTCOME MEASURES</h3> Any medical or surgical complication within 90 days from surgery. <h3>METHODS</h3> Adult spinal deformity patients were prospectively enrolled. Demographics, frailty index (ASD-FI), Charlson comorbidity index (CCI), Oswestry Disability Index (ODI), and whole blood were collected along with presence of any medical or surgical complications at 90 days. CpG methylation was quantified using the Illumina EPIC array platform. Raw methylation data were processed using a custom pipeline in R to extract 7 epigenetic metrics: Horvath Age, Hannum Age, instantaneous pace of aging (DunedinPACE), and 4 principal component (PC) corrected epigenetic age metrics (PC Horvath, PC Hannum, PC PhenoAge, and PC GrimAge). Telomere length was measured directly by qPCR (TSR) or indirectly by methylation-based estimation (PC DNAmTL), which estimates telomere length using specific methylation sequences and correlation to leukocyte telomere length. Linear regression with biweight midcorrelation (bicor) was used to compare continuous variables. Logistic regression with odds radio (OR) was used for complications. Gender and BMI were treated as fixed-effects and added to each model. <h3>RESULTS</h3> A total of 43 patients were included with mean age of 65 years and 21 women (49%). A mean of 11 levels were fused posteriorly with 21 combined anterior-posterior approaches (43%) and 18 three-column osteotomies (42%). There were no significant differences in age, gender, BMI, preoperative ASA classification, CCI score, ODI, or surgical variables between patients who had complications compared to those without. CCI correlated with epigenetic age using 6 epigenetic clocks (Hannum Age, Horvath Age, PC Hannum, PC Horvath, PC PhenoAge, PC GrimAge) and estimated telomere length (PC DNAmTL). ASD-FI correlated with epigenetic age using the DunedinPACE epigenetic clock (bicor=0.439, p=0.003). ODI showed a trend toward correlation with epigenetic age using DunedinPACE, but did not meet statistical significance (bicor=0.262, p=0.098). Both direct and indirect telomere measures were associated with 90-day complications (TSR, OR=1,466, p=0.014 and PC DNAmTL, OR=279, p=0.010), while epigenetic age using the PC GrimAge clock showed only a trend (OR=1.09, p=0.067). <h3>CONCLUSIONS</h3> Epigenetic clocks seem to correlate with comorbidity (CCI) and disease-specific frailty (ASD-FI), while telomere length is significantly associated with complications. Perhaps most importantly, both direct and indirect measures of telomere length showed significant associations with complications, validating both approaches for this application. Integration of biomarkers into current risk calculators has significant potential for improved prediction accuracy, preoperative optimization and tailored surgical planning. <h3>FDA DEVICE/DRUG STATUS</h3> This abstract does not discuss or include any applicable devices or drugs.

A Comparison between robust methods in canonical correlation by using empirical influence function

Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.&#x0D; In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biweight Midcorrelation coefficient (Bi) and Kendall-tau correlation coefficient (Ke).&#x0D; From the comparison between these two methods through the empirical influence function with standard scaled and transformed estimator, the results indicated the efficiency and the preference of the (Bi) method. The study also has application with real data followed a multivariate normal distribution with two sets; the first group represents monthly averages for quantities of exported oil from three OPEC countries, namely Saudi Arabia, Iraq, and Kuwait, the other group represents the returns of those quantities for the period from 2015 to 2019, after applied (Bi) method and estimate IF, the strongest influence about CC was at thirty four-months and the lowest was at twenty-seven

A Novel Computational Framework to Predict Disease-Related Copy Number Variations by Integrating Multiple Data Sources.

Copy number variation (CNV) may contribute to the development of complex diseases. However, due to the complex mechanism of path association and the lack of sufficient samples, understanding the relationship between CNV and cancer remains a major challenge. The unprecedented abundance of CNV, gene, and disease label data provides us with an opportunity to design a new machine learning framework to predict potential disease-related CNVs. In this paper, we developed a novel machine learning approach, namely, IHI-BMLLR (Integrating Heterogeneous Information sources with Biweight Mid-correlation and L1-regularized Logistic Regression under stability selection), to predict the CNV-disease path associations by using a data set containing CNV, disease state labels, and gene data. CNVs, genes, and diseases are connected through edges and then constitute a biological association network. To construct a biological network, we first used a self-adaptive biweight mid-correlation (BM) formula to calculate correlation coefficients between CNVs and genes. Then, we used logistic regression with L1 penalty (LLR) function to detect genes related to disease. We added stability selection strategy, which can effectively reduce false positives, when using self-adaptive BM and LLR. Finally, a weighted path search algorithm was applied to find top D path associations and important CNVs. The experimental results on both simulation and prostate cancer data show that IHI-BMLLR is significantly better than two state-of-the-art CNV detection methods (i.e., CCRET and DPtest) under false-positive control. Furthermore, we applied IHI-BMLLR to prostate cancer data and found significant path associations. Three new cancer-related genes were discovered in the paths, and these genes need to be verified by biological research in the future.

Using Scaled And Translated Measure To Compare Between Robust Estimators In Canonical Correlation

Many researches have dealt with analysis of classical canonical correlation based on either covariance (heterogeneity) or correlation matrix where the coefficient of correlation used is Pearson which is biased to the outlier’s values, because of it depends on mean in the calculation. In our research we find robust canonical correlation depend on robust methods which is insensitive towards outliers value. Methods are used Percentage bend correlation coefficient (Pe) & Biweight midcorrelation coefficient correlation (Bi) to estimate canonical correlation (CC) instead of Pearson correlation. The researchers addressed robustness measurement to check the ability of robust methods for contaminated values, we used biased and translated estimator of empirical influence function to make the comparison between robust methods when we use simulation and choose (Bi) method to apply it on real data.

Host Genetic Background and Gut Microbiota Contribute to Differential Metabolic Responses to Fructose Consumption in Mice

It is unclear how high fructose consumption induces disparate metabolic responses in genetically diverse mouse strains. We aimed to investigate whether the gut microbiota contributes to differential metabolic responses to fructose. Eight-week-old male C57BL/6J (B6), DBA/2J (DBA), and FVB/NJ (FVB) mice were given 8% fructose solution or regular water (control) for 12 wk. The gut microbiota composition in cecum and feces was analyzed using 16S ribosomal DNA sequencing, and permutational multivariate ANOVA (PERMANOVA) was used to compare community across mouse strains, treatments, and time points. Microbiota abundance was correlated with metabolic phenotypes and host gene expression in hypothalamus, liver, and adipose tissues using Biweight midcorrelation. To test the causal role of the gut microbiota in determining fructose response, we conducted fecal transplants from B6 to DBA mice and vice versa for 4 wk, as well as gavaged antibiotic-treated DBA mice with Akkermansia for 9 wk, accompanied with or without fructose treatment. Compared with B6 and FVB, DBA mice had significantly higher Firmicutes to Bacteroidetes ratio and lower baseline abundance of Akkermansia and S24-7 (P <0.05), accompanied by metabolic dysregulation after fructose consumption. Fructose altered specific microbial taxa in individual mouse strains, such as a 7.27-fold increase in Akkermansia in B6 and 0.374-fold change in Rikenellaceae in DBA (false discovery rate <5%), which demonstrated strain-specific correlations with host metabolic and transcriptomic phenotypes. Fecal transplant experiments indicated that B6 microbes conferred resistance to fructose-induced weight gain in DBA mice (F=43.1, P <0.001), and Akkermansia colonization abrogated the fructose-induced weight gain (F=17.8, P<0.001) and glycemic dysfunctions (F=11.8, P=0.004) in DBA mice. Our findings support that differential microbiota composition between mouse strains is partially responsible for host metabolic sensitivity to fructose, and that Akkermansia is a key bacterium that confers resistance to fructose-induced metabolic dysregulation.

Abstract 2332: Correlation of lifestyle factors with epigenetic aging unveiled in the practice of a DNA methylation-based age test

Abstract Background: DNA methylation clocks have been developed recently to estimate epigenetic age which is associated with chronological age in mouse and human. Changes in epigenetic age were reported in patients with health conditions including cancer. Different from genetic variations, epigenetic properties can be modified by environmental factors. Epigenetic age tests using blood samples have been offered directly to customers recently. We sought to analyze relationships between epigenetic aging and lifestyle factors, medication and aging interventions in the hope of assisting healthier living. Methods: Epigenetic age, called DNAge, is estimated using linear regression of DNA methylation levels at 206 loci containing 1344 CpGs and chronological age. Delta age is defined as the difference of epigenetic age minus chronological age. Correlations between lifestyle factors or medication and delta age of hundreds of whole blood samples were evaluated using biweight midcorrelation. Statistical significance is set at 0.05. Results: Our results showed positive correlations between accelerated epigenetic aging and BMI (bicor=0.148, p=0.009, n=311), current smoker (bicor=0.143, p=0.011, n=315), or stress (bicor=0.088, p=0.128, n=302). Factors with positive correlation but not reaching statistical significance included total cholesterol, alcohol consumption and Keto diet. Factors with negative correlation but not statistically significant included exercise, balanced diet, mostly meat, mostly vegetables, and education. Conclusions: The epigenetic age analysis of real customer data confirmed beneficial and adversarial health effects of certain lifestyle factors. The DNAge test offered proves to be useful as a biomarker for biological age and as a practical tool for monitoring and evaluation of health status which may be used in cancer epidemiology study and help cancer prevention. Citation Format: Wei Guo, Yap Ching Chew, Xiaojing Yang, Michiko Suwoto, Taikun Yamada, Xi Yu Jia. Correlation of lifestyle factors with epigenetic aging unveiled in the practice of a DNA methylation-based age test [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2332.

Construction, analysis and validation of co-expression network to understand stress adaptation in Deinococcus radiodurans R1.

Systems biology based approaches have been effectively utilized to mine high throughput data. In the current study, we have performed system-level analysis for Deinococcus radiodurans R1 by constructing a gene co-expression network based on several microarray datasets available in the public domain. This condition-independent network was constructed by Weighted Gene Co-expression Network Analysis (WGCNA) with 61 microarray samples from 9 different experimental conditions. We identified 13 co-expressed modules, of which, 11 showed functional enrichments of one or more pathway/s or biological process. Comparative analysis of differentially expressed genes and proteins from radiation and desiccation stress studies with our co-expressed modules revealed the association of cyan with radiation response. Interestingly, two modules viz darkgreen and tan was associated with radiation as well as desiccation stress responses. The functional analysis of these modules showed enrichment of pathways important for adaptation of radiation or desiccation stress. To decipher the regulatory roles of these stress responsive modules, we identified transcription factors (TFs) and then calculated a Biweight mid correlation between modules hub gene and the identified TFs. We obtained 7 TFs for radiation and desiccation responsive modules. The expressions of 3 TFs were validated in response to gamma radiation using qRT-PCR. Along with the TFs, selected close neighbor genes of two important TFs, viz., DR_0997 (CRP) and DR_2287 (AsnC family transcriptional regulator) in the darkgreen module were also validated. In our network, among 13 hub genes associated with 13 modules, the functionality of 5 hub genes which are annotated as hypothetical proteins (hypothetical hub genes) in D. radiodurans genome has been revealed. Overall the study provided a better insight of pathways and regulators associated with relevant DNA damaging stress response in D. radiodurans.

Epigenome-Wide Tobacco-Related Methylation Signature Identification and Their Multilevel Regulatory Network Inference for Lung Adenocarcinoma.

Tobacco exposure is one of the major risks for the initiation and progress of lung cancer. The exact corresponding mechanisms, however, are mainly unknown. Recently, a growing body of evidence has been collected supporting the involvement of DNA methylation in the regulation of gene expression in cancer cells. The identification of tobacco-related signature methylation probes and the analysis of their regulatory networks at different molecular levels may be of a great help for understanding tobacco-related tumorigenesis. Three independent lung adenocarcinoma (LUAD) datasets were used to train and validate the tobacco exposure pattern classification model. A deep selecting method was proposed and used to identify methylation signature probes from hundreds of thousands of the whole epigenome probes. Then, BIMC (biweight midcorrelation coefficient) algorithm, SRC (Spearman's rank correlation) analysis, and shortest path tracing method were explored to identify associated genes at gene regulation level and protein-protein interaction level, respectively. Afterwards, the KEGG (Kyoto Encyclopedia of Genes and Genomes) pathway analysis and GO (Gene Ontology) enrichment analysis were used to analyze their molecular functions and associated pathways. 105 probes were identified as tobacco-related DNA methylation signatures. They belong to 95 genes which are involved in hsa04512, hsa04151, and other important pathways. At gene regulation level, 33 genes are uncovered to be highly related to signature probes by both BIMC and SRC methods. Among them, FARSB and other eight genes were uncovered as Hub genes in the gene regulatory network. Meanwhile, the PPI network about these 33 genes showed that MAGOH, FYN, and other five genes were the most connected core genes among them. These analysis results may provide clues for a clear biological interpretation in the molecular mechanism of tumorigenesis. Moreover, the identified signature probes may serve as potential drug targets for the precision medicine of LUAD.

Optimizing wavelength selection by using informative vectors for parsimonious infrared spectra modelling

Infrared spectroscopy has been widely adopted by various agricultural research. The typical spectra variables contain thousands of wavelengths. These large number of spectra variables often contribute to collinearity, and redundancies rather than relevant information. Variable selection of the predictors is an important step to create a robust calibration model from these spectra data. This paper presents an algorithm for spectra variable selection based on a combination of informative vectors and an ordered predictor selection (OPS) approach with an exponentially decreasing function (EDF) selection. Informative vectors are features derived from statistical principles that can be used to describe the relationship between the dependent variables and the predictors (spectra). The informative vectors analysed include regression coefficient vector (b), variable influence on projection (V), residual vector (S), net analyte signal vector (Na), linear correlation vector (COR), biweight mid-correlation vector (BIC), mutual information based on adjacency matrix (AMI), covariance procedures matrix (COV). These eight informative vectors can be joined in pairs and become 22 combination vectors. This approach was tested with near-infrared soil spectra for predicting the properties of pH, clay and sand content, cation exchange capacity (CEC), and total carbon content. This example used the Cubist regression tree and partial least squares regression (PLSR) models for calibration. By utilizing the subset of the spectra (retaining those that are significant based on the absolute values of the informative vectors), the regression models were still able to enhance the prediction capability. Overall, the PLSR model performed better than the Cubist model. The informative vector b (and its combinations) and S (and its combinations) were found to be the ones that provide the most accurate predictions for this dataset. Although the performance of the subset model does not perform better than the full spectra model, the number of wavelengths variable used in the model is significantly reduced to, on average, 25%.

Genetic algorithm for assigning weights to gene expressions using functional annotations

A method, named genetic algorithm for assigning weights to gene expressions using functional annotations (GAAWGEFA), is developed to assign proper weights to the gene expressions at each time point. The weights are estimated using functional annotations of the genes in a genetic algorithm framework. The method shows gene similarity in an improved manner as compared with other existing methods because it takes advantage of the existing functional annotations of the genes. The weight combination for the expressions at different time points is determined by maximizing the fitness function of GAAWGEFA in terms of the positive predictive value (PPV) for the top 10,000 gene pairs. The performance of the proposed method is primarily compared with Biweight mid correlation (BICOR) and original expression values for the six Saccharomyces cerevisiae datasets and one Bacillus subtilis dataset. The utility of GAAWGEFA is shown in predicting the functions of 48 unclassified genes (using p-value cutoff 10−13) from Saccharomyces cerevisiae microarray data where the expressions are weighted using GAAWGEFA and are clustered using k-medoids algorithm. The related code along with various parameters is available at http://sampa.droppages.com/GAAWGEFA.html.

Integration of Multi-omics Data for Gene Regulatory Network Inference and Application to Breast Cancer.

Underlying a cancer phenotype is a specific gene regulatory network that represents the complex regulatory relationships between genes. However, it remains a challenge to find cancer-related gene regulatory network because of insufficient sample sizes and complex regulatory mechanisms in which gene is influenced by not only other genes but also other biological factors. With the development of high-throughput technologies and the unprecedented wealth of multi-omics data give us a new opportunity to design machine learning method to investigate underlying gene regulatory network. In this paper, we propose an approach, which use biweight midcorrelation to measure the correlation between factors and make use of nonconvex penalty based sparse regression for gene regulatory network inference (BMNPGRN). BMNCGRN incorporates multi-omics data (including DNA methylation and copy number variation) and their interactions in gene regulatory network model. The experimental results on synthetic datasets show that BMNPGRN outperforms popular and state-of-the-art methods (including DCGRN, ARACNE and CLR) under false positive control. Furthermore, we applied BMNPGRN on breast cancer (BRCA) data from The Cancer Genome Atlas database and provided gene regulatory network.

Soil mapping via diffuse reflectance spectroscopy based on variable indicators: An ordered predictor selection approach

Diffuse reflectance spectroscopy (DRS) has shown its potential as a feasible, rapid and non-invasive soil characterization tool. Nevertheless, the use of whole VisNIR spectra in DRS models often incorporates different disruptive and masking effects, eventually producing inefficient model predictions. Thus the careful choice of informative spectral variables is a significant step toward producing robust and useful DRS-based models. This study evaluated the feasibility of combining variable indicator-based DRS outputs and geostatistical interpolations to rapidly produce soil spatial variability maps for six soil properties [sand, clay, silt, total carbon (TC), total nitrogen (TN) and loss-on-ignition organic matter (LOI)]. A total of 300 samples were collected from three catenas of Transylvanian Plain, Romania. First derivative spectra were used to calculate Pearson's correlation coefficient (r), biweight midcorrelation (bicor), mutual information based adjacency (AMI), variable importance in the projection (VIP), and their combinations. This variable indicator suite was combined with an ordered predictor selection (OPS) method to choose the optimum number of spectral variables (NSV). This method was tested with partial least squares regression (PLSR) and support vector regression (SVR) with independent validation. Results indicated that the variable indicator-based SVR model yielded superior predictability relative to full-spectrum PLSR model for all soil parameters. Moreover, both PLSR and SVR optimal models used the identical best variable indicators. While AMI appeared as the best indicator for four soil attributes (clay, TN, TC and LOI), bicor was selected as the best indicator for sand and silt. Spatial variability mapping using optimal SVR model outputs satisfactorily demonstrated management and landscape dynamics across the catenas like the place of manure stockpiles. Summarily, the results of this study indicated that a successful combination of OPS-based variable indicators and their subsequent incorporation into DRS-based chemometric models can potentially improve model predictions that can be further combined with geostatistical interpolation methods to produce spatial maps of soil properties.

PhenoMeter: A Metabolome Database Search Tool Using Statistical Similarity Matching of Metabolic Phenotypes for High-Confidence Detection of Functional Links.

This article describes PhenoMeter (PM), a new type of metabolomics database search that accepts metabolite response patterns as queries and searches the MetaPhen database of reference patterns for responses that are statistically significantly similar or inverse for the purposes of detecting functional links. To identify a similarity measure that would detect functional links as reliably as possible, we compared the performance of four statistics in correctly top-matching metabolic phenotypes of Arabidopsis thaliana metabolism mutants affected in different steps of the photorespiration metabolic pathway to reference phenotypes of mutants affected in the same enzymes by independent mutations. The best performing statistic, the PM score, was a function of both Pearson correlation and Fisher’s Exact Test of directional overlap. This statistic outperformed Pearson correlation, biweight midcorrelation and Fisher’s Exact Test used alone. To demonstrate general applicability, we show that the PM reliably retrieved the most closely functionally linked response in the database when queried with responses to a wide variety of environmental and genetic perturbations. Attempts to match metabolic phenotypes between independent studies were met with varying success and possible reasons for this are discussed. Overall, our results suggest that integration of pattern-based search tools into metabolomics databases will aid functional annotation of newly recorded metabolic phenotypes analogously to the way sequence similarity search algorithms have aided the functional annotation of genes and proteins. PM is freely available at MetabolomeExpress (https://www.metabolome-express.org/phenometer.php).

Module Based Differential Coexpression Analysis Method for Type 2 Diabetes.

More and more studies have shown that many complex diseases are contributed jointly by alterations of numerous genes. Genes often coordinate together as a functional biological pathway or network and are highly correlated. Differential coexpression analysis, as a more comprehensive technique to the differential expression analysis, was raised to research gene regulatory networks and biological pathways of phenotypic changes through measuring gene correlation changes between disease and normal conditions. In this paper, we propose a gene differential coexpression analysis algorithm in the level of gene sets and apply the algorithm to a publicly available type 2 diabetes (T2D) expression dataset. Firstly, we calculate coexpression biweight midcorrelation coefficients between all gene pairs. Then, we select informative correlation pairs using the “differential coexpression threshold” strategy. Finally, we identify the differential coexpression gene modules using maximum clique concept and k-clique algorithm. We apply the proposed differential coexpression analysis method on simulated data and T2D data. Two differential coexpression gene modules about T2D were detected, which should be useful for exploring the biological function of the related genes.

Gene differential coexpression analysis based on biweight correlation and maximum clique.

Differential coexpression analysis usually requires the definition of 'distance' or 'similarity' between measured datasets. Until now, the most common choice is Pearson correlation coefficient. However, Pearson correlation coefficient is sensitive to outliers. Biweight midcorrelation is considered to be a good alternative to Pearson correlation since it is more robust to outliers. In this paper, we introduce to use Biweight Midcorrelation to measure 'similarity' between gene expression profiles, and provide a new approach for gene differential coexpression analysis. Firstly, we calculate the biweight midcorrelation coefficients between all gene pairs. Then, we filter out non-informative correlation pairs using the 'half-thresholding' strategy and calculate the differential coexpression value of gene, The experimental results on simulated data show that the new approach performed better than three previously published differential coexpression analysis (DCEA) methods. Moreover, we use the maximum clique analysis to gene subset included genes identified by our approach and previously reported T2D-related genes, many additional discoveries can be found through our method.

Dependency Measures for Assessing the Covariation of Spectrally Active and Inactive Soil Properties in Diffuse Reflectance Spectroscopy

Diffuse reflectance spectroscopy (DRS) is a rapid and noninvasive assessment technique for several spectrally active soil properties (chromophores) such as sand, clay, organic C, and Fe contents. The approach is also used for estimating many spectrally inactive constituents (non‐chromophores) based on the assumption of covariation between non‐chromophores and chromophores. The linkage between covariation and the ability of DRS to estimate a non‐chromophore has not been reported in the literature. In this study, we evaluated the covariation assumption using three dependency measures (Pearson correlation coefficient, r; biweight midcorrelation, bicor; and mutual information based adjacency, AMI), five chromophores (organic C, Fe, clay, and sand contents, and geometric mean diameter), and seven non‐chromophores (pH, electrical conductivity, P, K, B, Zn, and Al contents) measured in 247 Alfisol and 249 Vertisol samples. An average dependency index (ADI) was developed for each of the three measures (ADIr, ADIbicor, and ADIAMI). The first derivative of the reflectance in conjunction with partial least squares regression was used for data modeling. Model accuracy was evaluated using residual prediction deviation (RPD). The relationships between RPD values of non‐chromophores and the ADI values were examined for different chromophore groups (physical, chemical, and combined). The performance of ADIAMI was found to be superior to ADIr and ADIbicor. The ADIAMI computed using chemical chromophores gave strong linear relationships (R2 = 0.93) between ADIAMI and the RPD of chemical non‐chromophores, suggesting that the AMI may be used as a robust dependency measure to assess the covariation of non‐chromophores with chromophores in DRS.

Comparison of co-expression measures: mutual information, correlation, and model based indices

BackgroundCo-expression measures are often used to define networks among genes. Mutual information (MI) is often used as a generalized correlation measure. It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Further, it is important to assess what transformations of these and other co-expression measures lead to biologically meaningful modules (clusters of genes).ResultsWe provide a comprehensive comparison between mutual information and several correlation measures in 8 empirical data sets and in simulations. We also study different approaches for transforming an adjacency matrix, e.g. using the topological overlap measure. Overall, we confirm close relationships between MI and correlation in all data sets which reflects the fact that most gene pairs satisfy linear or monotonic relationships. We discuss rare situations when the two measures disagree. We also compare correlation and MI based approaches when it comes to defining co-expression network modules. We show that a robust measure of correlation (the biweight midcorrelation transformed via the topological overlap transformation) leads to modules that are superior to MI based modules and maximal information coefficient (MIC) based modules in terms of gene ontology enrichment. We present a function that relates correlation to mutual information which can be used to approximate the mutual information from the corresponding correlation coefficient. We propose the use of polynomial or spline regression models as an alternative to MI for capturing non-linear relationships between quantitative variables.ConclusionThe biweight midcorrelation outperforms MI in terms of elucidating gene pairwise relationships. Coupled with the topological overlap matrix transformation, it often leads to more significantly enriched co-expression modules. Spline and polynomial networks form attractive alternatives to MI in case of non-linear relationships. Our results indicate that MI networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data.

FastRFunctions for Robust Correlations and Hierarchical Clustering

Many high-throughput biological data analyses require the calculation of large correlation matrices and/or clustering of a large number of objects. The standard R function for calculating Pearson correlation can handle calculations without missing values efficiently, but is inefficient when applied to data sets with a relatively small number of missing data. We present an implementation of Pearson correlation calculation that can lead to substantial speedup on data with relatively small number of missing entries. Further, we parallelize all calculations and thus achieve further speedup on systems where parallel processing is available. A robust correlation measure, the biweight midcorrelation, is implemented in a similar manner and provides comparable speed. The functions cor and bicor for fast Pearson and biweight midcorrelation, respectively, are part of the updated, freely available R package WGCNA.The hierarchical clustering algorithm implemented in R function hclust is an order n(3) (n is the number of clustered objects) version of a publicly available clustering algorithm (Murtagh 2012). We present the package flashClust that implements the original algorithm which in practice achieves order approximately n(2), leading to substantial time savings when clustering large data sets.