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Background Patterns of multi-locus differentiation (i.e., genomic clines) often extend broadly across hybrid zones and their quantification can help diagnose how species boundaries are shaped by adaptive processes, both intrinsic and extrinsic. In this sense, the transitioning of loci across admixed individuals can be contrasted as a function of the genome-wide trend, in turn allowing an expansion of clinal theory across a much wider array of biodiversity. However, computational tools that serve to interpret and consequently visualize ‘genomic clines’ are limited, and users must often write custom, relatively complex code to do so. Results Here, we introduce the ClineHelpR R-package for visualizing genomic clines and detecting outlier loci using output generated by two popular software packages, bgc and Introgress. ClineHelpR bundles both input generation (i.e., filtering datasets and creating specialized file formats) and output processing (e.g., MCMC thinning and burn-in) with functions that directly facilitate interpretation and hypothesis testing. Tools are also provided for post-hoc analyses that interface with external packages such as ENMeval and RIdeogram. Conclusions Our package increases the reproducibility and accessibility of genomic cline methods, thus allowing an expanded user base and promoting these methods as mechanisms to address diverse evolutionary questions in both model and non-model organisms. Furthermore, the ClineHelpR extended functionality can evaluate genomic clines in the context of spatial and environmental features, allowing users to explore underlying processes potentially contributing to the observed patterns and helping facilitate effective conservation management strategies.

Background Principal component analysis (PCA) is commonly applied to the atomic trajectories of biopolymers to extract essential dynamics that describe biologically relevant motions. Although application of PCA is straightforward, specialized software to facilitate workflows and analysis of molecular dynamics simulation data to fully harness the power of PCA is lacking. The Java Essential Dynamics inspector (JEDi) software is a major upgrade from the previous JED software. Results Employing multi-threading, JEDi features a user-friendly interface to control rapid workflows for interrogating conformational motions of biopolymers at various spatial resolutions and within subregions, including multiple chain proteins. JEDi has options for Cartesian-based coordinates (cPCA) and internal distance pair coordinates (dpPCA) to construct covariance (Q), correlation (R), and partial correlation (P) matrices. Shrinkage and outlier thresholding are implemented for the accurate estimation of covariance. The effect of rare events is quantified using outlier and inlier filters. Applying sparsity thresholds in statistical models identifies latent correlated motions. Within a hierarchical approach, small-scale atomic motion is first calculated with a separate local cPCA calculation per residue to obtain eigenresidues. Then PCA on the eigenresidues yields rapid and accurate description of large-scale motions. Local cPCA on all residue pairs creates a map of all residue-residue dynamical couplings. Additionally, kernel PCA is implemented. JEDi output gives high quality PNG images by default, with options for text files that include aligned coordinates, several metrics that quantify mobility, PCA modes with their eigenvalues, and displacement vector projections onto the top principal modes. JEDi provides PyMol scripts together with PDB files to visualize individual cPCA modes and the essential dynamics occurring within user-selected time scales. Subspace comparisons performed on the most relevant eigenvectors using several statistical metrics quantify similarity/overlap of high dimensional vector spaces. Free energy landscapes are available for both cPCA and dpPCA. Conclusion JEDi is a convenient toolkit that applies best practices in multivariate statistics for comparative studies on the essential dynamics of similar biopolymers. JEDi helps identify functional mechanisms through many integrated tools and visual aids for inspecting and quantifying similarity/differences in mobility and dynamic correlations.

BackgroundPrevious studies have reported that labeling errors are not uncommon in omics data. Potential outliers may severely undermine the correct classification of patients and the identification of reliable biomarkers for a particular disease. Three methods have been proposed to address the problem: sparse label-noise-robust logistic regression (Rlogreg), robust elastic net based on the least trimmed square (enetLTS), and Ensemble. Ensemble is an ensembled classification based on distinct feature selection and modeling strategies. The accuracy of biomarker selection and outlier detection of these methods needs to be evaluated and compared so that the appropriate method can be chosen.ResultsThe accuracy of variable selection, outlier identification, and prediction of three methods (Ensemble, enetLTS, Rlogreg) were compared for simulated and an RNA-seq dataset. On simulated datasets, Ensemble had the highest variable selection accuracy, as measured by a comprehensive index, and lowest false discovery rate among the three methods. When the sample size was large and the proportion of outliers was ≤5%, the positive selection rate of Ensemble was similar to that of enetLTS. However, when the proportion of outliers was 10% or 15%, Ensemble missed some variables that affected the response variables.Overall, enetLTS had the best outlier detection accuracy with false positive rates< 0.05 and high sensitivity, and enetLTS still performed well when the proportion of outliers was relatively large. With 1% or 2% outliers, Ensemble showed high outlier detection accuracy, but with higher proportions of outliers Ensemble missed many mislabeled samples. Rlogreg and Ensemble were less accurate in identifying outliers than enetLTS. The prediction accuracy of enetLTS was better than that of Rlogreg. Running Ensemble on a subset of data after removing the outliers identified by enetLTS improved the variable selection accuracy of Ensemble.ConclusionsWhen the proportion of outliers is ≤5%, Ensemble can be used for variable selection. When the proportion of outliers is > 5%, Ensemble can be used for variable selection on a subset after removing outliers identified by enetLTS. For outlier identification, enetLTS is the recommended method. In practice, the proportion of outliers can be estimated according to the inaccuracy of the diagnostic methods used.

Background Transcriptome analysis aims at gaining insight into cellular processes through discovering gene expression patterns across various experimental conditions. Biclustering is a standard approach to discover genes subsets with similar expression across subgroups of samples to be identified. The result is a set of biclusters, each forming a specific submatrix of rows (e.g. genes) and columns (e.g. samples). Relevant biclusters can, however, be missed when, due to the presence of a few outliers, they lack the assumed homogeneity of expression values among a few gene/sample combinations. The Max-Sum SubMatrix problem addresses this issue by looking at highly expressed subsets of genes and of samples, without enforcing such homogeneity. Results We present here the algorithm to identify K relevant submatrices. Our main contribution is to show that this approach outperforms biclustering algorithms to identify several gene subsets representative of specific subgroups of samples. Experiments are conducted on 35 gene expression datasets from human tissues and yeast samples. We report comparative results with those obtained by several biclustering algorithms, including , , , , and . Gene enrichment analysis demonstrates the benefits of the proposed approach to identify more statistically significant gene subsets. The most significant Gene Ontology terms identified with are shown consistent with the controlled conditions of each dataset. This analysis supports the biological relevance of the identified gene subsets. An additional contribution is the statistical validation protocol proposed here to assess the relative performances of biclustering algorithms and of the proposed method. It relies on a Friedman test and the Hochberg’s sequential procedure to report critical differences of ranks among all algorithms. Conclusions We propose here the method, a computationally efficient algorithm to identify K max-sum submatrices in a large gene expression matrix. Comparisons show that it identifies more significantly enriched subsets of genes and specific subgroups of samples which are easily interpretable by biologists. Experiments also show its ability to identify more reliable GO terms. These results illustrate the benefits of the proposed approach in terms of interpretability and of biological enrichment quality. Open implementation of this algorithm is available as an R package.

BackgroundIdentifying interaction effects between genes is one of the main tasks of genome-wide association studies aiming to shed light on the biological mechanisms underlying complex diseases. Multifactor dimensionality reduction (MDR) is a popular approach for detecting gene–gene interactions that has been extended in various forms to handle binary and continuous phenotypes. However, only few multivariate MDR methods are available for multiple related phenotypes. Current approaches use Hotelling’s T2statistic to evaluate interaction models, but it is well known that Hotelling’s T2statistic is highly sensitive to heavily skewed distributions and outliers.ResultsWe propose a robust approach based on nonparametric statistics such as spatial signs and ranks. The new multivariate rank-based MDR (MR-MDR) is mainly suitable for analyzing multiple continuous phenotypes and is less sensitive to skewed distributions and outliers. MR-MDR utilizes fuzzy k-means clustering and classifies multi-locus genotypes into two groups. Then, MR-MDR calculates a spatial rank-sum statistic as an evaluation measure and selects the best interaction model with the largest statistic. Our novel idea lies in adopting nonparametric statistics as an evaluation measure for robust inference. We adopt tenfold cross-validation to avoid overfitting. Intensive simulation studies were conducted to compare the performance of MR-MDR with current methods. Application of MR-MDR to a real dataset from a Korean genome-wide association study demonstrated that it successfully identified genetic interactions associated with four phenotypes related to kidney function. The R code for conducting MR-MDR is available athttps://github.com/statpark/MR-MDR.ConclusionsIntensive simulation studies comparing MR-MDR with several current methods showed that the performance of MR-MDR was outstanding for skewed distributions. Additionally, for symmetric distributions, MR-MDR showed comparable power. Therefore, we conclude that MR-MDR is a useful multivariate non-parametric approach that can be used regardless of the phenotype distribution, the correlations between phenotypes, and sample size.

Background Normalization of RNA-seq data aims at identifying biological expression differentiation between samples by removing the effects of unwanted confounding factors. Explicitly or implicitly, the justification of normalization requires a set of housekeeping genes. However, the existence of housekeeping genes common for a very large collection of samples, especially under a wide range of conditions, is questionable. Results We propose to carry out pairwise normalization with respect to multiple references, selected from representative samples. Then the pairwise intermediates are integrated based on a linear model that adjusts the reference effects. Motivated by the notion of housekeeping genes and their statistical counterparts, we adopt the robust least trimmed squares regression in pairwise normalization. The proposed method (MUREN) is compared with other existing tools on some standard data sets. The goodness of normalization emphasizes on preserving possible asymmetric differentiation, whose biological significance is exemplified by a single cell data of cell cycle. MUREN is implemented as an R package. The code under license GPL-3 is available on the github platform: github.com/hippo-yf/MUREN and on the conda platform: anaconda.org/hippo-yf/r-muren. Conclusions MUREN performs the RNA-seq normalization using a two-step statistical regression induced from a general principle. We propose that the densities of pairwise differentiations are used to evaluate the goodness of normalization. MUREN adjusts the mode of differentiation toward zero while preserving the skewness due to biological asymmetric differentiation. Moreover, by robustly integrating pre-normalized counts with respect to multiple references, MUREN is immune to individual outlier samples.

Background Moonlighting proteins (MPs) are a subclass of multifunctional proteins in which more than one independent or usually distinct function occurs in a single polypeptide chain. Identification of unknown cellular processes, understanding novel protein mechanisms, improving the prediction of protein functions, and gaining information about protein evolution are the main reasons to study MPs. They also play an important role in disease pathways and drug-target discovery. Since detecting MPs experimentally is quite a challenge, most of them are detected randomly. Therefore, introducing an appropriate computational approach to predict MPs seems reasonable. Results In this study, we introduced a competent model for detecting moonlighting and non-MPs through extracted features from protein sequences. We attempted to set up a well-judged scheme for detecting outlier proteins. Consequently, 37 distinct feature vectors were utilized to study each protein’s impact on detecting MPs. Furthermore, 8 different classification methods were assessed to find the best performance. To detect outliers, each one of the classifications was executed 100 times by tenfold cross-validation on feature vectors; proteins which misclassified 90 times or more were grouped. This process was applied to every single feature vector and eventually the intersection of these groups was determined as the outlier proteins. The results of tenfold cross-validation on a dataset of 351 samples (containing 215 moonlighting and 136 non-moonlighting proteins) reveal that the SVM method on all feature vectors has the highest performance among all methods in this study and other available methods. Besides, the study of outliers showed that 57 of 351 proteins in the dataset could be an appropriate candidate for the outlier. Among the outlier proteins, there were non-MPs (such as P69797) that have been misclassified in 8 different classification methods with 16 different feature vectors. Because these proteins have been obtained by computational methods, the results of this study could reduce the likelihood of hypothesizing whether these proteins are non-moonlighting at all. Conclusions MPs are difficult to be identified through experimentation. Using distinct feature vectors, our method enabled identification of novel moonlighting proteins. The study also pinpointed that a number of non-MPs are likely to be moonlighting.

Background Parametric feature selection methods for machine learning and association studies based on genetic data are not robust with respect to outliers or influential observations. While rank-based, distribution-free statistics offer a robust alternative to parametric methods, their practical utility can be limited, as they demand significant computational resources when analyzing high-dimensional data. For genetic studies that seek to identify variants, the hypothesis is constrained, since it is typically assumed that the effect of the genotype on the phenotype is monotone (e.g., an additive genetic effect). Similarly, predictors for machine learning applications may have natural ordering constraints. Cross-validation for feature selection in these high-dimensional contexts necessitates highly efficient computational algorithms for the robust evaluation of many features. Results We have developed an R extension package, fastJT, for conducting genome-wide association studies and feature selection for machine learning using the Jonckheere-Terpstra statistic for constrained hypotheses. The kernel of the package features an efficient algorithm for calculating the statistics, replacing the pairwise comparison and counting processes with a data sorting and searching procedure, reducing computational complexity from O(n2) to O(n log(n)). The computational efficiency is demonstrated through extensive benchmarking, and example applications to real data are presented. Conclusions fastJT is an open-source R extension package, applying the Jonckheere-Terpstra statistic for robust feature selection for machine learning and association studies. The package implements an efficient algorithm which leverages internal information among the samples to avoid unnecessary computations, and incorporates shared-memory parallel programming to further boost performance on multi-core machines. Electronic supplementary material The online version of this article (10.1186/s12859-019-2869-3) contains supplementary material, which is available to authorized users.

Background Recent comparative studies have brought to our attention how somatic mutation detection from next-generation sequencing data is still an open issue in bioinformatics, because different pipelines result in a low consensus. In this context, it is suggested to integrate results from multiple calling tools, but this operation is not trivial and the burden of merging, comparing, filtering and explaining the results demands appropriate software. Results We developed isma (integrative somatic mutation analysis), an R package for the integrative analysis of somatic mutations detected by multiple pipelines for matched tumor-normal samples. The package provides a series of functions to quantify the consensus, estimate the variability, underline outliers, integrate evidences from publicly available mutation catalogues and filter sites. We illustrate the capabilities of isma analysing breast cancer somatic mutations generated by The Cancer Genome Atlas (TCGA) using four pipelines. Conclusions Comparing different “points of view” on the same data, isma generates a unique mutation catalogue and a series of reports that underline common patterns, variability, as well as sites already catalogued by other studies (e.g. TCGA), so as to design and apply filtering strategies to screen more reliable sites. The package is available for non-commercial users at the URL https://www.itb.cnr.it/isma. Electronic supplementary material The online version of this article (10.1186/s12859-019-2701-0) contains supplementary material, which is available to authorized users.

Background Relatively small changes to gene expression data dramatically affect co-expression networks inferred from that data which, in turn, can significantly alter the subsequent biological interpretation. This error propagation is an underappreciated problem that, while hinted at in the literature, has not yet been thoroughly explored. Resampling methods (e.g. bootstrap aggregation, random subspace method) are hypothesized to alleviate variability in network inference methods by minimizing outlier effects and distilling persistent associations in the data. But the efficacy of the approach assumes the generalization from statistical theory holds true in biological network inference applications. Results We evaluated the effect of bootstrap aggregation on inferred networks using commonly applied network inference methods in terms of stability, or resilience to perturbations in the underlying expression data, a metric for accuracy, and functional enrichment of edge interactions. Conclusion Bootstrap aggregation results in improved stability and, depending on the size of the input dataset, a marginal improvement to accuracy assessed by each method’s ability to link genes in the same functional pathway. Electronic supplementary material The online version of this article (10.1186/s12859-018-2402-0) contains supplementary material, which is available to authorized users.

Background As a machine learning method with high performance and excellent generalization ability, extreme learning machine (ELM) is gaining popularity in various studies. Various ELM-based methods for different fields have been proposed. However, the robustness to noise and outliers is always the main problem affecting the performance of ELM. Results In this paper, an integrated method named correntropy induced loss based sparse robust graph regularized extreme learning machine (CSRGELM) is proposed. The introduction of correntropy induced loss improves the robustness of ELM and weakens the negative effects of noise and outliers. By using the L2,1-norm to constrain the output weight matrix, we tend to obtain a sparse output weight matrix to construct a simpler single hidden layer feedforward neural network model. By introducing the graph regularization to preserve the local structural information of the data, the classification performance of the new method is further improved. Besides, we design an iterative optimization method based on the idea of half quadratic optimization to solve the non-convex problem of CSRGELM. Conclusions The classification results on the benchmark dataset show that CSRGELM can obtain better classification results compared with other methods. More importantly, we also apply the new method to the classification problems of cancer samples and get a good classification effect.

Background High throughput RNA sequencing is a powerful approach to study gene expression. Due to the complex multiple-steps protocols in data acquisition, extreme deviation of a sample from samples of the same treatment group may occur due to technical variation or true biological differences. The high-dimensionality of the data with few biological replicates make it challenging to accurately detect those samples, and this issue is not well studied in the literature currently. Robust statistics is a family of theories and techniques aim to detect the outliers by first fitting the majority of the data and then flagging data points that deviate from it. Robust statistics have been widely used in multivariate data analysis for outlier detection in chemometrics and engineering. Here we apply robust statistics on RNA-seq data analysis. Results We report the use of two robust principal component analysis (rPCA) methods, PcaHubert and PcaGrid, to detect outlier samples in multiple simulated and real biological RNA-seq data sets with positive control outlier samples. PcaGrid achieved 100% sensitivity and 100% specificity in all the tests using positive control outliers with varying degrees of divergence. We applied rPCA methods and classical principal component analysis (cPCA) on an RNA-Seq data set profiling gene expression of the external granule layer in the cerebellum of control and conditional SnoN knockout mice. Both rPCA methods detected the same two outlier samples but cPCA failed to detect any. We performed differentially expressed gene detection before and after outlier removal as well as with and without batch effect modeling. We validated gene expression changes using quantitative reverse transcription PCR and used the result as reference to compare the performance of eight different data analysis strategies. Removing outliers without batch effect modeling performed the best in term of detecting biologically relevant differentially expressed genes. Conclusions rPCA implemented in the PcaGrid function is an accurate and objective method to detect outlier samples. It is well suited for high-dimensional data with small sample sizes like RNA-seq data. Outlier removal can significantly improve the performance of differential gene detection and downstream functional analysis.

Background Skewness is an under-utilized statistical measure that captures the degree of asymmetry in the distribution of any dataset. This study applied a new metric based on skewness to identify regulators or genes that have outlier expression in large patient cohorts. Results We investigated whether specific patterns of skewed expression were related to the enrichment of biological pathways or genomic properties like DNA methylation status. Our study used publicly available datasets that were generated using both RNA-sequencing and microarray technology platforms. For comparison, the datasets selected for this study also included different samples derived from control donors and cancer patients. When comparing the shift in expression skewness between cancer and control datasets, we observed an enrichment of pathways related to the immune function that reflects an increase towards positive skewness in the cancer relative to control datasets. A significant correlation was also detected between expression skewness and the top 500 genes corresponding to the most significant differential DNA methylation occurring in the promotor regions for four Cancer Genome Atlas cancer cohorts. Conclusions Our results indicate that expression skewness can reveal new insights into transcription based on outlier and asymmetrical behaviour in large patient cohorts.

© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated., Background: Learning accurate models from 'omics data is bringing many challenges due to their inherent high-dimensionality, e.g. the number of gene expression variables, and comparatively lower sample sizes, which leads to ill-posed inverse problems. Furthermore, the presence of outliers, either experimental errors or interesting abnormal clinical cases, may severely hamper a correct classification of patients and the identification of reliable biomarkers for a particular disease. We propose to address this problem through an ensemble classification setting based on distinct feature selection and modeling strategies, including logistic regression with elastic net regularization, Sparse Partial Least Squares - Discriminant Analysis (SPLS-DA) and Sparse Generalized PLS (SGPLS), coupled with an evaluation of the individuals' outlierness based on the Cook's distance. The consensus is achieved with the Rank Product statistics corrected for multiple testing, which gives a final list of sorted observations by their outlierness level. Results: We applied this strategy for the classification of Triple-Negative Breast Cancer (TNBC) RNA-Seq and clinical data from the Cancer Genome Atlas (TCGA). The detected 24 outliers were identified as putative mislabeled samples, corresponding to individuals with discrepant clinical labels for the HER2 receptor, but also individuals with abnormal expression values of ER, PR and HER2, contradictory with the corresponding clinical labels, which may invalidate the initial TNBC label. Moreover, the model consensus approach leads to the selection of a set of genes that may be linked to the disease. These results are robust to a resampling approach, either by selecting a subset of patients or a subset of genes, with a significant overlap of the outlier patients identified. Conclusions: The proposed ensemble outlier detection approach constitutes a robust procedure to identify abnormal cases and consensus covariates, which may improve biomarker selection for precision medicine applications. The method can also be easily extended to other regression models and datasets., This work was partially supported by the European Union Horizon 2020 research and innovation program under grant agreement No. 633974 (SOUND project), and the Portuguese Foundation for Science & Technology (FCT), through IDMEC, under LAETA, projects UID/EMS/50022/2013 and PERSEIDS (PTDC/EMS-SIS/0642/2014). André Veríssimo acknowledges support from FCT (SFRH/BD/97415/2013). Susana Vinga acknowledges support by Program Investigador FCT (IF/00653/2012) from FCT, co-funded by the European Social Fund (ESF) through the Operational Program Human Potential (POPH).

Quality Control in any high-throughput sequencing technology is a critical step, which if overlooked can compromise the data. A number of methods exist to identify biases during sequencing or alignment, yet not many tools exist to interpret biases due to outliers or batch effects. Hence, we developed iSeqQC, an expression-based QC tool that detects outliers either produced by batch effects due to laboratory conditions or due to dissimilarity within a phenotypic group. iSeqQC implements various statistical approaches including unsupervised clustering, agglomerative hierarchical clustering and correlation coefficients to provide insight into outliers. It can be utilized either through command-line (Github: https://github.com/gkumar09/iSeqQC) or web-interface (http://cancerwebpa.jefferson.edu/iSeqQC). iSeqQC is a fast, light-weight, expression-based QC tool that detects outliers by implementing various statistical approaches.

Background Understanding the phenotypic drug response on cancer cell lines plays a vital role in anti-cancer drug discovery and re-purposing. The Genomics of Drug Sensitivity in Cancer (GDSC) database provides open data for researchers in phenotypic screening to build and test their models. Previously, most research in these areas starts from the molecular fingerprints or physiochemical features of drugs, instead of their structures. Results In this paper, a model called twin Convolutional Neural Network for drugs in SMILES format (tCNNS) is introduced for phenotypic screening. tCNNS uses a convolutional network to extract features for drugs from their simplified molecular input line entry specification (SMILES) format and uses another convolutional network to extract features for cancer cell lines from the genetic feature vectors respectively. After that, a fully connected network is used to predict the interaction between the drugs and the cancer cell lines. When the training set and the testing set are divided based on the interaction pairs between drugs and cell lines, tCNNS achieves 0.826, 0.831 for the mean and top quartile of the coefficient of determinant (R2) respectively and 0.909, 0.912 for the mean and top quartile of the Pearson correlation (Rp) respectively, which are significantly better than those of the previous works (Ammad-Ud-Din et al., J Chem Inf Model 54:2347–9, 2014), (Haider et al., PLoS ONE 10:0144490, 2015), (Menden et al., PLoS ONE 8:61318, 2013). However, when the training set and the testing set are divided exclusively based on drugs or cell lines, the performance of tCNNS decreases significantly and Rp and R2 drop to barely above 0. Conclusions Our approach is able to predict the drug effects on cancer cell lines with high accuracy, and its performance remains stable with less but high-quality data, and with fewer features for the cancer cell lines. tCNNS can also solve the problem of outliers in other feature space. Besides achieving high scores in these statistical metrics, tCNNS also provides some insights into the phenotypic screening. However, the performance of tCNNS drops in the blind test. Electronic supplementary material The online version of this article (10.1186/s12859-019-2910-6) contains supplementary material, which is available to authorized users.

Background Analyses of replicates in sets of discrete data, typically acquired in multi-well plate formats, is a recurring task in many contemporary areas in the Life Sciences. The availability of accessible cross-platform data analysis tools for such fundamental tasks in varied projects and environments is an important prerequisite to ensuring a reliable and timely turnaround as well as to provide practical analytical tools for student training. Results We have developed an easy-to-use, interactive software tool for the analysis of multiple data sets comprising replicates of discrete bivariate data points. For each dataset, the software identifies the replicate data points from a defined matrix layout and calculates their means and standard errors. The averaged values are then automatically fitted using either a linear or a logistic dose response function. Conclusions DRfit is a practical and convenient tool for the analysis of one or multiple sets of discrete data points acquired as replicates from multi-well plate assays. The design of the graphical user interface and the built-in analysis features make it a flexible and useful tool for a wide range of different assays. Electronic supplementary material The online version of this article (10.1186/s12859-019-2891-5) contains supplementary material, which is available to authorized users.

Background Recently differential variability has been showed to be valuable in evaluating the association of DNA methylation to the risks of complex human diseases. The statistical tests based on both differential methylation level and differential variability can be more powerful than those based only on differential methylation level. Anh and Wang (2013) proposed a joint score test (AW) to simultaneously detect for differential methylation and differential variability. However, AW’s method seems to be quite conservative and has not been fully compared with existing joint tests. Results We proposed three improved joint score tests, namely iAW.Lev, iAW.BF, and iAW.TM, and have made extensive comparisons with the joint likelihood ratio test (jointLRT), the Kolmogorov-Smirnov (KS) test, and the AW test. Systematic simulation studies showed that: 1) the three improved tests performed better (i.e., having larger power, while keeping nominal Type I error rates) than the other three tests for data with outliers and having different variances between cases and controls; 2) for data from normal distributions, the three improved tests had slightly lower power than jointLRT and AW. The analyses of two Illumina HumanMethylation27 data sets GSE37020 and GSE20080 and one Illumina Infinium MethylationEPIC data set GSE107080 demonstrated that three improved tests had higher true validation rates than those from jointLRT, KS, and AW. Conclusions The three proposed joint score tests are robust against the violation of normality assumption and presence of outlying observations in comparison with other three existing tests. Among the three proposed tests, iAW.BF seems to be the most robust and effective one for all simulated scenarios and also in real data analyses. Electronic supplementary material The online version of this article (10.1186/s12859-018-2185-3) contains supplementary material, which is available to authorized users.

Background The identification of differential metabolites in metabolomics is still a big challenge and plays a prominent role in metabolomics data analyses. Metabolomics datasets often contain outliers because of analytical, experimental, and biological ambiguity, but the currently available differential metabolite identification techniques are sensitive to outliers. Results We propose a kernel weight based outlier-robust volcano plot for identifying differential metabolites from noisy metabolomics datasets. Two numerical experiments are used to evaluate the performance of the proposed technique against nine existing techniques, including the t-test and the Kruskal-Wallis test. Artificially generated data with outliers reveal that the proposed method results in a lower misclassification error rate and a greater area under the receiver operating characteristic curve compared with existing methods. An experimentally measured breast cancer dataset to which outliers were artificially added reveals that our proposed method produces only two non-overlapping differential metabolites whereas the other nine methods produced between seven and 57 non-overlapping differential metabolites. Conclusion Our data analyses show that the performance of the proposed differential metabolite identification technique is better than that of existing methods. Thus, the proposed method can contribute to analysis of metabolomics data with outliers. The R package and user manual of the proposed method are available at https://github.com/nishithkumarpaul/Rvolcano. Electronic supplementary material The online version of this article (10.1186/s12859-018-2117-2) contains supplementary material, which is available to authorized users.

A requirement for precision medicine is the accurate prediction of the sensitivity of a given drug on an individual patient. A very common method for this prediction is the use of Random Forest built on Genomic Features such as gene expression. However, effective drug sensitivity prediction requires the use of multiple heterogeneous dataset but it is rare that all such information is available for all drug and cell line combinations. To effectively incorporate all available data into a drug sensitivity prediction problem requires the use of stacking multiple models, built using a variety of different methods and data. In this article we investigate stacking in the context of drug sensitivity prediction. First, we examine basic models utilized in drug sensitivity prediction including the Random Forest, Neural Network, and K-Nearest Neighbor approach. To stack individual models we utilize a linear stacking method built utilizing a held-out validation set. We then investigate which form of stacking is most effective in improving accuracy. The two forms of stacking investigate are vertical stacking, in which our training samples are split and then stacked, and horizontal stacking, where our features are split before stacking. From a theoretical standpoint we have shown that horizontal stacking outperforms vertical stacking, especially as the sample size becomes large. Our theory is then proven utilizing both synthetically generated data, as well as data extracted from the Cancer Cell Line Encyclopedia. Despite having the best individual predictor, vertical stacking consistently underperformed compared to horizontal stacking. Finally, we build a stacked model utilizing data extracted from a variety of sources. Gene Expression for individual cell lines are taken from the GDSC database, drug target data is data mined from Pubchem and physical features are extracted utilizing PaDEL-Descriptor software. Using this data we aim to predict the Area Under the Curve value for individual drug-cell line combinations. We examine the performance of individual and stacked models. We note that stacking models built on two heterogeneous datasets provide superior performance to stacking different models built on the same dataset. It is also noted that stacking provides a noticeable reduction in the bias of our predictors when the dominant eigenvalue of the principle axis of variation in the residuals is significantly higher than the remaining eigenvalues.

Background Cluster analysis is the most common unsupervised method for finding hidden groups in data. Clustering presents two main challenges: (1) finding the optimal number of clusters, and (2) removing “outliers” among the objects being clustered. Few clustering algorithms currently deal directly with the outlier problem. Furthermore, existing methods for identifying the number of clusters still have some drawbacks. Thus, there is a need for a better algorithm to tackle both challenges. Results We present a new approach, implemented in an R package called Thresher, to cluster objects in general datasets. Thresher combines ideas from principal component analysis, outlier filtering, and von Mises-Fisher mixture models in order to select the optimal number of clusters. We performed a large Monte Carlo simulation study to compare Thresher with other methods for detecting outliers and determining the number of clusters. We found that Thresher had good sensitivity and specificity for detecting and removing outliers. We also found that Thresher is the best method for estimating the optimal number of clusters when the number of objects being clustered is smaller than the number of variables used for clustering. Finally, we applied Thresher and eleven other methods to 25 sets of breast cancer data downloaded from the Gene Expression Omnibus; only Thresher consistently estimated the number of clusters to lie in the range of 4–7 that is consistent with the literature. Conclusions Thresher is effective at automatically detecting and removing outliers. By thus cleaning the data, it produces better estimates of the optimal number of clusters when there are more variables than objects. When we applied Thresher to a variety of breast cancer datasets, it produced estimates that were both self-consistent and consistent with the literature. We expect Thresher to be useful for studying a wide variety of biological datasets. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1998-9) contains supplementary material, which is available to authorized users.

Background Normalization is an important data preparation step in gene expression analyses, designed to remove various systematic noise. Sample variance is greatly reduced after normalization, hence the power of subsequent statistical analyses is likely to increase. On the other hand, variance reduction is made possible by borrowing information across all genes, including differentially expressed genes (DEGs) and outliers, which will inevitably introduce some bias. This bias typically inflates type I error; and can reduce statistical power in certain situations. In this study we propose a new differential expression analysis pipeline, dubbed as super-delta, that consists of a multivariate extension of the global normalization and a modified t-test. A robust procedure is designed to minimize the bias introduced by DEGs in the normalization step. The modified t-test is derived based on asymptotic theory for hypothesis testing that suitably pairs with the proposed robust normalization. Results We first compared super-delta with four commonly used normalization methods: global, median-IQR, quantile, and cyclic loess normalization in simulation studies. Super-delta was shown to have better statistical power with tighter control of type I error rate than its competitors. In many cases, the performance of super-delta is close to that of an oracle test in which datasets without technical noise were used. We then applied all methods to a collection of gene expression datasets on breast cancer patients who received neoadjuvant chemotherapy. While there is a substantial overlap of the DEGs identified by all of them, super-delta were able to identify comparatively more DEGs than its competitors. Downstream gene set enrichment analysis confirmed that all these methods selected largely consistent pathways. Detailed investigations on the relatively small differences showed that pathways identified by super-delta have better connections to breast cancer than other methods. Conclusions As a new pipeline, super-delta provides new insights to the area of differential gene expression analysis. Solid theoretical foundation supports its asymptotic unbiasedness and technical noise-free properties. Implementation on real and simulated datasets demonstrates its decent performance compared with state-of-art procedures. It also has the potential of expansion to be incorporated with other data type and/or more general between-group comparison problems. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1992-2) contains supplementary material, which is available to authorized users.

Background Digital PCR (dPCR) is a technique for estimating the concentration of a target nucleic acid by loading a sample into a large number of partitions, amplifying the target and using a fluorescent marker to identify which partitions contain the target. The standard analysis uses only the proportion of partitions containing target to estimate the concentration and depends on the assumption that the initial distribution of molecules in partitions is Poisson. In this paper we describe a way to extend such analysis using the quantification cycle (Cq) data that may also be available, but rather than assuming the Poisson distribution the more general Conway-Maxwell-Poisson distribution is used instead. Results A software package for the open source language R has been created for performing the analysis. This was used to validate the method by analysing Cq data from dPCR experiments involving 3 types of DNA (attenuated, virulent and plasmid) at 3 concentrations. Results indicate some deviation from the Poisson distribution, which is strongest for the virulent DNA sample. Theoretical calculations indicate that the deviation from the Poisson distribution results in a bias of around 5 % for the analysed data if the standard analysis is used, but that it could be larger for higher concentrations. Compared to the estimates of subsequent efficiency, the estimates of 1st cycle efficiency are much lower for the virulent DNA, moderately lower for the attenuated DNA and close for the plasmid DNA. Further method validation using simulated data gave results closer to the true values and with lower standard deviations than the standard method, for concentrations up to approximately 2.5 copies/partition. Conclusions The Cq-based method is effective at estimating DNA concentration and is not seriously affected by data issues such as outliers and moderately non-linear trends. The data analysis suggests that the Poisson assumption of the standard approach does lead to a bias that is fairly small, though more research is needed. Estimates of the 1st cycle efficiency being lower than estimates of the subsequent efficiency may indicate samples that are mixtures of single-stranded and double-stranded DNA. The model can reduce or eliminate the resulting bias. Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-1275-3) contains supplementary material, which is available to authorized users.

Background Chemical or small interfering (si) RNA screens measure the effects of many independent experimental conditions, each applied to a population of cells (e.g., all of the cells in a well). High-content screens permit a readout (e.g., fluorescence, luminescence, cell morphology) from each cell in the population. Most analysis approaches compare the average effect on each population, precluding identification of outliers that affect the distribution of the reporter in the population but not its average. Other approaches only measure changes to the distribution with a single parameter, precluding accurate distinction and clustering of interesting outlier distributions. Results We describe a methodology to identify outlier conditions by considering the cell-level measurements from each condition as a sample of an underlying distribution. With appropriate selection of a distance metric, all effects can be embedded in a fixed-dimensionality Euclidean basis, facilitating identification and clustering of biologically interesting outliers. We demonstrate that measurement of distances with the Hellinger distance metric offers substantial computational efficiencies over alternative metrics. We validate this methodology using an RNA interference (RNAi) screen in mouse embryonic stem cells (ESC) with a Nanog reporter. The methodology clusters effects of multiple control siRNAs into their true identities better than conventional approaches describing the median cell fluorescence or the commonly used Kolmogorov-Smirnov distance between the observed fluorescence distribution and the null distribution. It identifies outlier genes with effects on the reporter distribution that would have been missed by other methods. Among them, siRNA targeting Chek1 leads to a wider Nanog reporter fluorescence distribution. Similarly, siRNA targeting Med14 or Med27 leads to a narrower Nanog reporter fluorescence distribution. We confirm the roles of these three genes in regulating pluripotency by mRNA expression and alkaline phosphatase staining using independent short hairpin (sh) RNAs. Conclusions Using our methodology, we describe each experimental condition by a probability distribution. Measuring distances between probability distributions permits a multivariate rather than univariate readout. Clustering points derived from these distances allows us to obtain greater biological insight than methods based solely on single parameters. We find several outliers from a mouse ESC RNAi screen that we confirm to be pluripotency regulators. Many of these outliers would have been missed by other analysis methods. Electronic supplementary material The online version of this article (doi:10.1186/s12859-015-0636-7) contains supplementary material, which is available to authorized users.

The Kruskal-Wallis test is a popular non-parametric statistical test for identifying expression quantitative trait loci (eQTLs) from genome-wide data due to its robustness against variations in the underlying genetic model and expression trait distribution, but testing billions of marker-trait combinations one-by-one can become computationally prohibitive. We developed kruX, an algorithm implemented in Matlab, Python and R that uses matrix multiplications to simultaneously calculate the Kruskal-Wallis test statistic for several millions of marker-trait combinations at once. KruX is more than ten thousand times faster than computing associations one-by-one on a typical human dataset. We used kruX and a dataset of more than 500k SNPs and 20k expression traits measured in 102 human blood samples to compare eQTLs detected by the Kruskal-Wallis test to eQTLs detected by the parametric ANOVA and linear model methods. We found that the Kruskal-Wallis test is more robust against data outliers and heterogeneous genotype group sizes and detects a higher proportion of non-linear associations, but is more conservative for calling additive linear associations. In summary, kruX enables the use of robust non-parametric methods for massive eQTL mapping without the need for a high-performance computing infrastructure., minor revision; 6 pages, 5 figures; software available at http://krux.googlecode.com

Background Modeling high-dimensional data involving thousands of variables is particularly important for gene expression profiling experiments, nevertheless,it remains a challenging task. One of the challenges is to implement an effective method for selecting a small set of relevant genes, buried in high-dimensional irrelevant noises. RELIEF is a popular and widely used approach for feature selection owing to its low computational cost and high accuracy. However, RELIEF based methods suffer from instability, especially in the presence of noisy and/or high-dimensional outliers. Results We propose an innovative feature weighting algorithm, called LHR, to select informative genes from highly noisy data. LHR is based on RELIEF for feature weighting using classical margin maximization. The key idea of LHR is to estimate the feature weights through local approximation rather than global measurement, which is typically used in existing methods. The weights obtained by our method are very robust in terms of degradation of noisy features, even those with vast dimensions. To demonstrate the performance of our method, extensive experiments involving classification tests have been carried out on both synthetic and real microarray benchmark datasets by combining the proposed technique with standard classifiers, including the support vector machine (SVM), k-nearest neighbor (KNN), hyperplane k-nearest neighbor (HKNN), linear discriminant analysis (LDA) and naive Bayes (NB). Conclusion Experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed feature selection method combined with supervised learning in three aspects: 1) high classification accuracy, 2) excellent robustness to noise and 3) good stability using to various classification algorithms.

Background Genome-wide association studies can provide novel insights into diseases of interest, as well as to the responsiveness of an individual to specific treatments. In such studies, it is very important to correct for population stratification, which refers to allele frequency differences between cases and controls due to systematic ancestry differences. Population stratification can cause spurious associations if not adjusted properly. The principal component analysis (PCA) method has been relied upon as a highly useful methodology to adjust for population stratification in these types of large-scale studies. Recently, the linear mixed model (LMM) has also been proposed to account for family structure or cryptic relatedness. However, neither of these approaches may be optimal in properly correcting for sample structures in the presence of subject outliers. Results We propose to use robust PCA combined with k-medoids clustering to deal with population stratification. This approach can adjust for population stratification for both continuous and discrete populations with subject outliers, and it can be considered as an extension of the PCA method and the multidimensional scaling (MDS) method. Through simulation studies, we compare the performance of our proposed methods with several widely used stratification methods, including PCA and MDS. We show that subject outliers can greatly influence the analysis results from several existing methods, while our proposed robust population stratification methods perform very well for both discrete and admixed populations with subject outliers. We illustrate the new method using data from a rheumatoid arthritis study. Conclusions We demonstrate that subject outliers can greatly influence the analysis result in GWA studies, and propose robust methods for dealing with population stratification that outperform existing population stratification methods in the presence of subject outliers.

Background Microarray data enables the high-throughput survey of mRNA expression profiles at the genomic level; however, the data presents a challenging statistical problem because of the large number of transcripts with small sample sizes that are obtained. To reduce the dimensionality, various Bayesian or empirical Bayes hierarchical models have been developed. However, because of the complexity of the microarray data, no model can explain the data fully. It is generally difficult to scrutinize the irregular patterns of expression that are not expected by the usual statistical gene by gene models. Results As an extension of empirical Bayes (EB) procedures, we have developed the β-empirical Bayes (β-EB) approach based on a β-likelihood measure which can be regarded as an ’evidence-based’ weighted (quasi-) likelihood inference. The weight of a transcript t is described as a power function of its likelihood, f β ( y t | θ ). Genes with low likelihoods have unexpected expression patterns and low weights. By assigning low weights to outliers, the inference becomes robust. The value of β, which controls the balance between the robustness and efficiency, is selected by maximizing the predictive β 0-likelihood by cross-validation. The proposed β-EB approach identified six significant (p < 10−5) contaminated transcripts as differentially expressed (DE) in normal/tumor tissues from the head and neck of cancer patients. These six genes were all confirmed to be related to cancer; they were not identified as DE genes by the classical EB approach. When applied to the eQTL analysis of Arabidopsis thaliana, the proposed β-EB approach identified some potential master regulators that were missed by the EB approach. Conclusions The simulation data and real gene expression data showed that the proposed β-EB method was robust against outliers. The distribution of the weights was used to scrutinize the irregular patterns of expression and diagnose the model statistically. When β-weights outside the range of the predicted distribution were observed, a detailed inspection of the data was carried out. The β-weights described here can be applied to other likelihood-based statistical models for diagnosis, and may serve as a useful tool for transcriptome and proteome studies.

Background Gradual or sudden transitions among different states as exhibited by cell populations in a biological sample under particular conditions or stimuli can be detected and profiled by flow cytometric time course data. Often such temporal profiles contain features due to transient states that present unique modeling challenges. These could range from asymmetric non-Gaussian distributions to outliers and tail subpopulations, which need to be modeled with precision and rigor. Results To ensure precision and rigor, we propose a parametric modeling framework StateProfiler based on finite mixtures of skew t-Normal distributions that are robust against non-Gaussian features caused by asymmetry and outliers in data. Further, we present in StateProfiler a new greedy EM algorithm for fast and optimal model selection. The parsimonious approach of our greedy algorithm allows us to detect the genuine dynamic variation in the key features as and when they appear in time course data. We also present a procedure to construct a well-fitted profile by merging any redundant model components in a way that minimizes change in entropy of the resulting model. This allows precise profiling of unusually shaped distributions and less well-separated features that may appear due to cellular heterogeneity even within clonal populations. Conclusions By modeling flow cytometric data measured over time course and marker space with StateProfiler, specific parametric characteristics of cellular states can be identified. The parameters are then tested statistically for learning global and local patterns of spatio-temporal change. We applied StateProfiler to identify the temporal features of yeast cell cycle progression based on knockout of S-phase triggering cyclins Clb5 and Clb6, and then compared the S-phase delay phenotypes due to differential regulation of the two cyclins. We also used StateProfiler to construct the temporal profile of clonal divergence underlying lineage selection in mammalian hematopoietic progenitor cells.

Background Non-negative matrix factorization (NMF) has been shown to be a powerful tool for clustering gene expression data, which are widely used to classify cancers. NMF aims to find two non-negative matrices whose product closely approximates the original matrix. Traditional NMF methods minimize either the l 2 norm or the Kullback-Leibler distance between the product of the two matrices and the original matrix. Correntropy was recently shown to be an effective similarity measurement due to its stability to outliers or noise. Results We propose a maximum correntropy criterion (MCC)-based NMF method (NMF-MCC) for gene expression data-based cancer clustering. Instead of minimizing the l 2 norm or the Kullback-Leibler distance, NMF-MCC maximizes the correntropy between the product of the two matrices and the original matrix. The optimization problem can be solved by an expectation conditional maximization algorithm. Conclusions Extensive experiments on six cancer benchmark sets demonstrate that the proposed method is significantly more accurate than the state-of-the-art methods in cancer clustering.

Background Many methods for dimensionality reduction of large data sets such as those generated in microarray studies boil down to the Singular Value Decomposition (SVD). Although singular vectors associated with the largest singular values have strong optimality properties and can often be quite useful as a tool to summarize the data, they are linear combinations of up to all of the data points, and thus it is typically quite hard to interpret those vectors in terms of the application domain from which the data are drawn. Recently, an alternative dimensionality reduction paradigm, CUR matrix decompositions, has been proposed to address this problem and has been applied to genetic and internet data. CUR decompositions are low-rank matrix decompositions that are explicitly expressed in terms of a small number of actual columns and/or actual rows of the data matrix. Since they are constructed from actual data elements, CUR decompositions are interpretable by practitioners of the field from which the data are drawn. Results We present an implementation to perform CUR matrix decompositions, in the form of a freely available, open source R-package called rCUR. This package will help users to perform CUR-based analysis on large-scale data, such as those obtained from different high-throughput technologies, in an interactive and exploratory manner. We show two examples that illustrate how CUR-based techniques make it possible to reduce significantly the number of probes, while at the same time maintaining major trends in data and keeping the same classification accuracy. Conclusions The package rCUR provides functions for the users to perform CUR-based matrix decompositions in the R environment. In gene expression studies, it gives an additional way of analysis of differential expression and discriminant gene selection based on the use of statistical leverage scores. These scores, which have been used historically in diagnostic regression analysis to identify outliers, can be used by rCUR to identify the most informative data points with respect to which to express the remaining data points.

Background Machine learning methods are nowadays used for many biological prediction problems involving drugs, ligands or polypeptide segments of a protein. In order to build a prediction model a so called training data set of molecules with measured target properties is needed. For many such problems the size of the training data set is limited as measurements have to be performed in a wet lab. Furthermore, the considered problems are often complex, such that it is not clear which molecular descriptors (features) may be suitable to establish a strong correlation with the target property. In many applications all available descriptors are used. This can lead to difficult machine learning problems, when thousands of descriptors are considered and only few (e.g. below hundred) molecules are available for training. Results The CoEPrA contest provides four data sets, which are typical for biological regression problems (few molecules in the training data set and thousands of descriptors). We applied the same two-step training procedure for all four regression tasks. In the first stage, we used optimized L1 regularization to select the most relevant features. Thus, the initial set of more than 6,000 features was reduced to about 50. In the second stage, we used only the selected features from the preceding stage applying a milder L2 regularization, which generally yielded further improvement of prediction performance. Our linear model employed a soft loss function which minimizes the influence of outliers. Conclusions The proposed two-step method showed good results on all four CoEPrA regression tasks. Thus, it may be useful for many other biological prediction problems where for training only a small number of molecules are available, which are described by thousands of descriptors.

Background In previous work, we reported the development of caCORRECT, a novel microarray quality control system built to identify and correct spatial artifacts commonly found on Affymetrix arrays. We have made recent improvements to caCORRECT, including the development of a model-based data-replacement strategy and integration with typical microarray workflows via caCORRECT's web portal and caBIG grid services. In this report, we demonstrate that caCORRECT improves the reproducibility and reliability of experimental results across several common Affymetrix microarray platforms. caCORRECT represents an advance over state-of-art quality control methods such as Harshlighting, and acts to improve gene expression calculation techniques such as PLIER, RMA and MAS5.0, because it incorporates spatial information into outlier detection as well as outlier information into probe normalization. The ability of caCORRECT to recover accurate gene expressions from low quality probe intensity data is assessed using a combination of real and synthetic artifacts with PCR follow-up confirmation and the affycomp spike in data. The caCORRECT tool can be accessed at the website: http://cacorrect.bme.gatech.edu. Results We demonstrate that (1) caCORRECT's artifact-aware normalization avoids the undesirable global data warping that happens when any damaged chips are processed without caCORRECT; (2) When used upstream of RMA, PLIER, or MAS5.0, the data imputation of caCORRECT generally improves the accuracy of microarray gene expression in the presence of artifacts more than using Harshlighting or not using any quality control; (3) Biomarkers selected from artifactual microarray data which have undergone the quality control procedures of caCORRECT are more likely to be reliable, as shown by both spike in and PCR validation experiments. Finally, we present a case study of the use of caCORRECT to reliably identify biomarkers for renal cell carcinoma, yielding two diagnostic biomarkers with potential clinical utility, PRKAB1 and NNMT. Conclusions caCORRECT is shown to improve the accuracy of gene expression, and the reproducibility of experimental results in clinical application. This study suggests that caCORRECT will be useful to clean up possible artifacts in new as well as archived microarray data.

Background Cluster analysis of gene expression data is a useful tool for identifying biologically relevant groups of genes that show similar expression patterns under multiple experimental conditions. Performance of clustering algorithms is largely dependent on selected similarity measure. Efficiency in handling outliers is a major contributor to the success of a similarity measure. In gene expression data, there may be pairs of genes that have completely different expression values over a few samples under certain experimental condition(s), although they exhibit similar behavior over the other samples. Depending on the algorithms, these outliers are either placed in single element clusters (hierarchical clustering), are allowed to be in a cluster that is more similar compared to others (partitioning clustering) or they may be completely discarded from grouping (density-based, grid-based and graph-based clustering). In all these cases outliers affect the outcome of a clustering result. Measurement errors or conditional changes during microarray experiments may cause a single sample, if not more, differing in expression level to a great extent compared to the other samples. Expression value of the single or a very few outlier samples may cause a gene to be an outlier. We formulate a new weighted function based method to reduce the effect of outliers on similarity measures. The better the similarity measure is in measuring similarity between genes in the presence of outliers, the better the

Background Post-genomic molecular biology has resulted in an explosion of data, providing measurements for large numbers of genes, proteins and metabolites. Time series experiments have become increasingly common, necessitating the development of novel analysis tools that capture the resulting data structure. Outlier measurements at one or more time points present a significant challenge, while potentially valuable replicate information is often ignored by existing techniques. Results We present a generative model-based Bayesian hierarchical clustering algorithm for microarray time series that employs Gaussian process regression to capture the structure of the data. By using a mixture model likelihood, our method permits a small proportion of the data to be modelled as outlier measurements, and adopts an empirical Bayes approach which uses replicate observations to inform a prior distribution of the noise variance. The method automatically learns the optimum number of clusters and can incorporate non-uniformly sampled time points. Using a wide variety of experimental data sets, we show that our algorithm consistently yields higher quality and more biologically meaningful clusters than current state-of-the-art methodologies. We highlight the importance of modelling outlier values by demonstrating that noisy genes can be grouped with other genes of similar biological function. We demonstrate the importance of including replicate information, which we find enables the discrimination of additional distinct expression profiles. Conclusions By incorporating outlier measurements and replicate values, this clustering algorithm for time series microarray data provides a step towards a better treatment of the noise inherent in measurements from high-throughput genomic technologies. Timeseries BHC is available as part of the R package 'BHC' (version 1.5), which is available for download from Bioconductor (version 2.9 and above) via http://www.bioconductor.org/packages/release/bioc/html/BHC.html?pagewanted=all.

Background Prediction of protein subcellular localization generally involves many complex factors, and using only one or two aspects of data information may not tell the true story. For this reason, some recent predictive models are deliberately designed to integrate multiple heterogeneous data sources for exploiting multi-aspect protein feature information. Gene ontology, hereinafter referred to as GO, uses a controlled vocabulary to depict biological molecules or gene products in terms of biological process, molecular function and cellular component. With the rapid expansion of annotated protein sequences, gene ontology has become a general protein feature that can be used to construct predictive models in computational biology. Existing models generally either concatenated the GO terms into a flat binary vector or applied majority-vote based ensemble learning for protein subcellular localization, both of which can not estimate the individual discriminative abilities of the three aspects of gene ontology. Results In this paper, we propose a Gene Ontology Based Transfer Learning Model (GO-TLM) for large-scale protein subcellular localization. The model transfers the signature-based homologous GO terms to the target proteins, and further constructs a reliable learning system to reduce the adverse affect of the potential false GO terms that are resulted from evolutionary divergence. We derive three GO kernels from the three aspects of gene ontology to measure the GO similarity of two proteins, and derive two other spectrum kernels to measure the similarity of two protein sequences. We use simple non-parametric cross validation to explicitly weigh the discriminative abilities of the five kernels, such that the time & space computational complexities are greatly reduced when compared to the complicated semi-definite programming and semi-indefinite linear programming. The five kernels are then linearly merged into one single kernel for protein subcellular localization. We evaluate GO-TLM performance against three baseline models: MultiLoc, MultiLoc-GO and Euk-mPLoc on the benchmark datasets the baseline models adopted. 5-fold cross validation experiments show that GO-TLM achieves substantial accuracy improvement against the baseline models: 80.38% against model Euk-mPLoc 67.40% with 12.98% substantial increase; 96.65% and 96.27% against model MultiLoc-GO 89.60% and 89.60%, with 7.05% and 6.67% accuracy increase on dataset MultiLoc plant and dataset MultiLoc animal, respectively; 97.14%, 95.90% and 96.85% against model MultiLoc-GO 83.70%, 90.10% and 85.70%, with accuracy increase 13.44%, 5.8% and 11.15% on dataset BaCelLoc plant, dataset BaCelLoc fungi and dataset BaCelLoc animal respectively. For BaCelLoc independent sets, GO-TLM achieves 81.25%, 80.45% and 79.46% on dataset BaCelLoc plant holdout, dataset BaCelLoc plant holdout and dataset BaCelLoc animal holdout, respectively, as compared against baseline model MultiLoc-GO 76%, 60.00% and 73.00%, with accuracy increase 5.25%, 20.45% and 6.46%, respectively. Conclusions Since direct homology-based GO term transfer may be prone to introducing noise and outliers to the target protein, we design an explicitly weighted kernel learning system (called Gene Ontology Based Transfer Learning Model, GO-TLM) to transfer to the target protein the known knowledge about related homologous proteins, which can reduce the risk of outliers and share knowledge between homologous proteins, and thus achieve better predictive performance for protein subcellular localization. Cross validation and independent test experimental results show that the homology-based GO term transfer and explicitly weighing the GO kernels substantially improve the prediction performance.

Background Data generated using 'omics' technologies are characterized by high dimensionality, where the number of features measured per subject vastly exceeds the number of subjects in the study. In this paper, we consider issues relevant in the design of biomedical studies in which the goal is the discovery of a subset of features and an associated algorithm that can predict a binary outcome, such as disease status. We compare the performance of four commonly used classifiers (K-Nearest Neighbors, Prediction Analysis for Microarrays, Random Forests and Support Vector Machines) in high-dimensionality data settings. We evaluate the effects of varying levels of signal-to-noise ratio in the dataset, imbalance in class distribution and choice of metric for quantifying performance of the classifier. To guide study design, we present a summary of the key characteristics of 'omics' data profiled in several human or animal model experiments utilizing high-content mass spectrometry and multiplexed immunoassay based techniques. Results The analysis of data from seven 'omics' studies revealed that the average magnitude of effect size observed in human studies was markedly lower when compared to that in animal studies. The data measured in human studies were characterized by higher biological variation and the presence of outliers. The results from simulation studies indicated that the classifier Prediction Analysis for Microarrays (PAM) had the highest power when the class conditional feature distributions were Gaussian and outcome distributions were balanced. Random Forests was optimal when feature distributions were skewed and when class distributions were unbalanced. We provide a free open-source R statistical software library (MVpower) that implements the simulation strategy proposed in this paper. Conclusion No single classifier had optimal performance under all settings. Simulation studies provide useful guidance for the design of biomedical studies involving high-dimensionality data.

Background Accurate classification into genotypes is critical in understanding evolution of divergent viruses. Here we report a new approach, MuLDAS, which classifies a query sequence based on the statistical genotype models learned from the known sequences. Thus, MuLDAS utilizes full spectra of well characterized sequences as references, typically of an order of hundreds, in order to estimate the significance of each genotype assignment. Results MuLDAS starts by aligning the query sequence to the reference multiple sequence alignment and calculating the subsequent distance matrix among the sequences. They are then mapped to a principal coordinate space by multidimensional scaling, and the coordinates of the reference sequences are used as features in developing linear discriminant models that partition the space by genotype. The genotype of the query is then given as the maximum a posteriori estimate. MuLDAS tests the model confidence by leave-one-out cross-validation and also provides some heuristics for the detection of 'outlier' sequences that fall far outside or in-between genotype clusters. We have tested our method by classifying HIV-1 and HCV nucleotide sequences downloaded from NCBI GenBank, achieving the overall concordance rates of 99.3% and 96.6%, respectively, with the benchmark test dataset retrieved from the respective databases of Los Alamos National Laboratory. Conclusions The highly accurate genotype assignment coupled with several measures for evaluating the results makes MuLDAS useful in analyzing the sequences of rapidly evolving viruses such as HIV-1 and HCV. A web-based genotype prediction server is available at http://www.muldas.org/MuLDAS/.