BiC2PAM: constraint-guided biclustering for biological data analysis with domain knowledge

Background

Biclustering has been largely used in biological data analysis, enabling the discovery of putative functional modules from omic and network data. Despite the recognized importance of incorporating domain knowledge to guide biclustering and guarantee a focus on relevant and non-trivial biclusters, this possibility has not yet been comprehensively addressed. This results from the fact that the majority of existing algorithms are only able to deliver sub-optimal solutions with restrictive assumptions on the structure, coherency and quality of biclustering solutions, thus preventing the up-front satisfaction of knowledge-driven constraints. Interestingly, in recent years, a clearer understanding of the synergies between pattern mining and biclustering gave rise to a new class of algorithms, termed as pattern-based biclustering algorithms. These algorithms, able to efficiently discover flexible biclustering solutions with optimality guarantees, are thus positioned as good candidates for knowledge incorporation. In this context, this work aims to bridge the current lack of solid views on the use of background knowledge to guide (pattern-based) biclustering tasks.

Methods

This work extends (pattern-based) biclustering algorithms to guarantee the satisfiability of constraints derived from background knowledge and to effectively explore efficiency gains from their incorporation. In this context, we first show the relevance of constraints with succinct, (anti-)monotone and convertible properties for the analysis of expression data and biological networks. We further show how pattern-based biclustering algorithms can be adapted to effectively prune of the search space in the presence of such constraints, as well as be guided in the presence of biological annotations. Relying on these contributions, we propose BiClustering with Constraints using PAttern Mining (BiC2PAM), an extension of BicPAM and BicNET biclustering algorithms.

Results

Experimental results on biological data demonstrate the importance of incorporating knowledge within biclustering to foster efficiency and enable the discovery of non-trivial biclusters with heightened biological relevance.

Conclusions

This work provides the first comprehensive view and sound algorithm for biclustering biological data with constraints derived from user expectations, knowledge repositories and/or literature.

     

A systematic comparison and evaluation of biclustering methods for gene expression data

MOTIVATION: In recent years, there have been various efforts to overcome the limitations of standard clustering approaches for the analysis of gene expression data by grouping genes and samples simultaneously. The underlying concept, which is often referred to as biclustering, allows to identify sets of genes sharing compatible expression patterns across subsets of samples, and its usefulness has been demonstrated for different organisms and datasets. Several biclustering methods have been proposed in the literature; however, it is not clear how the different techniques compare with each other with respect to the biological relevance of the clusters as well as with other characteristics such as robustness and sensitivity to noise. Accordingly, no guidelines concerning the choice of the biclustering method are currently available. RESULTS: First, this paper provides a methodology for comparing and validating biclustering methods that includes a simple binary reference model. Although this model captures the essential features of most biclustering approaches, it is still simple enough to exactly determine all optimal groupings; to this end, we propose a fast divide-and-conquer algorithm (Bimax). Second, we evaluate the performance of five salient biclustering algorithms together with the reference model and a hierarchical clustering method on various synthetic and real datasets for Saccharomyces cerevisiae and Arabidopsis thaliana. The comparison reveals that (1) biclustering in general has advantages over a conventional hierarchical clustering approach, (2) there are considerable performance differences between the tested methods and (3) already the simple reference model delivers relevant patterns within all considered settings.     

BicAT: a biclustering analysis toolbox

SUMMARY: Besides classical clustering methods such as hierarchical clustering, in recent years biclustering has become a popular approach to analyze biological data sets, e.g. gene expression data. The Biclustering Analysis Toolbox (BicAT) is a software platform for clustering-based data analysis that integrates various biclustering and clustering techniques in terms of a common graphical user interface. Furthermore, BicAT provides different facilities for data preparation, inspection and postprocessing such as discretization, filtering of biclusters according to specific criteria or gene pair analysis for constructing gene interconnection graphs. The possibility to use different biclustering algorithms inside a single graphical tool allows the user to compare clustering results and choose the algorithm that best fits a specific biological scenario. The toolbox is described in the context of gene expression analysis, but is also applicable to other types of data, e.g. data from proteomics or synthetic lethal experiments. AVAILABILITY: The BicAT toolbox is freely available at http://www.tik.ee.ethz.ch/sop/bicat and runs on all operating systems. The Java source code of the program and a developer's guide is provided on the website as well. Therefore, users may modify the program and add further algorithms or extensions.     

QUBIC: a qualitative biclustering algorithm for analyses of gene expression data

Biclustering extends the traditional clustering techniques by attempting to find (all) subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. Still the real power of this clustering strategy is yet to be fully realized due to the lack of effective and efficient algorithms for reliably solving the general biclustering problem. We report a QUalitative BIClustering algorithm (QUBIC) that can solve the biclustering problem in a more general form, compared to existing algorithms, through employing a combination of qualitative (or semi-quantitative) measures of gene expression data and a combinatorial optimization technique. One key unique feature of the QUBIC algorithm is that it can identify all statistically significant biclusters including biclusters with the so-called ‘scaling patterns’, a problem considered to be rather challenging; another key unique feature is that the algorithm solves such general biclustering problems very efficiently, capable of solving biclustering problems with tens of thousands of genes under up to thousands of conditions in a few minutes of the CPU time on a desktop computer. We have demonstrated a considerably improved biclustering performance by our algorithm compared to the existing algorithms on various benchmark sets and data sets of our own. QUBIC was written in ANSI C and tested using GCC (version 4.1.2) on Linux. Its source code is available at: http://csbl.bmb.uga.edu/∼maqin/bicluster. A server version of QUBIC is also available upon request.     

微阵列数据的多目标免疫优化双聚类

DNA微阵列技术的发展为基因表达研究提供更有效的工具。分析这些大规模基因数据主要应用聚类方法。最近,提出双聚类技术来发现子矩阵以揭示各种生物模式。多目标优化算法可以同时优化多个相互冲突的目标,因而是求解基因表达矩阵的双聚类的一种很好的方法。本文基于克隆选择原理提出了一个新奇的多目标免疫优化双聚类算法,来挖掘微阵列数据的双聚类。在两个真实数据集上的实验结果表明该方法比其他多目标进化双聚娄算法表现出更优越的性能。     

EDISA: extracting biclusters from multiple time-series of gene expression profiles

Background  

Cells dynamically adapt their gene expression patterns in response to various stimuli. This response is orchestrated into a number of gene expression modules consisting of co-regulated genes. A growing pool of publicly available microarray datasets allows the identification of modules by monitoring expression changes over time. These time-series datasets can be searched for gene expression modules by one of the many clustering methods published to date. For an integrative analysis, several time-series datasets can be joined into a three-dimensional gene-condition-time dataset, to which standard clustering or biclustering methods are, however, not applicable. We thus devise a probabilistic clustering algorithm for gene-condition-time datasets.     

Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies

Background  

The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters.     

Modeling Longitudinal Microbiome Compositional Data: A Two-Part Linear Mixed Model with Shared Random Effects

Longitudinal microbiome studies have been widely used to unveil the dynamics in the complex host-microbial ecosystems. Modeling the longitudinal microbiome compositional data, which is semi-continuous in nature, is challenging in several aspects: the overabundance of zeros, the heavy skewness of non-zero values that are bounded in (0, 1), and the dependence between the binary and non-zero parts. To deal with these challenges, we first extended the work of Chen and Li [1] and proposed a two-part zero-inflated Beta regression model with shared random effects (ZIBR-SRE), which characterize the dependence between the binary and the continuous parts. Besides, the microbiome compositional data have unit-sum constraint, indicating the existence of negative correlations among taxa. As ZIBR-SRE models each taxon separately, it does not satisfy the sum-to-one constraint. We then proposed a two-part linear mixed model (TPLMM) with shared random effects to formulate the log-transformed standardized relative abundances rather than the original ones. Such transformation is called “additive logistic transformation”, initially developed for cross-sectional compositional data. We extended it to analyze the longitudinal microbiome compositions and showed that the unit-sum constraint can be automatically satisfied under the TPLMM framework. Model performances of TPLMM and ZIBR-SRE were compared with existing methods in simulation studies. Under settings adopted from real data, TPLMM had the best performance and is recommended for practical use. An oral microbiome application further showed that TPLMM and ZIBR-SRE estimated a strong correlation structure in the binary and the continuous parts, suggesting models without accounting for this dependence would lead to biased inferences.

     

A general framework for biclustering gene expression data

A large number of biclustering methods have been proposed to detect patterns in gene expression data. All these methods try to find some type of biclusters but no one can discover all the types of patterns in the data. Furthermore, researchers have to design new algorithms in order to find new types of biclusters/patterns that interest biologists. In this paper, we propose a novel approach for biclustering that, in general, can be used to discover all computable patterns in gene expression data. The method is based on the theory of Kolmogorov complexity. More precisely, we use Kolmogorov complexity to measure the randomness of submatrices as the merit of biclusters because randomness naturally consists in a lack of regularity, which is a common property of all types of patterns. On the basis of algorithmic probability measure, we develop a Markov Chain Monte Carlo algorithm to search for biclusters. Our method can also be easily extended to solve the problems of conventional clustering and checkerboard type biclustering. The preliminary experiments on simulated as well as real data show that our approach is very versatile and promising.     

Extended graphical lasso for multiple interaction networks for high dimensional omics data

There has been a spate of interest in association networks in biological and medical research, for example, genetic interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional omics data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem and solve it with an alternating direction method of multipliers (ADMM) algorithm. The proposed method can also be adapted to estimate interaction networks for high dimensional compositional data such as microbial interaction networks. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease.     

Biclustering algorithms for biological data analysis: a survey

A large number of clustering approaches have been proposed for the analysis of gene expression data obtained from microarray experiments. However, the results from the application of standard clustering methods to genes are limited. This limitation is imposed by the existence of a number of experimental conditions where the activity of genes is uncorrelated. A similar limitation exists when clustering of conditions is performed. For this reason, a number of algorithms that perform simultaneous clustering on the row and column dimensions of the data matrix has been proposed. The goal is to find submatrices, that is, subgroups of genes and subgroups of conditions, where the genes exhibit highly correlated activities for every condition. In this paper, we refer to this class of algorithms as biclustering. Biclustering is also referred in the literature as coclustering and direct clustering, among others names, and has also been used in fields such as information retrieval and data mining. In this comprehensive survey, we analyze a large number of existing approaches to biclustering, and classify them in accordance with the type of biclusters they can find, the patterns of biclusters that are discovered, the methods used to perform the search, the approaches used to evaluate the solution, and the target applications.     

Robust and Powerful Differential Composition Tests for Clustered Microbiome Data

Thanks to advances in high-throughput sequencing technologies, the importance of microbiome to human health and disease has been increasingly recognized. Analyzing microbiome data from sequencing experiments is challenging due to their unique features such as compositional data, excessive zero observations, overdispersion, and complex relations among microbial taxa. Clustered microbiome data have become prevalent in recent years from designs such as longitudinal studies, family studies, and matched case–control studies. The within-cluster dependence compounds the challenge of the microbiome data analysis. Methods that properly accommodate intra-cluster correlation and features of the microbiome data are needed. We develop robust and powerful differential composition tests for clustered microbiome data. The methods do not rely on any distributional assumptions on the microbial compositions, which provides flexibility to model various correlation structures among taxa and among samples within a cluster. By leveraging the adjusted sandwich covariance estimate, the methods properly accommodate sample dependence within a cluster. The two-part version of the test can further improve power in the presence of excessive zero observations. Different types of confounding variables can be easily adjusted for in the methods. We perform extensive simulation studies under commonly adopted clustered data designs to evaluate the methods. We demonstrate that the methods properly control the type I error under all designs and are more powerful than existing methods in many scenarios. The usefulness of the proposed methods is further demonstrated with two real datasets from longitudinal microbiome studies on pregnant women and inflammatory bowel disease patients. The methods have been incorporated into the R package “miLineage” publicly available at https://tangzheng1.github.io/tanglab/software.html.

     

环境微生物研究中机器学习算法及应用

微生物在环境中无处不在，它们不仅是生物地球化学循环和环境演化的关键参与者，也在环境监测、生态治理和保护中发挥着重要作用。随着高通量技术的发展，大量微生物数据产生，运用机器学习对环境微生物大数据进行建模和分析，在微生物标志物识别、污染物预测和环境质量预测等领域的科学研究和社会应用方面均具有重要意义。机器学习可分为监督学习和无监督学习2大类。在微生物组学研究当中，无监督学习通过聚类、降维等方法高效地学习输入数据的特征，进而对微生物数据进行整合和归类。监督学习运用有特征和标记的微生物数据集训练模型，在面对只有特征没有标记的数据时可以判断出标记，从而实现对新数据的分类、识别和预测。然而，复杂的机器学习算法通常以牺牲可解释性为代价来重点关注模型预测的准确性。机器学习模型通常可以看作预测特定结果的“黑匣子”，即对模型如何得出预测所知甚少。为了将机器学习更多地运用于微生物组学研究、提高我们提取有价值的微生物信息的能力，深入了解机器学习算法、提高模型的可解释性尤为重要。本文主要介绍在环境微生物领域常用的机器学习算法和基于微生物组数据的机器学习模型的构建步骤，包括特征选择、算法选择、模型构建和评估等，并对各种机器学习模型在环境微生物领域的应用进行综述，深入探究微生物组与周围环境之间的关联，探讨提高模型可解释性的方法，并为未来环境监测、环境健康预测提供科学参考。     

Identification of coherent patterns in gene expression data using an efficient biclustering algorithm and parallel coordinate visualization

Background  

The DNA microarray technology allows the measurement of expression levels of thousands of genes under tens/hundreds of different conditions. In microarray data, genes with similar functions usually co-express under certain conditions only [1]. Thus, biclustering which clusters genes and conditions simultaneously is preferred over the traditional clustering technique in discovering these coherent genes. Various biclustering algorithms have been developed using different bicluster formulations. Unfortunately, many useful formulations result in NP-complete problems. In this article, we investigate an efficient method for identifying a popular type of biclusters called additive model. Furthermore, parallel coordinate (PC) plots are used for bicluster visualization and analysis.     

It's all relative: Regression analysis with compositional predictors

Compositional data reside in a simplex and measure fractions or proportions of parts to a whole. Most existing regression methods for such data rely on log-ratio transformations that are inadequate or inappropriate in modeling high-dimensional data with excessive zeros and hierarchical structures. Moreover, such models usually lack a straightforward interpretation due to the interrelation between parts of a composition. We develop a novel relative-shift regression framework that directly uses proportions as predictors. The new framework provides a paradigm shift for regression analysis with compositional predictors and offers a superior interpretation of how shifting concentration between parts affects the response. New equi-sparsity and tree-guided regularization methods and an efficient smoothing proximal gradient algorithm are developed to facilitate feature aggregation and dimension reduction in regression. A unified finite-sample prediction error bound is derived for the proposed regularized estimators. We demonstrate the efficacy of the proposed methods in extensive simulation studies and a real gut microbiome study. Guided by the taxonomy of the microbiome data, the framework identifies important taxa at different taxonomic levels associated with the neurodevelopment of preterm infants.     

Microbial Interaction Network Estimation via Bias-Corrected Graphical Lasso

With the increasing availability of microbiome 16S data, network estimation has become a useful approach to studying the interactions between microbial taxa. Network estimation on a set of variables is frequently explored using graphical models, in which the relationship between two variables is modeled via their conditional dependency given the other variables. Various methods for sparse inverse covariance estimation have been proposed to estimate graphical models in the high-dimensional setting, including graphical lasso. However, current methods do not address the compositional count nature of microbiome data, where abundances of microbial taxa are not directly measured, but are reflected by the observed counts in an error-prone manner. Adding to the challenge is that the sum of the counts within each sample, termed “sequencing depth,” is an experimental technicality that carries no biological information but can vary drastically across samples. To address these issues, we develop a new approach to network estimation, called BC-GLASSO (bias-corrected graphical lasso), which models the microbiome data using a logistic normal multinomial distribution with the sequencing depths explicitly incorporated, corrects the bias of the naive empirical covariance estimator arising from the heterogeneity in sequencing depths, and builds the inverse covariance estimator via graphical lasso. We demonstrate the advantage of BC-GLASSO over current approaches to microbial interaction network estimation under a variety of simulation scenarios. We also illustrate the efficacy of our method in an application to a human microbiome data set.

     

Identification of Bicluster Regions in a Binary Matrix and Its Applications

Biclustering has emerged as an important approach to the analysis of large-scale datasets. A biclustering technique identifies a subset of rows that exhibit similar patterns on a subset of columns in a data matrix. Many biclustering methods have been proposed, and most, if not all, algorithms are developed to detect regions of “coherence” patterns. These methods perform unsatisfactorily if the purpose is to identify biclusters of a constant level. This paper presents a two-step biclustering method to identify constant level biclusters for binary or quantitative data. This algorithm identifies the maximal dimensional submatrix such that the proportion of non-signals is less than a pre-specified tolerance δ. The proposed method has much higher sensitivity and slightly lower specificity than several prominent biclustering methods from the analysis of two synthetic datasets. It was further compared with the Bimax method for two real datasets. The proposed method was shown to perform the most robust in terms of sensitivity, number of biclusters and number of serotype-specific biclusters identified. However, dichotomization using different signal level thresholds usually leads to different sets of biclusters; this also occurs in the present analysis.