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.     

A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series

Background  

The ability to monitor the change in expression patterns over time, and to observe the emergence of coherent temporal responses using gene expression time series, obtained from microarray experiments, is critical to advance our understanding of complex biological processes. In this context, biclustering algorithms have been recognized as an important tool for the discovery of local expression patterns, which are crucial to unravel potential regulatory mechanisms. Although most formulations of the biclustering problem are NP-hard, when working with time series expression data the interesting biclusters can be restricted to those with contiguous columns. This restriction leads to a tractable problem and enables the design of efficient biclustering algorithms able to identify all maximal contiguous column coherent biclusters.     

A new geometric biclustering algorithm based on the Hough transform for analysis of large-scale microarray data

Biclustering is an important tool in microarray analysis when only a subset of genes co-regulates in a subset of conditions. Different from standard clustering analyses, biclustering performs simultaneous classification in both gene and condition directions in a microarray data matrix. However, the biclustering problem is inherently intractable and computationally complex. In this paper, we present a new biclustering algorithm based on the geometrical viewpoint of coherent gene expression profiles. In this method, we perform pattern identification based on the Hough transform in a column-pair space. The algorithm is especially suitable for the biclustering analysis of large-scale microarray data. Our studies show that the approach can discover significant biclusters with respect to the increased noise level and regulatory complexity. Furthermore, we also test the ability of our method to locate biologically verifiable biclusters within an annotated set of genes.     

Quality Measures for Gene Expression Biclusters

An noticeable number of biclustering approaches have been proposed proposed for the study of gene expression data, especially for discovering functionally related gene sets under different subsets of experimental conditions. In this context, recognizing groups of co-expressed or co-regulated genes, that is, genes which follow a similar expression pattern, is one of the main objectives. Due to the problem complexity, heuristic searches are usually used instead of exhaustive algorithms. Furthermore, most of biclustering approaches use a measure or cost function that determines the quality of biclusters. Having a suitable quality metric for bicluster is a critical aspect, not only for guiding the search, but also for establishing a comparison criteria among the results obtained by different biclustering techniques. In this paper, we analyse a large number of existing approaches to quality measures for gene expression biclusters, as well as we present a comparative study of them based on their capability to recognize different expression patterns in biclusters.     

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.     

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.     

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.     

Query-driven module discovery in microarray data

MOTIVATION: Existing (bi)clustering methods for microarray data analysis often do not answer the specific questions of interest to a biologist. Such specific questions could be derived from other information sources, including expert prior knowledge. More specifically, given a set of seed genes which are believed to have a common function, we would like to recruit genes with similar expression profiles as the seed genes in a significant subset of experimental conditions. RESULTS: We introduce QDB, a novel Bayesian query-driven biclustering framework in which the prior distributions allow introducing knowledge from a set of seed genes (query) to guide the pattern search. In two well-known yeast compendia, we grow highly functionally enriched biclusters from small sets of seed genes using a resolution sweep approach. In addition, relevant conditions are identified and modularity of the biclusters is demonstrated, including the discovery of overlapping modules. Finally, our method deals with missing values naturally, performs well on artificial data from a recent biclustering benchmark study and has a number of conceptual advantages when compared to existing approaches for focused module search.     

Discovering coherent biclusters from gene expression data using zero-suppressed binary decision diagrams

The biclustering method can be a very useful analysis tool when some genes have multiple functions and experimental conditions are diverse in gene expression measurement. This is because the biclustering approach, in contrast to the conventional clustering techniques, focuses on finding a subset of the genes and a subset of the experimental conditions that together exhibit coherent behavior. However, the biclustering problem is inherently intractable, and it is often computationally costly to find biclusters with high levels of coherence. In this work, we propose a novel biclustering algorithm that exploits the zero-suppressed binary decision diagrams (ZBDDs) data structure to cope with the computational challenges. Our method can find all biclusters that satisfy specific input conditions, and it is scalable to practical gene expression data. We also present experimental results confirming the effectiveness of our approach.     

Discovering statistically significant biclusters in gene expression data

In gene expression data, a bicluster is a subset of the genes exhibiting consistent patterns over a subset of the conditions. We propose a new method to detect significant biclusters in large expression datasets. Our approach is graph theoretic coupled with statistical modelling of the data. Under plausible assumptions, our algorithm is polynomial and is guaranteed to find the most significant biclusters. We tested our method on a collection of yeast expression profiles and on a human cancer dataset. Cross validation results show high specificity in assigning function to genes based on their biclusters, and we are able to annotate in this way 196 uncharacterized yeast genes. We also demonstrate how the biclusters lead to detecting new concrete biological associations. In cancer data we are able to detect and relate finer tissue types than was previously possible. We also show that the method outperforms the biclustering algorithm of Cheng and Church (2000).     

Biclustering microarray data by Gibbs sampling

MOTIVATION: Gibbs sampling has become a method of choice for the discovery of noisy patterns, known as motifs, in DNA and protein sequences. Because handling noise in microarray data presents similar challenges, we have adapted this strategy to the biclustering of discretized microarray data. RESULTS: In contrast with standard clustering that reveals genes that behave similarly over all the conditions, biclustering groups genes over only a subset of conditions for which those genes have a sharp probability distribution. We have opted for a simple probabilistic model of the biclusters because it has the key advantage of providing a transparent probabilistic interpretation of the biclusters in the form of an easily interpretable fingerprint. Furthermore, Gibbs sampling does not suffer from the problem of local minima that often characterizes Expectation-Maximization. We demonstrate the effectiveness of our approach on two synthetic data sets as well as a data set from leukemia patients.     

Gene expression data analysis using a novel approach to biclustering combining discrete and continuous data

Many different methods exist for pattern detection in gene expression data. In contrast to classical methods, biclustering has the ability to cluster a group of genes together with a group of conditions (replicates, set of patients or drug compounds). However, since the problem is NP-complex, most algorithms use heuristic search functions and therefore might converge towards local maxima. By using the results of biclustering on discrete data as a starting point for a local search function on continuous data, our algorithm avoids the problem of heuristic initialization. Similar to OPSM, our algorithm aims to detect biclusters whose rows and columns can be ordered such that row values are growing across the bicluster's columns and vice-versa. Results have been generated on the yeast genome (Saccharomyces cerevisiae), a human cancer dataset and random data. Results on the yeast genome showed that 89% of the one hundred biggest non-overlapping biclusters were enriched with Gene Ontology annotations. A comparison with OPSM and ISA demonstrated a better efficiency when using gene and condition orders. We present results on random and real datasets that show the ability of our algorithm to capture statistically significant and biologically relevant biclusters.     

A framework for generalized subspace pattern mining in high-dimensional datasets

Background

A generalized notion of biclustering involves the identification of patterns across subspaces within a data matrix. This approach is particularly well-suited to analysis of heterogeneous molecular biology datasets, such as those collected from populations of cancer patients. Different definitions of biclusters will offer different opportunities to discover information from datasets, making it pertinent to tailor the desired patterns to the intended application. This paper introduces ‘GABi’, a customizable framework for subspace pattern mining suited to large heterogeneous datasets. Most existing biclustering algorithms discover biclusters of only a few distinct structures. However, by enabling definition of arbitrary bicluster models, the GABi framework enables the application of biclustering to tasks for which no existing algorithm could be used.

Results

First, a series of artificial datasets were constructed to represent three clearly distinct scenarios for applying biclustering. With a bicluster model created for each distinct scenario, GABi is shown to recover the correct solutions more effectively than a panel of alternative approaches, where the bicluster model may not reflect the structure of the desired solution. Secondly, the GABi framework is used to integrate clinical outcome data with an ovarian cancer DNA methylation dataset, leading to the discovery that widespread dysregulation of DNA methylation associates with poor patient prognosis, a result that has not previously been reported. This illustrates a further benefit of the flexible bicluster definition of GABi, which is that it enables incorporation of multiple sources of data, with each data source treated in a specific manner, leading to a means of intelligent integrated subspace pattern mining across multiple datasets.

Conclusions

The GABi framework enables discovery of biologically relevant patterns of any specified structure from large collections of genomic data. An R implementation of the GABi framework is available through CRAN (http://cran.r-project.org/web/packages/GABi/index.html).

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0355-5) contains supplementary material, which is available to authorized users.     

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。     

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.

     

Finding distinct biclusters from background in gene expression matrices

Biclustering, or the discovery of subsets of samples and genes that are homogeneous and distinct from the background, has become an important technique in analyzing current microarray datasets. Most existing biclustering methods define a bicluster type as a fixed (predefined) pattern and then trying to get results in some searching process. In this work, we propose a novel method for finding biclusters or 2-dimensional patterns that are significantly distinct from the background without the need for pre-defining a pattern within the bicluster. The method named Distinct 2-Dimensional Pattern Finder (D2D) is composed of an iterative reordering step of the rows and columns in the matrix using a new similarity measure, and a flexible scanning-and-growing step to identify the biclusters. Experiments on a large variety of simulation data show that the method works consistently well under different conditions, whereas the existing methods compared may work well under some certain conditions but fail under some other conditions. The impact of noise levels, overlapping degrees between clusters and different setting of parameters were also investigated, which indicated that the D2D method is robust against these factors. The proposed D2D method can efficiently discover many different types of biclusters given that they have distinctive features from the background. The computer program is available upon request.     

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.