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.     

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.     

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).     

Discovering local structure in gene expression data: the order-preserving submatrix problem.

This paper concerns the discovery of patterns in gene expression matrices, in which each element gives the expression level of a given gene in a given experiment. Most existing methods for pattern discovery in such matrices are based on clustering genes by comparing their expression levels in all experiments, or clustering experiments by comparing their expression levels for all genes. Our work goes beyond such global approaches by looking for local patterns that manifest themselves when we focus simultaneously on a subset G of the genes and a subset T of the experiments. Specifically, we look for order-preserving submatrices (OPSMs), in which the expression levels of all genes induce the same linear ordering of the experiments (we show that the OPSM search problem is NP-hard in the worst case). Such a pattern might arise, for example, if the experiments in T represent distinct stages in the progress of a disease or in a cellular process and the expression levels of all genes in G vary across the stages in the same way. We define a probabilistic model in which an OPSM is hidden within an otherwise random matrix. Guided by this model, we develop an efficient algorithm for finding the hidden OPSM in the random matrix. In data generated according to the model, the algorithm recovers the hidden OPSM with a very high success rate. Application of the methods to breast cancer data seem to reveal significant local patterns.     

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.     

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.     

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.     

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。     

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.     

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.     

Shifting and scaling patterns from gene expression data

MOTIVATION: During the last years, the discovering of biclusters in data is becoming more and more popular. Biclustering aims at extracting a set of clusters, each of which might use a different subset of attributes. Therefore, it is clear that the usefulness of biclustering techniques is beyond the traditional clustering techniques, especially when datasets present high or very high dimensionality. Also, biclustering considers overlapping, which is an interesting aspect, algorithmically and from the point of view of the result interpretation. Since the Cheng and Church's works, the mean squared residue has turned into one of the most popular measures to search for biclusters, which ideally should discover shifting and scaling patterns. RESULTS: In this work, we identify both types of patterns (shifting and scaling) and demonstrate that the mean squared residue is very useful to search for shifting patterns, but it is not appropriate to find scaling patterns because even when we find a perfect scaling pattern the mean squared residue is not zero. In addition, we provide an interesting result: the mean squared residue is highly dependent on the variance of the scaling factor, which makes possible that any algorithm based on this measure might not find these patterns in data when the variance of gene values is high. The main contribution of this paper is to prove that the mean squared residue is not precise enough from the mathematical point of view in order to discover shifting and scaling patterns at the same time. CONTACT: aguilar@lsi.us.es.     

Seed-based biclustering of gene expression data

Background

Accumulated biological research outcomes show that biological functions do not depend on individual genes, but on complex gene networks. Microarray data are widely used to cluster genes according to their expression levels across experimental conditions. However, functionally related genes generally do not show coherent expression across all conditions since any given cellular process is active only under a subset of conditions. Biclustering finds gene clusters that have similar expression levels across a subset of conditions. This paper proposes a seed-based algorithm that identifies coherent genes in an exhaustive, but efficient manner.

Methods

In order to find the biclusters in a gene expression dataset, we exhaustively select combinations of genes and conditions as seeds to create candidate bicluster tables. The tables have two columns (a) a gene set, and (b) the conditions on which the gene set have dissimilar expression levels to the seed. First, the genes with less than the maximum number of dissimilar conditions are identified and a table of these genes is created. Second, the rows that have the same dissimilar conditions are grouped together. Third, the table is sorted in ascending order based on the number of dissimilar conditions. Finally, beginning with the first row of the table, a test is run repeatedly to determine whether the cardinality of the gene set in the row is greater than the minimum threshold number of genes in a bicluster. If so, a bicluster is outputted and the corresponding row is removed from the table. Repeating this process, all biclusters in the table are systematically identified until the table becomes empty.

Conclusions

This paper presents a novel biclustering algorithm for the identification of additive biclusters. Since it involves exhaustively testing combinations of genes and conditions, the additive biclusters can be found more readily.     

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.

     

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.