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1.  Identification of coherent patterns in gene expression data using an efficient biclustering algorithm and parallel coordinate visualization 
BMC Bioinformatics  2008;9:210.
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.
We develop a novel and efficient biclustering algorithm which can be regarded as a greedy version of an existing algorithm known as pCluster algorithm. By relaxing the constraint in homogeneity, the proposed algorithm has polynomial-time complexity in the worst case instead of exponential-time complexity as in the pCluster algorithm. Experiments on artificial datasets verify that our algorithm can identify both additive-related and multiplicative-related biclusters in the presence of overlap and noise. Biologically significant biclusters have been validated on the yeast cell-cycle expression dataset using Gene Ontology annotations. Comparative study shows that the proposed approach outperforms several existing biclustering algorithms. We also provide an interactive exploratory tool based on PC plot visualization for determining the parameters of our biclustering algorithm.
We have proposed a novel biclustering algorithm which works with PC plots for an interactive exploratory analysis of gene expression data. Experiments show that the biclustering algorithm is efficient and is capable of detecting co-regulated genes. The interactive analysis enables an optimum parameter determination in the biclustering algorithm so as to achieve the best result. In future, we will modify the proposed algorithm for other bicluster models such as the coherent evolution model.
PMCID: PMC2396181  PMID: 18433478
2.  Discovery of error-tolerant biclusters from noisy gene expression data 
BMC Bioinformatics  2011;12(Suppl 12):S1.
An important analysis performed on microarray gene-expression data is to discover biclusters, which denote groups of genes that are coherently expressed for a subset of conditions. Various biclustering algorithms have been proposed to find different types of biclusters from these real-valued gene-expression data sets. However, these algorithms suffer from several limitations such as inability to explicitly handle errors/noise in the data; difficulty in discovering small bicliusters due to their top-down approach; inability of some of the approaches to find overlapping biclusters, which is crucial as many genes participate in multiple biological processes. Association pattern mining also produce biclusters as their result and can naturally address some of these limitations. However, traditional association mining only finds exact biclusters, which limits its applicability in real-life data sets where the biclusters may be fragmented due to random noise/errors. Moreover, as they only work with binary or boolean attributes, their application on gene-expression data require transforming real-valued attributes to binary attributes, which often results in loss of information. Many past approaches have tried to address the issue of noise and handling real-valued attributes independently but there is no systematic approach that addresses both of these issues together.
In this paper, we first propose a novel error-tolerant biclustering model, ‘ET-bicluster’, and then propose a bottom-up heuristic-based mining algorithm to sequentially discover error-tolerant biclusters directly from real-valued gene-expression data. The efficacy of our proposed approach is illustrated by comparing it with a recent approach RAP in the context of two biological problems: discovery of functional modules and discovery of biomarkers. For the first problem, two real-valued S.Cerevisiae microarray gene-expression data sets are used to demonstrate that the biclusters obtained from ET-bicluster approach not only recover larger set of genes as compared to those obtained from RAP approach but also have higher functional coherence as evaluated using the GO-based functional enrichment analysis. The statistical significance of the discovered error-tolerant biclusters as estimated by using two randomization tests, reveal that they are indeed biologically meaningful and statistically significant. For the second problem of biomarker discovery, we used four real-valued Breast Cancer microarray gene-expression data sets and evaluate the biomarkers obtained using MSigDB gene sets.
The results obtained for both the problems: functional module discovery and biomarkers discovery, clearly signifies the usefulness of the proposed ET-bicluster approach and illustrate the importance of explicitly incorporating noise/errors in discovering coherent groups of genes from gene-expression data.
PMCID: PMC3247082  PMID: 22168285
3.  A Novel Biclustering Algorithm for the Discovery of Meaningful Biological Correlations between microRNAs and their Target Genes 
BMC Bioinformatics  2013;14(Suppl 7):S8.
microRNAs (miRNAs) are a class of small non-coding RNAs which have been recognized as ubiquitous post-transcriptional regulators. The analysis of interactions between different miRNAs and their target genes is necessary for the understanding of miRNAs' role in the control of cell life and death. In this paper we propose a novel data mining algorithm, called HOCCLUS2, specifically designed to bicluster miRNAs and target messenger RNAs (mRNAs) on the basis of their experimentally-verified and/or predicted interactions. Indeed, existing biclustering approaches, typically used to analyze gene expression data, fail when applied to miRNA:mRNA interactions since they usually do not extract possibly overlapping biclusters (miRNAs and their target genes may have multiple roles), extract a huge amount of biclusters (difficult to browse and rank on the basis of their importance) and work on similarities of feature values (do not limit the analysis to reliable interactions).
To overcome these limitations, HOCCLUS2 i) extracts possibly overlapping biclusters, to catch multiple roles of both miRNAs and their target genes; ii) extracts hierarchically organized biclusters, to facilitate bicluster browsing and to distinguish between universe and pathway-specific miRNAs; iii) extracts highly cohesive biclusters, to consider only reliable interactions; iv) ranks biclusters according to the functional similarities, computed on the basis of Gene Ontology, to facilitate bicluster analysis.
Our results show that HOCCLUS2 is a valid tool to support biologists in the identification of context-specific miRNAs regulatory modules and in the detection of possibly unknown miRNAs target genes. Indeed, results prove that HOCCLUS2 is able to extract cohesiveness-preserving biclusters, when compared with competitive approaches, and statistically confirm (at a confidence level of 99%) that mRNAs which belong to the same biclusters are, on average, more functionally similar than mRNAs which belong to different biclusters. Finally, the hierarchy of biclusters provides useful insights to understand the intrinsic hierarchical organization of miRNAs and their potential multiple interactions on target genes.
PMCID: PMC3633049  PMID: 23815553
4.  Automatic layout and visualization of biclusters 
Biclustering has emerged as a powerful algorithmic tool for analyzing measurements of gene expression. A number of different methods have emerged for computing biclusters in gene expression data. Many of these algorithms may output a very large number of biclusters with varying degrees of overlap. There are no systematic methods that create a two-dimensional layout of the computed biclusters and display overlaps between them.
We develop a novel algorithm for laying out biclusters in a two-dimensional matrix whose rows (respectively, columns) are rows (respectively, columns) of the original dataset. We display each bicluster as a contiguous submatrix in the layout. We allow the layout to have repeated rows and/or columns from the original matrix as required, but we seek a layout of the smallest size. We also develop a web-based search interface for the user to query the genes and samples of interest and visualise the layout of biclusters matching the queries.
We demonstrate the usefulness of our approach on gene expression data for two types of leukaemia and on protein-DNA binding data for two growth conditions in Saccharomyces cerevisiae. The software implementing the layout algorithm is available at .
PMCID: PMC1624833  PMID: 16952321
5.  A comparative analysis of biclustering algorithms for gene expression data 
Briefings in Bioinformatics  2012;14(3):279-292.
The need to analyze high-dimension biological data is driving the development of new data mining methods. Biclustering algorithms have been successfully applied to gene expression data to discover local patterns, in which a subset of genes exhibit similar expression levels over a subset of conditions. However, it is not clear which algorithms are best suited for this task. Many algorithms have been published in the past decade, most of which have been compared only to a small number of algorithms. Surveys and comparisons exist in the literature, but because of the large number and variety of biclustering algorithms, they are quickly outdated. In this article we partially address this problem of evaluating the strengths and weaknesses of existing biclustering methods. We used the BiBench package to compare 12 algorithms, many of which were recently published or have not been extensively studied. The algorithms were tested on a suite of synthetic data sets to measure their performance on data with varying conditions, such as different bicluster models, varying noise, varying numbers of biclusters and overlapping biclusters. The algorithms were also tested on eight large gene expression data sets obtained from the Gene Expression Omnibus. Gene Ontology enrichment analysis was performed on the resulting biclusters, and the best enrichment terms are reported. Our analyses show that the biclustering method and its parameters should be selected based on the desired model, whether that model allows overlapping biclusters, and its robustness to noise. In addition, we observe that the biclustering algorithms capable of finding more than one model are more successful at capturing biologically relevant clusters.
PMCID: PMC3659300  PMID: 22772837
biclustering; microarray; gene expression; clustering
6.  A comparison and evaluation of five biclustering algorithms by quantifying goodness of biclusters for gene expression data 
BioData Mining  2012;5:8.
Several biclustering algorithms have been proposed to identify biclusters, in which genes share similar expression patterns across a number of conditions. However, different algorithms would yield different biclusters and further lead to distinct conclusions. Therefore, some testing and comparisons between these algorithms are strongly required.
In this study, five biclustering algorithms (i.e. BIMAX, FABIA, ISA, QUBIC and SAMBA) were compared with each other in the cases where they were used to handle two expression datasets (GDS1620 and pathway) with different dimensions in Arabidopsis thaliana (A. thaliana)
GO (gene ontology) annotation and PPI (protein-protein interaction) network were used to verify the corresponding biological significance of biclusters from the five algorithms. To compare the algorithms’ performance and evaluate quality of identified biclusters, two scoring methods, namely weighted enrichment (WE) scoring and PPI scoring, were proposed in our study. For each dataset, after combining the scores of all biclusters into one unified ranking, we could evaluate the performance and behavior of the five biclustering algorithms in a better way.
Both WE and PPI scoring methods has been proved effective to validate biological significance of the biclusters, and a significantly positive correlation between the two sets of scores has been tested to demonstrate the consistence of these two methods.
A comparative study of the above five algorithms has revealed that: (1) ISA is the most effective one among the five algorithms on the dataset of GDS1620 and BIMAX outperforms the other algorithms on the dataset of pathway. (2) Both ISA and BIMAX are data-dependent. The former one does not work well on the datasets with few genes, while the latter one holds well for the datasets with more conditions. (3) FABIA and QUBIC perform poorly in this study and they may be suitable to large datasets with more genes and more conditions. (4) SAMBA is also data-independent as it performs well on two given datasets. The comparison results provide useful information for researchers to choose a suitable algorithm for each given dataset.
PMCID: PMC3447720  PMID: 22824157
7.  DeBi: Discovering Differentially Expressed Biclusters using a Frequent Itemset Approach 
The analysis of massive high throughput data via clustering algorithms is very important for elucidating gene functions in biological systems. However, traditional clustering methods have several drawbacks. Biclustering overcomes these limitations by grouping genes and samples simultaneously. It discovers subsets of genes that are co-expressed in certain samples. Recent studies showed that biclustering has a great potential in detecting marker genes that are associated with certain tissues or diseases. Several biclustering algorithms have been proposed. However, it is still a challenge to find biclusters that are significant based on biological validation measures. Besides that, there is a need for a biclustering algorithm that is capable of analyzing very large datasets in reasonable time.
Here we present a fast biclustering algorithm called DeBi (Differentially Expressed BIclusters). The algorithm is based on a well known data mining approach called frequent itemset. It discovers maximum size homogeneous biclusters in which each gene is strongly associated with a subset of samples. We evaluate the performance of DeBi on a yeast dataset, on synthetic datasets and on human datasets.
We demonstrate that the DeBi algorithm provides functionally more coherent gene sets compared to standard clustering or biclustering algorithms using biological validation measures such as Gene Ontology term and Transcription Factor Binding Site enrichment. We show that DeBi is a computationally efficient and powerful tool in analyzing large datasets. The method is also applicable on multiple gene expression datasets coming from different labs or platforms.
PMCID: PMC3152888  PMID: 21699691
8.  Biclustering for the comprehensive search of correlated gene expression patterns using clustered seed expansion 
BMC Genomics  2013;14:144.
In a functional analysis of gene expression data, biclustering method can give crucial information by showing correlated gene expression patterns under a subset of conditions. However, conventional biclustering algorithms still have some limitations to show comprehensive and stable outputs.
We propose a novel biclustering approach called “BIclustering by Correlated and Large number of Individual Clustered seeds (BICLIC)” to find comprehensive sets of correlated expression patterns in biclusters using clustered seeds and their expansion with correlation of gene expression. BICLIC outperformed competing biclustering algorithms by completely recovering implanted biclusters in simulated datasets with various types of correlated patterns: shifting, scaling, and shifting-scaling. Furthermore, in a real yeast microarray dataset and a lung cancer microarray dataset, BICLIC found more comprehensive sets of biclusters that are significantly enriched to more diverse sets of biological terms than those of other competing biclustering algorithms.
BICLIC provides significant benefits in finding comprehensive sets of correlated patterns and their functional implications from a gene expression dataset.
PMCID: PMC3618306  PMID: 23496895
9.  Finding distinct biclusters from background in gene expression matrices 
Bioinformation  2007;2(5):207-215.
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.
PMCID: PMC2241930  PMID: 18305830
gene expression matrices; simulation; biclusters; Distinct 2-Dimensional (D2D); noise
10.  Pattern-driven neighborhood search for biclustering of microarray data 
BMC Bioinformatics  2012;13(Suppl 7):S11.
Biclustering aims at finding subgroups of genes that show highly correlated behaviors across a subgroup of conditions. Biclustering is a very useful tool for mining microarray data and has various practical applications. From a computational point of view, biclustering is a highly combinatorial search problem and can be solved with optimization methods.
We describe a stochastic pattern-driven neighborhood search algorithm for the biclustering problem. Starting from an initial bicluster, the proposed method improves progressively the quality of the bicluster by adjusting some genes and conditions. The adjustments are based on the quality of each gene and condition with respect to the bicluster and the initial data matrix. The performance of the method was evaluated on two well-known microarray datasets (Yeast cell cycle and Saccharomyces cerevisiae), showing that it is able to obtain statistically and biologically significant biclusters. The proposed method was also compared with six reference methods from the literature.
The proposed method is computationally fast and can be applied to discover significant biclusters. It can also used to effectively improve the quality of existing biclusters provided by other biclustering methods.
PMCID: PMC3348021  PMID: 22594997
11.  Biclustering of microarray data with MOSPO based on crowding distance 
BMC Bioinformatics  2009;10(Suppl 4):S9.
High-throughput microarray technologies have generated and accumulated massive amounts of gene expression datasets that contain expression levels of thousands of genes under hundreds of different experimental conditions. The microarray datasets are usually presented in 2D matrices, where rows represent genes and columns represent experimental conditions. The analysis of such datasets can discover local structures composed by sets of genes that show coherent expression patterns under subsets of experimental conditions. It leads to the development of sophisticated algorithms capable of extracting novel and useful knowledge from a biomedical point of view. In the medical domain, these patterns are useful for understanding various diseases, and aid in more accurate diagnosis, prognosis, treatment planning, as well as drug discovery.
In this work we present the CMOPSOB (Crowding distance based Multi-objective Particle Swarm Optimization Biclustering), a novel clustering approach for microarray datasets to cluster genes and conditions highly related in sub-portions of the microarray data. The objective of biclustering is to find sub-matrices, i.e. maximal subgroups of genes and subgroups of conditions where the genes exhibit highly correlated activities over a subset of conditions. Since these objectives are mutually conflicting, they become suitable candidates for multi-objective modelling. Our approach CMOPSOB is based on a heuristic search technique, multi-objective particle swarm optimization, which simulates the movements of a flock of birds which aim to find food. In the meantime, the nearest neighbour search strategies based on crowding distance and ϵ-dominance can rapidly converge to the Pareto front and guarantee diversity of solutions. We compare the potential of this methodology with other biclustering algorithms by analyzing two common and public datasets of gene expression profiles. In all cases our method can find localized structures related to sets of genes that show consistent expression patterns across subsets of experimental conditions. The mined patterns present a significant biological relevance in terms of related biological processes, components and molecular functions in a species-independent manner.
The proposed CMOPSOB algorithm is successfully applied to biclustering of microarray dataset. It achieves a good diversity in the obtained Pareto front, and rapid convergence. Therefore, it is a useful tool to analyze large microarray datasets.
PMCID: PMC2681067  PMID: 19426457
12.  A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series 
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.
In this work, we propose e-CCC-Biclustering, a biclustering algorithm that finds and reports all maximal contiguous column coherent biclusters with approximate expression patterns in time polynomial in the size of the time series gene expression matrix. This polynomial time complexity is achieved by manipulating a discretized version of the original matrix using efficient string processing techniques. We also propose extensions to deal with missing values, discover anticorrelated and scaled expression patterns, and different ways to compute the errors allowed in the expression patterns. We propose a scoring criterion combining the statistical significance of expression patterns with a similarity measure between overlapping biclusters.
We present results in real data showing the effectiveness of e-CCC-Biclustering and its relevance in the discovery of regulatory modules describing the transcriptomic expression patterns occurring in Saccharomyces cerevisiae in response to heat stress. In particular, the results show the advantage of considering approximate patterns when compared to state of the art methods that require exact matching of gene expression time series.
The identification of co-regulated genes, involved in specific biological processes, remains one of the main avenues open to researchers studying gene regulatory networks. The ability of the proposed methodology to efficiently identify sets of genes with similar expression patterns is shown to be instrumental in the discovery of relevant biological phenomena, leading to more convincing evidence of specific regulatory mechanisms.
A prototype implementation of the algorithm coded in Java together with the dataset and examples used in the paper is available in .
PMCID: PMC2709627  PMID: 19497096
13.  Discovering biclusters in gene expression data based on high-dimensional linear geometries 
BMC Bioinformatics  2008;9:209.
In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns.
In this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes.
We have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis.
PMCID: PMC2386490  PMID: 18433477
14.  Extracting expression modules from perturbational gene expression compendia 
BMC Systems Biology  2008;2:33.
Compendia of gene expression profiles under chemical and genetic perturbations constitute an invaluable resource from a systems biology perspective. However, the perturbational nature of such data imposes specific challenges on the computational methods used to analyze them. In particular, traditional clustering algorithms have difficulties in handling one of the prominent features of perturbational compendia, namely partial coexpression relationships between genes. Biclustering methods on the other hand are specifically designed to capture such partial coexpression patterns, but they show a variety of other drawbacks. For instance, some biclustering methods are less suited to identify overlapping biclusters, while others generate highly redundant biclusters. Also, none of the existing biclustering tools takes advantage of the staple of perturbational expression data analysis: the identification of differentially expressed genes.
We introduce a novel method, called ENIGMA, that addresses some of these issues. ENIGMA leverages differential expression analysis results to extract expression modules from perturbational gene expression data. The core parameters of the ENIGMA clustering procedure are automatically optimized to reduce the redundancy between modules. In contrast to the biclusters produced by most other methods, ENIGMA modules may show internal substructure, i.e. subsets of genes with distinct but significantly related expression patterns. The grouping of these (often functionally) related patterns in one module greatly aids in the biological interpretation of the data. We show that ENIGMA outperforms other methods on artificial datasets, using a quality criterion that, unlike other criteria, can be used for algorithms that generate overlapping clusters and that can be modified to take redundancy between clusters into account. Finally, we apply ENIGMA to the Rosetta compendium of expression profiles for Saccharomyces cerevisiae and we analyze one pheromone response-related module in more detail, demonstrating the potential of ENIGMA to generate detailed predictions.
It is increasingly recognized that perturbational expression compendia are essential to identify the gene networks underlying cellular function, and efforts to build these for different organisms are currently underway. We show that ENIGMA constitutes a valuable addition to the repertoire of methods to analyze such data.
PMCID: PMC2386865  PMID: 18402676
15.  Biclustering of Linear Patterns In Gene Expression Data 
Journal of Computational Biology  2012;19(6):619-631.
Identifying a bicluster, or submatrix of a gene expression dataset wherein the genes express similar behavior over the columns, is useful for discovering novel functional gene interactions. In this article, we introduce a new algorithm for finding biClusters with Linear Patterns (CLiP). Instead of solely maximizing Pearson correlation, we introduce a fitness function that also considers the correlation of complementary genes and conditions. This eliminates the need for a priori determination of the bicluster size. We employ both greedy search and the genetic algorithm in optimization, incorporating resampling for more robust discovery. When applied to both real and simulation datasets, our results show that CLiP is superior to existing methods. In analyzing RNA-seq fly and worm time-course data from modENCODE, we uncover a set of similarly expressed genes suggesting maternal dependence. Supplementary Material is available online (at
PMCID: PMC3375643  PMID: 22697238
algorithms; gene clusters; probability
16.  Dynamic biclustering of microarray data by multi-objective immune optimization 
BMC Genomics  2011;12(Suppl 2):S11.
Newly microarray technologies yield large-scale datasets. The microarray datasets are usually presented in 2D matrices, where rows represent genes and columns represent experimental conditions. Systematic analysis of those datasets provides the increasing amount of information, which is urgently needed in the post-genomic era. Biclustering, which is a technique developed to allow simultaneous clustering of rows and columns of a dataset, might be useful to extract more accurate information from those datasets. Biclustering requires the optimization of two conflicting objectives (residue and volume), and a multi-objective artificial immune system capable of performing a multi-population search. As a heuristic search technique, artificial immune systems (AISs) can be considered a new computational paradigm inspired by the immunological system of vertebrates and designed to solve a wide range of optimization problems. During biclustering several objectives in conflict with each other have to be optimized simultaneously, so multi-objective optimization model is suitable for solving biclustering problem.
Based on dynamic population, this paper proposes a novel dynamic multi-objective immune optimization biclustering (DMOIOB) algorithm to mine coherent patterns from microarray data. Experimental results on two common and public datasets of gene expression profiles show that our approach can effectively find significant localized structures related to sets of genes that show consistent expression patterns across subsets of experimental conditions. The mined patterns present a significant biological relevance in terms of related biological processes, components and molecular functions in a species-independent manner.
The proposed DMOIOB algorithm is an efficient tool to analyze large microarray datasets. It achieves a good diversity and rapid convergence.
PMCID: PMC3194232  PMID: 21989068
17.  Biclustering of gene expression data using reactive greedy randomized adaptive search procedure 
BMC Bioinformatics  2009;10(Suppl 1):S27.
Biclustering algorithms belong to a distinct class of clustering algorithms that perform simultaneous clustering of both rows and columns of the gene expression matrix and can be a very useful analysis tool when some genes have multiple functions and experimental conditions are diverse. Cheng and Church have introduced a measure called mean squared residue score to evaluate the quality of a bicluster and has become one of the most popular measures to search for biclusters. In this paper, we review basic concepts of the metaheuristics Greedy Randomized Adaptive Search Procedure (GRASP)-construction and local search phases and propose a new method which is a variant of GRASP called Reactive Greedy Randomized Adaptive Search Procedure (Reactive GRASP) to detect significant biclusters from large microarray datasets. The method has two major steps. First, high quality bicluster seeds are generated by means of k-means clustering. In the second step, these seeds are grown using the Reactive GRASP, in which the basic parameter that defines the restrictiveness of the candidate list is self-adjusted, depending on the quality of the solutions found previously.
We performed statistical and biological validations of the biclusters obtained and evaluated the method against the results of basic GRASP and as well as with the classic work of Cheng and Church. The experimental results indicate that the Reactive GRASP approach outperforms the basic GRASP algorithm and Cheng and Church approach.
The Reactive GRASP approach for the detection of significant biclusters is robust and does not require calibration efforts.
PMCID: PMC2648745  PMID: 19208127
18.  A visual analytics approach for understanding biclustering results from microarray data 
BMC Bioinformatics  2008;9:247.
Microarray analysis is an important area of bioinformatics. In the last few years, biclustering has become one of the most popular methods for classifying data from microarrays. Although biclustering can be used in any kind of classification problem, nowadays it is mostly used for microarray data classification. A large number of biclustering algorithms have been developed over the years, however little effort has been devoted to the representation of the results.
We present an interactive framework that helps to infer differences or similarities between biclustering results, to unravel trends and to highlight robust groupings of genes and conditions. These linked representations of biclusters can complement biological analysis and reduce the time spent by specialists on interpreting the results. Within the framework, besides other standard representations, a visualization technique is presented which is based on a force-directed graph where biclusters are represented as flexible overlapped groups of genes and conditions. This microarray analysis framework (BicOverlapper), is available at
The main visualization technique, tested with different biclustering results on a real dataset, allows researchers to extract interesting features of the biclustering results, especially the highlighting of overlapping zones that usually represent robust groups of genes and/or conditions. The visual analytics methodology will permit biology experts to study biclustering results without inspecting an overwhelming number of biclusters individually.
PMCID: PMC2416653  PMID: 18505552
19.  Differential co-expression framework to quantify goodness of biclusters and compare biclustering algorithms 
Biclustering is an important analysis procedure to understand the biological mechanisms from microarray gene expression data. Several algorithms have been proposed to identify biclusters, but very little effort was made to compare the performance of different algorithms on real datasets and combine the resultant biclusters into one unified ranking.
In this paper we propose differential co-expression framework and a differential co-expression scoring function to objectively quantify quality or goodness of a bicluster of genes based on the observation that genes in a bicluster are co-expressed in the conditions belonged to the bicluster and not co-expressed in the other conditions. Furthermore, we propose a scoring function to stratify biclusters into three types of co-expression. We used the proposed scoring functions to understand the performance and behavior of the four well established biclustering algorithms on six real datasets from different domains by combining their output into one unified ranking.
Differential co-expression framework is useful to provide quantitative and objective assessment of the goodness of biclusters of co-expressed genes and performance of biclustering algorithms in identifying co-expression biclusters. It also helps to combine the biclusters output by different algorithms into one unified ranking i.e. meta-biclustering.
PMCID: PMC2892498  PMID: 20507637
20.  Biclustering of Gene Expression Data by Correlation-Based Scatter Search 
BioData Mining  2011;4:3.
The analysis of data generated by microarray technology is very useful to understand how the genetic information becomes functional gene products. Biclustering algorithms can determine a group of genes which are co-expressed under a set of experimental conditions. Recently, new biclustering methods based on metaheuristics have been proposed. Most of them use the Mean Squared Residue as merit function but interesting and relevant patterns from a biological point of view such as shifting and scaling patterns may not be detected using this measure. However, it is important to discover this type of patterns since commonly the genes can present a similar behavior although their expression levels vary in different ranges or magnitudes.
Scatter Search is an evolutionary technique that is based on the evolution of a small set of solutions which are chosen according to quality and diversity criteria. This paper presents a Scatter Search with the aim of finding biclusters from gene expression data. In this algorithm the proposed fitness function is based on the linear correlation among genes to detect shifting and scaling patterns from genes and an improvement method is included in order to select just positively correlated genes.
The proposed algorithm has been tested with three real data sets such as Yeast Cell Cycle dataset, human B-cells lymphoma dataset and Yeast Stress dataset, finding a remarkable number of biclusters with shifting and scaling patterns. In addition, the performance of the proposed method and fitness function are compared to that of CC, OPSM, ISA, BiMax, xMotifs and Samba using Gene the Ontology Database.
PMCID: PMC3037342  PMID: 21261986
21.  A biclustering algorithm based on a Bicluster Enumeration Tree: application to DNA microarray data 
BioData Mining  2009;2:9.
In a number of domains, like in DNA microarray data analysis, we need to cluster simultaneously rows (genes) and columns (conditions) of a data matrix to identify groups of rows coherent with groups of columns. This kind of clustering is called biclustering. Biclustering algorithms are extensively used in DNA microarray data analysis. More effective biclustering algorithms are highly desirable and needed.
We introduce BiMine, a new enumeration algorithm for biclustering of DNA microarray data. The proposed algorithm is based on three original features. First, BiMine relies on a new evaluation function called Average Spearman's rho (ASR). Second, BiMine uses a new tree structure, called Bicluster Enumeration Tree (BET), to represent the different biclusters discovered during the enumeration process. Third, to avoid the combinatorial explosion of the search tree, BiMine introduces a parametric rule that allows the enumeration process to cut tree branches that cannot lead to good biclusters.
The performance of the proposed algorithm is assessed using both synthetic and real DNA microarray data. The experimental results show that BiMine competes well with several other biclustering methods. Moreover, we test the biological significance using a gene annotation web-tool to show that our proposed method is able to produce biologically relevant biclusters. The software is available upon request from the authors to academic users.
PMCID: PMC2804695  PMID: 20015398
22.  Seed-Based Biclustering of Gene Expression Data 
PLoS ONE  2012;7(8):e42431.
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.
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.
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.
PMCID: PMC3411756  PMID: 22879981
23.  A Composite Model for Subgroup Identification and Prediction via Bicluster Analysis 
PLoS ONE  2014;9(10):e111318.
A major challenges in the analysis of large and complex biomedical data is to develop an approach for 1) identifying distinct subgroups in the sampled populations, 2) characterizing their relationships among subgroups, and 3) developing a prediction model to classify subgroup memberships of new samples by finding a set of predictors. Each subgroup can represent different pathogen serotypes of microorganisms, different tumor subtypes in cancer patients, or different genetic makeups of patients related to treatment response.
This paper proposes a composite model for subgroup identification and prediction using biclusters. A biclustering technique is first used to identify a set of biclusters from the sampled data. For each bicluster, a subgroup-specific binary classifier is built to determine if a particular sample is either inside or outside the bicluster. A composite model, which consists of all binary classifiers, is constructed to classify samples into several disjoint subgroups. The proposed composite model neither depends on any specific biclustering algorithm or patterns of biclusters, nor on any classification algorithms.
The composite model was shown to have an overall accuracy of 97.4% for a synthetic dataset consisting of four subgroups. The model was applied to two datasets where the sample’s subgroup memberships were known. The procedure showed 83.7% accuracy in discriminating lung cancer adenocarcinoma and squamous carcinoma subtypes, and was able to identify 5 serotypes and several subtypes with about 94% accuracy in a pathogen dataset.
The composite model presents a novel approach to developing a biclustering-based classification model from unlabeled sampled data. The proposed approach combines unsupervised biclustering and supervised classification techniques to classify samples into disjoint subgroups based on their associated attributes, such as genotypic factors, phenotypic outcomes, efficacy/safety measures, or responses to treatments. The procedure is useful for identification of unknown species or new biomarkers for targeted therapy.
PMCID: PMC4210136  PMID: 25347824
24.  Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies 
BMC Bioinformatics  2008;9:458.
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.
In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods.
We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.
PMCID: PMC2605474  PMID: 18954459
25.  Configurable pattern-based evolutionary biclustering of gene expression data 
Biclustering algorithms for microarray data aim at discovering functionally related gene sets under different subsets of experimental conditions. Due to the problem complexity and the characteristics of microarray datasets, heuristic searches are usually used instead of exhaustive algorithms. Also, the comparison among different techniques is still a challenge. The obtained results vary in relevant features such as the number of genes or conditions, which makes it difficult to carry out a fair comparison. Moreover, existing approaches do not allow the user to specify any preferences on these properties.
Here, we present the first biclustering algorithm in which it is possible to particularize several biclusters features in terms of different objectives. This can be done by tuning the specified features in the algorithm or also by incorporating new objectives into the search. Furthermore, our approach bases the bicluster evaluation in the use of expression patterns, being able to recognize both shifting and scaling patterns either simultaneously or not. Evolutionary computation has been chosen as the search strategy, naming thus our proposal Evo-Bexpa (Evolutionary Biclustering based in Expression Patterns).
We have conducted experiments on both synthetic and real datasets demonstrating Evo-Bexpa abilities to obtain meaningful biclusters. Synthetic experiments have been designed in order to compare Evo-Bexpa performance with other approaches when looking for perfect patterns. Experiments with four different real datasets also confirm the proper performing of our algorithm, whose results have been biologically validated through Gene Ontology.
PMCID: PMC3668234  PMID: 23433178
Gene expression data analysis; Shifting and scaling expression patterns; Evolutionary biclustering

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