Using the bagging approach for biclustering of gene expression data

Several methods have been proposed for microarray data analysis that enables to identify groups of genes with similar expression profiles only under a subset of examples. We propose to improve the performance of these biclustering methods by adapting the approach of bagging to biclustering problems. The principle consists in generating a set of biclusters and aggregating the results. Our method has been tested with success on both synthetic and real datasets.     

An approximation ratio for biclustering

The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of under L₁-norm for 0-1 valued matrices, and of 2 under L₂-norm for real valued matrices.     

Permutation test for incomplete paired data with application to cDNA microarray data

A paired data set is common in microarray experiments, where the data are often incompletely observed for some pairs due to various technical reasons. In microarray paired data sets, it is of main interest to detect differentially expressed genes, which are usually identified by testing the equality of means of expressions within a pair. While much attention has been paid to testing mean equality with incomplete paired data in previous literature, the existing methods commonly assume the normality of data or rely on the large sample theory. In this paper, we propose a new test based on permutations, which is free from the normality assumption and large sample theory. We consider permutation statistics with linear mixtures of paired and unpaired samples as test statistics, and propose a procedure to find the optimal mixture that minimizes the conditional variances of the test statistics, given the observations. Simulations are conducted for numerical power comparisons between the proposed permutation tests and other existing methods. We apply the proposed method to find differentially expressed genes for a colorectal cancer study.     

A probabilistic relaxation labeling framework for reducing the noise effect in geometric biclustering of gene expression data

Biclustering is an important method in DNA microarray analysis which can be applied when only a subset of genes is co-expressed in a subset of conditions. Unlike standard clustering analyses, biclustering methodology can perform simultaneous classification on two dimensions of genes and conditions in a microarray data matrix. However, the performance of biclustering algorithms is affected by the inherent noise in data, types of biclusters and computational complexity. In this paper, we present a geometric biclustering method based on the Hough transform and the relaxation labeling technique. Unlike many existing biclustering algorithms, we first consider the biclustering patterns through geometric interpretation. Such a perspective makes it possible to unify the formulation of different types of biclusters as hyperplanes in spatial space and facilitates the use of a generic plane finding algorithm for bicluster detection. In our algorithm, the Hough transform is employed for hyperplane detection in sub-spaces to reduce the computational complexity. Then sub-biclusters are combined into larger ones under the probabilistic relaxation labeling framework. Our simulation studies demonstrate the robustness of the algorithm against noise and outliers. In addition, our method is able to extract biologically meaningful biclusters from real microarray gene expression data.     

Scatter search-based identification of local patterns with positive and negative correlations in gene expression data

This paper presents a scatter search approach based on linear correlations among genes to find biclusters, which include both shifting and scaling patterns and negatively correlated patterns contrarily to most of correlation-based algorithms published in the literature. The methodology established here for comparison is based on a priori biological information stored in the well-known repository Gene Ontology (GO). In particular, the three existing categories in GO, Biological Process, Cellular Components and Molecular Function, have been used. The performance of the proposed algorithm has been compared to other benchmark biclustering algorithms, specifically a group of classical biclustering algorithms and two algorithms that use correlation-based merit functions. The proposed algorithm outperforms the benchmark algorithms and finds patterns based on negative correlations. Although these patterns contain important relationship among genes, they are not found by most of biclustering algorithms. The experimental study also shows the importance of the size in a bicluster in addition to the value of its correlation. In particular, the size of a bicluster has an influence over its enrichment in a GO term.     

BicFinder: a biclustering algorithm for microarray data analysis

In the context of microarray data analysis, biclustering allows the simultaneous identification of a maximum group of genes that show highly correlated expression patterns through a maximum group of experimental conditions (samples). This paper introduces a heuristic algorithm called BicFinder (The BicFinder software is available at: ) for extracting biclusters from microarray data. BicFinder relies on a new evaluation function called Average Correspondence Similarity Index (ACSI) to assess the coherence of a given bicluster and utilizes a directed acyclic graph to construct its biclusters. The performance of BicFinder is evaluated on synthetic and three DNA microarray datasets. We test the biological significance using a gene annotation web-tool to show that our proposed algorithm is able to produce biologically relevant biclusters. Experimental results show that BicFinder is able to identify coherent and overlapping biclusters.     

Noise-robust algorithm for identifying functionally associated biclusters from gene expression data

Biclusters are subsets of genes that exhibit similar behavior over a set of conditions. A biclustering algorithm is a useful tool for uncovering groups of genes involved in the same cellular processes and groups of conditions under which these processes take place. In this paper, we propose a polynomial time algorithm to identify functionally highly correlated biclusters. Our algorithm identifies (1) gene sets that simultaneously exhibit additive, multiplicative, and combined patterns and allow high levels of noise, (2) multiple, possibly overlapped, and diverse gene sets, (3) biclusters that simultaneously exhibit negatively and positively correlated gene sets, and (4) gene sets for which the functional association is very high. We validate the level of functional association in our method by using the GO database, protein-protein interactions and KEGG pathways.     

Multi-objective evolutionary biclustering of gene expression data

Biclustering or simultaneous clustering of both genes and conditions have generated considerable interest over the past few decades, particularly related to the analysis of high-dimensional gene expression data in information retrieval, knowledge discovery, and data mining. The objective is to find sub-matrices, i.e., maximal subgroups of genes and subgroups of conditions where the genes exhibit highly correlated activities over a range of conditions. Since these two objectives are mutually conflicting, they become suitable candidates for multi-objective modeling. In this study, a novel multi-objective evolutionary biclustering framework is introduced by incorporating local search strategies. A new quantitative measure to evaluate the goodness of the biclusters is developed. The experimental results on benchmark datasets demonstrate better performance as compared to existing algorithms available in literature.     

An effective double-bounded tree-connected Isomap algorithm for microarray data classification

Isometric mapping (Isomap) is a popular nonlinear dimensionality reduction technique which has shown high potential in visualization and classification. However, it appears sensitive to noise or scarcity of observations. This inadequacy may hinder its application for the classification of microarray data, in which the expression levels of thousands of genes in a few normal and tumor sample tissues are measured. In this paper we propose a double-bounded tree-connected variant of Isomap, aimed at being more robust to noise and outliers when used for classification and also computationally more efficient. It differs from the original Isomap in the way the neighborhood graph is generated: in the first stage we apply a double-bounding rule that confines the search to at most k nearest neighbors contained within an ε-radius hypersphere; the resulting subgraphs are then joined by computing a minimum spanning tree among the connected components. We therefore achieve a connected graph without unnaturally inflating the values of k and ε. The computational experiences show that the new method performs significantly better in terms of accuracy with respect to Isomap, k-edge-connected Isomap and the direct application of support vector machines to data in the input space, consistently across seven microarray datasets considered in our tests.     

MicroCluster: efficient deterministic biclustering of microarray data

MicroCluster can mine different types of arbitrarily positioned and overlapping clusters of genetic data to find interesting patterns. Our approach has four key features. First, we mine only the maximal biclusters satisfying certain homogeneity criteria. Second, the clusters can be arbitrarily positioned anywhere in the input data matrix, and they can have arbitrary overlapping regions. Third, MicroCluster uses a flexible definition of a cluster that lets it mine several types of biclusters (which previously were studied independently). Finally, MicroCluster can delete or merge biclusters that have large overlaps. So, it can tolerate some noise in the data set and let users focus on the most important clusters. We've developed a set of metrics to evaluate the clustering quality and have tested MicroCluster's effectiveness on several synthetic and real data sets.     

Distributed feature selection: An application to microarray data classification

Feature selection is often required as a preliminary step for many pattern recognition problems. However, most of the existing algorithms only work in a centralized fashion, i.e. using the whole dataset at once. In this research a new method for distributing the feature selection process is proposed. It distributes the data by features, i.e. according to a vertical distribution, and then performs a merging procedure which updates the feature subset according to improvements in the classification accuracy. The effectiveness of our proposal is tested on microarray data, which has brought a difficult challenge for researchers due to the high number of gene expression contained and the small samples size. The results on eight microarray datasets show that the execution time is considerably shortened whereas the performance is maintained or even improved compared to the standard algorithms applied to the non-partitioned datasets.     

Variational algorithms for biclustering models

Biclustering is an important tool in exploratory statistical analysis which can be used to detect latent row and column groups of different response patterns. However, few studies include covariate data directly into their biclustering models to explain these variations. A novel biclustering framework that considers both stochastic block structures and covariate effects is proposed to address this modeling problem. Fast approximation estimation algorithms are also developed to deal with a large number of latent variables and covariate coefficients. These algorithms are derived from the variational generalized expectation–maximization (EM) framework where the goal is to increase, rather than maximize, the likelihood lower bound in both E and M steps. The utility of the proposed biclustering framework is demonstrated through two block modeling applications in model-based collaborative filtering and microarray analysis.     

Local likelihood regression in generalized linear single-index models with applications to microarray data

Searching for an effective dimension reduction space is an important problem in regression, especially for high-dimensional data such as microarray data. A major characteristic of microarray data consists in the small number of observations n and a very large number of genes p. This “large p, small n” paradigm makes the discriminant analysis for classification difficult. In order to offset this dimensionality problem a solution consists in reducing the dimension. Supervised classification is understood as a regression problem with a small number of observations and a large number of covariates. A new approach for dimension reduction is proposed. This is based on a semi-parametric approach which uses local likelihood estimates for single-index generalized linear models. The asymptotic properties of this procedure are considered and its asymptotic performances are illustrated by simulations. Applications of this method when applied to binary and multiclass classification of the three real data sets Colon, Leukemia and SRBCT are presented.     

一种基于双聚类的缺失数据填补方法

针对现实数据集的数据缺失问题,提出了一种基于双聚类的缺失数据填补新方法.该算法利用双聚类簇内平均平方残值越小簇内数据相似性越高的这一特性,将缺失数据的填补问题转换为求解特定双聚类簇最小平均平方残值的问题,进而实现了数据集中缺失元素的预测;再利用二次函数求解极小值的思想对包含有缺失数据的特定双聚类簇最小平均平方残值的问题进行求解,并进行了数学上的分析证明.最后进行仿真验证,通过观察UCI数据集的实验结果可知,提出的算法具有较高的填补准确性.     

Mining gene–sample–time microarray data: a coherent gene cluster discovery approach

Extensive studies have shown that mining microarray data sets is important in bioinformatics research and biomedical applications. In this paper, we explore a novel type of gene–sample–time microarray data sets that records the expression levels of various genes under a set of samples during a series of time points. In particular, we propose the mining of coherent gene clusters from such data sets. Each cluster contains a subset of genes and a subset of samples such that the genes are coherent on the samples along the time series. The coherent gene clusters may identify the samples corresponding to some phenotypes (e.g., diseases), and suggest the candidate genes correlated to the phenotypes. We present two efficient algorithms, namely the Sample-Gene Search and the Gene–Sample Search, to mine the complete set of coherent gene clusters. We empirically evaluate the performance of our approaches on both a real microarray data set and synthetic data sets. The test results have shown that our approaches are both efficient and effective to find meaningful coherent gene clusters. Daxin Jiang received the Ph.D. degree in computer science and engineering from the State University of New York at Buffalo in 2005. He received the B.S. degree in computer science from the University of Science and Technology of China. From 1998 to 2000, he was a M.S. student in Software Institute, Chinese Academy of Sciences. He is currently an assistant professor at the School of Computer Engineering, Nanyang Technology University, Singapore. His research interests include data mining, bioinformatics, machine learning, and information retrieval. Jian Pei received the Ph.D. degree in computing science from Simon Fraser University, Canada, in 2002, under Dr. Jiawei Han's supervision. He also received the B.Eng. and the M.Eng. degrees from Shanghai Jiao Tong University, China, in 1991 and 1993, respectively, both in Computer Science. He is currently an assistant professor of computing science at Simon Fraser University. His research interests include developing effective and efficient data analysis techniques for novel data intensive applications. He is currently interested in various techniques of data mining, data warehousing, online analytical processing, and database systems, as well as their applications in bioinformatics. His current research is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the National Science Foundation (NSF) of the United States. Since 2000, he has published over 70 research papers in refereed journals, conferences, and workshops, has served in the organization committees and the program committees of over 60 international conferences and workshops, and has been a reviewer for some leading academic journals. He is a member of the ACM, the ACM SIGMOD, and the ACM SIGKDD. Murali Ramanathan is an associate professor of pharmaceutical sciences and neurology. He received the B.Tech. (Honors) in chemical engineering from the Indian Institute of Technology, India, in 1983. After a 4-year stint in the chemical industry, he obtained the M.S. degree in chemical engineering from Iowa State University, Ames, IA, in 1987, and the Ph.D. degree in bioengineering from the University of California-San Francisco and University of California-Berkeley Joint Program in Bioengineering in 1994. Dr. Ramanathan research interests are primarily focused on the treatment of multiple sclerosis (MS), an inflammatory-demyelinating disease of the central nervous system that affects over 1 million patients worldwide. MS is a complex, variable disease that causes physical and cognitive disability and nearly 50% of patients diagnosed with MS are unable to walk after 15 years. The etiology and pathogenesis of MS remains poorly understood. Dr. Ramanathan's research interests include stochastic modeling of pharmaceutical systems and novel approaches to analyzing and using genetic and genomic data for improving patient care and optimizing therapy. Chuan Lin is currently a Ph.D. student in the Department of Computer Science and Engineering, State University of New York at Buffalo. She received the B.E. and the M.S. degrees in computer science and technology from Tsinghua University in China. Her research interests include bioinformatics, data mining, and machine learning. Chun Tang received the B.S. and M.S. degrees from Peking University, China, in 1996 and 1999, respectively, and the Ph.D. degree from State University of New York at Buffalo, USA, in 2005, all in computer science. Currently, she is a postdoctoral associate of Center for Medical Informatics, Yale University. Her research interests include bioinformatics, data mining, machine learning, database, and information retrieval. Aidong Zhang received the Ph.D. degree in computer science from Purdue University, West Lafayette, Indiana, in 1994. She was an assistant professor from 1994 to 1999, an associate professor from 1999 to 2002, and has been a professor since 2002 in the Department of Computer Science and Engineering at State University of New York at Buffalo. Her research interests include multimedia systems, content-based image retrieval, bioinformatics, and data mining. She is an author of over 140 research publications in these areas. Dr. Zhang's research has been funded by NSF, NIH, NIMA, and Xerox. Zhang serves on the editorial boards of International Journal of Bioinformatics Research and Applications (IJBRA), ACM Multimedia Systems, International Journal of Multimedia Tools and Applications, and International Journal of Distributed and Parallel Databases. She was the editor for ACM SIGMOD DiSC (Digital Symposium Collection) from 2001 to 2003. She was co-chair of the technical program committee for ACM Multimedia in 2001. She has also served on various conference program committees. Dr. Zhang is a recipient of the National Science Foundation CAREER award and SUNY Chancellor's Research Recognition award.     

A new measure for gene expression biclustering based on non-parametric correlation

Background

One of the emerging techniques for performing the analysis of the DNA microarray data known as biclustering is the search of subsets of genes and conditions which are coherently expressed. These subgroups provide clues about the main biological processes. Until now, different approaches to this problem have been proposed. Most of them use the mean squared residue as quality measure but relevant and interesting patterns can not be detected such as shifting, or scaling patterns. Furthermore, recent papers show that there exist new coherence patterns involved in different kinds of cancer and tumors such as inverse relationships between genes which can not be captured.

Results

The proposed measure is called Spearman's biclustering measure (SBM) which performs an estimation of the quality of a bicluster based on the non-linear correlation among genes and conditions simultaneously. The search of biclusters is performed by using a evolutionary technique called estimation of distribution algorithms which uses the SBM measure as fitness function. This approach has been examined from different points of view by using artificial and real microarrays. The assessment process has involved the use of quality indexes, a set of bicluster patterns of reference including new patterns and a set of statistical tests. It has been also examined the performance using real microarrays and comparing to different algorithmic approaches such as Bimax, CC, OPSM, Plaid and xMotifs.

Conclusions

SBM shows several advantages such as the ability to recognize more complex coherence patterns such as shifting, scaling and inversion and the capability to selectively marginalize genes and conditions depending on the statistical significance.     

Pipelining the ranking techniques for microarray data classification: A case study

Identification of relevant genes from microarray data is an apparent need in many applications. For such identification different ranking techniques with different evaluation criterion are used, which usually assign different ranks to the same gene. As a result, different techniques identify different gene subsets, which may not be the set of significant genes. To overcome such problems, in this study pipelining the ranking techniques is suggested. In each stage of pipeline, few of the lower ranked features are eliminated and at the end a relatively good subset of feature is preserved. However, the order in which the ranking techniques are used in the pipeline is important to ensure that the significant genes are preserved in the final subset. For this experimental study, twenty four unique pipeline models are generated out of four gene ranking strategies. These pipelines are tested with seven different microarray databases to find the suitable pipeline for such task. Further the gene subset obtained is tested with four classifiers and four performance metrics are evaluated. No single pipeline dominates other pipelines in performance; therefore a grading system is applied to the results of these pipelines to find out a consistent model. The finding of grading system that a pipeline model is significant is also established by Nemenyi post-hoc hypothetical test. Performance of this pipeline model is compared with four ranking techniques, though its performance is not superior always but majority of time it yields better results and can be suggested as a consistent model. However it requires more computational time in comparison to single ranking techniques.     

Selecting informative genes from microarray data by using hybrid methods for cancer classification

Gene expression technology, namely microarrays, offers the ability to measure the expression levels of thousands of genes simultaneously in biological organisms. Microarray data are expected to be of significant help in the development of an efficient cancer diagnosis and classification platform. A major problem in these data is that the number of genes greatly exceeds the number of tissue samples. These data also have noisy genes. It has been shown in literature reviews that selecting a small subset of informative genes can lead to improved classification accuracy. Therefore, this paper aims to select a small subset of informative genes that are most relevant for cancer classification. To achieve this aim, an approach using two hybrid methods has been proposed. This approach is assessed and evaluated on two well-known microarray data sets, showing competitive results. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Incremental wrapper-based gene selection from microarray data for cancer classification

Gene expression microarray is a rapidly maturing technology that provides the opportunity to assay the expression levels of thousands or tens of thousands of genes in a single experiment. We present a new heuristic to select relevant gene subsets in order to further use them for the classification task. Our method is based on the statistical significance of adding a gene from a ranked-list to the final subset. The efficiency and effectiveness of our technique is demonstrated through extensive comparisons with other representative heuristics. Our approach shows an excellent performance, not only at identifying relevant genes, but also with respect to the computational cost.