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586
Biclustering algorithms for biological data analysis: a survey
- IEEE/ACM Transactions on Computational Biology and Bioinformatics
, 2004
"... Abstract—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 ..."
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Cited by 481 (15 self)
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Abstract—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. Index Terms—Biclustering, simultaneous clustering, coclustering, subspace clustering, bidimensional clustering, direct clustering, block clustering, two-way clustering, two-mode clustering, two-sided clustering, microarray data analysis, biological data analysis, gene expression data. 1
Information-Theoretic Co-Clustering
- In KDD
, 2003
"... Two-dimensional contingency or co-occurrence tables arise frequently in important applications such as text, web-log and market-basket data analysis. A basic problem in contingency table analysis is co-clustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views ..."
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Cited by 342 (12 self)
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Two-dimensional contingency or co-occurrence tables arise frequently in important applications such as text, web-log and market-basket data analysis. A basic problem in contingency table analysis is co-clustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views the contingency table as an empirical joint probability distribution of two discrete random variables and poses the co-clustering problem as an optimization problem in information theory -- the optimal co-clustering maximizes the mutual information between the clustered random variables subject to constraints on the number of row and column clusters.
Discovering Statistically Significant Biclusters in Gene Expression Data
- In Proceedings of ISMB 2002
, 2002
"... 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 p ..."
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Cited by 299 (4 self)
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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).
Data Clustering: 50 Years Beyond K-Means
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 274 (6 self)
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Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is exploratory in nature to find structure in data. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty of designing a general purpose clustering algorithm and the illposed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection, and data clustering and large scale data clustering.
Discovering Local Structure in Gene Expression Data: The Order-Preserving Submatrix Problem
, 2002
"... 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 ex ..."
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Cited by 188 (1 self)
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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. Speci � cally, 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 de � ne a probabilistic model in which an OPSM is hidden within an otherwise random matrix. Guided by this model, we develop an ef � cient algorithm for � nding 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 signi � cant local patterns.
Cluster Analysis for Gene Expression Data: A Survey
- IEEE Transactions on Knowledge and Data Engineering
, 2004
"... Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity f ..."
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Cited by 142 (5 self)
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Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field. Index Terms—Microarray technology, gene expression data, clustering.
Spectral biclustering of microarray data: Coclustering genes and conditions
- Genome Research
, 2003
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A Generalized Maximum Entropy Approach to Bregman Co-clustering and Matrix Approximation
- In KDD
, 2004
"... Co-clustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic co-clustering approach applicable to empirical joint probability distributions was proposed. In many situations, co-clust ..."
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Cited by 133 (29 self)
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Co-clustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic co-clustering approach applicable to empirical joint probability distributions was proposed. In many situations, co-clustering of more general matrices is desired. In this paper, we present a substantially generalized co-clustering framework wherein any Bregman divergence can be used in the objective function, and various conditional expectation based constraints can be considered based on the statistics that need to be preserved. Analysis of the coclustering problem leads to the minimum Bregman information principle, which generalizes the maximum entropy principle, and yields an elegant meta algorithm that is guaranteed to achieve local optimality. Our methodology yields new algorithms and also encompasses several previously known clustering and co-clustering algorithms based on alternate minimization.
Barkai N: Iterative signature algorithm for the analysis of large-scale gene expression data
- Phys Rev E Stat Nonlin Soft Matter Phys 2003, 67(3 Pt 1):031902
"... We present a new approach for the analysis of genome-wide expression data. Our method is designed to overcome the limitations of traditional techniques, when applied to large-scale data. Rather than alloting each gene to a single cluster, we assign both genes and conditions to context-dependent and ..."
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Cited by 120 (5 self)
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We present a new approach for the analysis of genome-wide expression data. Our method is designed to overcome the limitations of traditional techniques, when applied to large-scale data. Rather than alloting each gene to a single cluster, we assign both genes and conditions to context-dependent and potentially overlapping transcription modules. We provide a rigorous definition of a transcription module as the object to be retrieved from the expression data. An efficient algorithm, that searches for the modules encoded in the data by iteratively refining sets of genes and conditions until they match this definition, is established. Each iteration involves a linear map, induced by the normalized expression matrix, followed by the application of a threshold function. We argue that our method is in fact a generalization of Singular Value Decomposition, which corresponds to the special case where no threshold is applied. We show analytically that for noisy expression data our approach leads to better classification due to the implementation of the threshold. This result is confirmed by numerical analyses based on in-silico expression data. We discuss briefly results obtained by applying our algorithm to expression data from the yeast S. cerevisiae.
Minimum sumsquared residue co-clustering of gene expression data
- In SDM
, 2004
"... Microarray experiments have been extensively used for simultaneously measuring DNA expression levels of thousands of genes in genome research. A key step in the analysis of gene expression data is the clustering of genes into groups that show similar expression values over a range of conditions. Sin ..."
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Cited by 115 (6 self)
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Microarray experiments have been extensively used for simultaneously measuring DNA expression levels of thousands of genes in genome research. A key step in the analysis of gene expression data is the clustering of genes into groups that show similar expression values over a range of conditions. Since only a small subset of the genes participate in any cellular process of interest, by focusing on subsets of genes and conditions, we can lower the noise induced by other genes and conditions — a co-cluster characterizes such a subset of interest. Cheng and Church [3] introduced an effective measure of co-cluster quality based on mean squared residue. In this paper, we use two similar squared residue measures and propose two fast k-means like co-clustering algorithms corresponding to the two residue measures. Our algorithms discover k row clusters and l column clusters simultaneously while monotonically decreasing the respective squared residues. Our co-clustering algorithms inherit the simplicity, efficiency and wide applicability of the k-means algorithm. Minimizing the residues may also be formulated as trace optimization problems that allow us to obtain a spectral relaxation that we use for a principled initialization for our iterative algorithms. We further enhance our algorithms by an incremental local search strategy that helps avoid empty clusters and escape poor local minima. We illustrate co-clustering results on a yeast cell cycle dataset and a human B-cell lymphoma dataset. Our experiments show that our co-clustering algorithms are efficient and are able to discover coherent co-clusters. Keywords: Gene-expression, co-clustering, biclustering, residue, spectral relaxation
