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

We present an unsupervised technique for detecting unusual activity in a large video set using many simple features. No complex activity models and no supervised feature selections are used. We divide the video into equal length segments and classify the extracted features into prototypes, from which a prototype--segment co-occurrence matrix is computed. Motivated by a similar problem in documentkeyword analysis, we seek a correspondence relationship between prototypes and video segments which satisfies the transitive closure constraint. We show that an important sub-family of correspondence functions can be reduced to co-embedding prototypes and segments to N-D Euclidean space. We prove that an efficient, globally optimal algorithm exists for the co-embedding problem. Experiments on various real-life videos have validated our approach.

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.

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

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Abstract. Given a matrix X composed of symbols, a bicluster is a submatrix of X obtained by removing some of the rows and some of the columns of X in such a way that each row of what is left reads the same string. In this paper, we are concerned with the problem of finding the bicluster with the largest area in a large matrix X. The problem is first proved to be NP-complete. We present a fast and efficient randomized algorithm that discovers the largest bicluster by random projections. A detailed probabilistic analysis of the algorithm and an asymptotic study of the statistical significance of the solutions are given. We report results of extensive simulations on synthetic data. 1

In recent years, co-clustering has emerged as a powerful data mining tool that can analyze dyadic data connecting two entities. However, almost all existing co-clustering techniques are partitional, and allow individual rows and columns of a data matrix to belong to only one cluster. Several current applications, such as recommendation systems and market basket analysis, can substantially benefit from a mixed membership of rows and columns. In this paper, we present Bayesian co-clustering (BCC) models, that allow a mixed membership in row and column clusters. BCC maintains separate Dirichlet priors for rows and columns over the mixed membership and assumes each observation to be generated by an exponential family distribution corresponding to its row and column clusters. We propose a fast variational algorithm for inference and parameter estimation. The model is designed to naturally handle sparse matrices as the inference is done only based on the nonmissing entries. In addition to finding a co-cluster structure in observations, the model outputs a low dimensional coembedding, and accurately predicts missing values in the original matrix. We demonstrate the efficacy of the model through experiments on both simulated and real data. 1

Co-clustering is the simultaneous partitioning of the rows and columns of a matrix such that the blocks induced by the row/column partitions are good clusters. Motivated by several applications in text mining, market-basket analysis, and bioinformatics, this problem has attracted severe attention in the past few years. Unfortunately, to date, most of the algorithmic work on this problem has been heuristic in nature. In this work we obtain the first approximation algorithms for the co-clustering problem. Our algorithms are simple and obtain constant-factor approximation solutions to the optimum. We also show that co-clustering is NP-hard, thereby complementing our algorithmic result.

Recent advances in high throughput profiling of gene expression have catalyzed an explosive growth in functional genomics aimed at the elucidation of genes that are differentially expressed in various tissue or cell types across a range of experimental conditions. These studies can lead to the identification of diagnostic genes, classification of genes into functional categories, association of genes with regulatory pathways, and clustering of genes into modules that are potentially coregulated by a group of transcription factors. Traditional clustering methods such as hierarchical clustering or principal component analysis are difficult to deploy effectively for several of these tasks since genes rarely exhibit similar expression pattern across a wide range of conditions. Bi-clustering of gene expression data is a promising methodology for identification of gene groups that show a coherent expression profile across a subset of conditions. This methodology can be a first step towards the discovery of co-regulated and co-expressed genes or modules. Although bi-clustering (also called block clustering) was introduced in statistics in 1974 few robust and efficient solutions exist for extracting gene expression modules in microarray data. In this paper, we propose a simple but promising new approach for bi-clustering based on a Gibbs sampling paradigm. Our algorithm is implemented in the program GEMS (Gene Expression Module Sampler). GEMS has been tested on synthetic data generated to evaluate the effect of noise on the performance of the algorithm as well as on published leukemia datasets. In our preliminary studies comparing GEMS with other biclustering software we show that GEMS is a reliable, flexible and computationally efficient approach for bi-clustering gene expression data.

With widespread popularity of smart phones, more and more users are accessing the Internet on the go. Understanding mobile user browsing behavior is of great significance for several reasons. For example, it can help cellular (data) service providers (CSPs) to improve service performance, thus increasing user satisfaction. It can also provide valuable insights about how to enhance mobile user experience by providing dynamic content personalization and recommendation, or location-aware services. In this paper, we try to understand mobile user browsing behavior by investigating whether there exists distinct “behavior patterns” among mobile users. Our study is based on real mobile network data collected from a large 3G CSP in North America. We formulate this user behavior profiling problem as a co-clustering problem, i.e., we group both users (who share similar browsing behavior), and browsing profiles (of like-minded users) simultaneously. We propose and develop a scalable co-clustering methodology, Phantom, using a novel hourglass model. The proposed hourglass model first reduces the dimensions of the input data and performs divisive hierarchical co-clustering on the lower dimensional data; it then carries out an expansion step that restores the original dimensions. Applying Phantom to the mobile network data, we find that there exists a number of prevalent and distinct behavior patterns that persist over time, suggesting that user browsing behavior in 3G cellular networks can be captured using a small number of co-clusters. For instance, behavior of most users can be classified as either homogeneous (users with very limited set of browsing interests) or heterogeneous (users with very diverse browsing interests), and such behavior profiles do not change significantly at either short (30-min) or long (6 hour) time scales. 1.