Coclustering targets on grouping the samples (e.g., documents and users) and the features (e.g., words and ratings) simultaneously. It employs the dual relation and the bilateral information between the samples and features. In many real-world applications, data usually reside on a submanifold of the ambient Euclidean space, but it is nontrivial to estimate the intrinsic manifold of the data space in a principled way. In this paper, we focus on improving the coclustering performance via manifold ensemble learning, which is able to maximally approximate the intrinsic manifolds of both the sample and feature spaces. To achieve this, we develop a novel coclustering algorithm called relational multimanifold coclustering based on symmetric nonnegative matrix trifactorization, which decomposes the relational data matrix into three submatrices. This method considers the intertype relationship revealed by the relational data matrix and also the intratype information reflected by the affinity matrices encoded on the sample and feature data distributions. Specifically, we assume that the intrinsic manifold of the sample or feature space lies in a convex hull of some predefined candidate manifolds. We want to learn a convex combination of them to maximally approach the desired intrinsic manifold. To optimize the objective function, the multiplicative rules are utilized to update the submatrices alternatively. In addition, both the entropic mirror descent algorithm and the coordinate descent algorithm are exploited to learn the manifold coefficient vector. Extensive experiments on documents, images, and gene expression data sets have demonstrated the superiority of the proposed algorithm compared with other well-established methods.
@cite_14: In this paper, we present a novel graph theoretic approach to the problem of document-word co-clustering. In our approach, documents and words are modeled as the two vertices of a bipartite graph. We then propose isoperimetric co-clustering algorithm (ICA) - a new method for partitioning the document-word bipartite graph. ICA requires a simple solution to a sparse system of linear equations instead of the eigenvalue or SVD problem in the popular spectral co-clustering approach. Our extensive experiments performed on publicly available datasets demonstrate the advantages of ICA over spectral approach in terms of the quality, efficiency and stability in partitioning the document-word bipartite graph.
@cite_36: Co-clustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an information-theoretic 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 co-clustering 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.
@cite_42: 
@cite_3: Both document clustering and word clustering are well studied problems. Most existing algorithms cluster documents and words separately but not simultaneously. In this paper we present the novel idea of modeling the document collection as a bipartite graph between documents and words, using which the simultaneous clustering problem can be posed as a bipartite graph partitioning problem. To solve the partitioning problem, we use a new spectral co-clustering algorithm that uses the second left and right singular vectors of an appropriately scaled word-document matrix to yield good bipartitionings. The spectral algorithm enjoys some optimality properties; it can be shown that the singular vectors solve a real relaxation to the NP-complete graph bipartitioning problem. We present experimental results to verify that the resulting co-clustering algorithm works well in practice.
@cite_0: We present a novel implementation of the recently introduced information bottleneck method for unsupervised document clustering. Given a joint empirical distribution of words and documents, p(x, y), we first cluster the words, Y, so that the obtained word clusters, Ytilde;, maximally preserve the information on the documents. The resulting joint distribution. p(X, Ytilde;), contains most of the original information about the documents, I(X; Ytilde;) a I(X; Y), but it is much less sparse and noisy. Using the same procedure we then cluster the documents, X, so that the information about the word-clusters is preserved. Thus, we first find word-clusters that capture most of the mutual information about to set of documents, and then find document clusters, that preserve the information about the word clusters. We tested this procedure over several document collections based on subsets taken from the standard 20Newsgroups corpus. The results were assessed by calculating the correlation between the document clusters and the correct labels for these documents. Finding from our experiments show that this double clustering procedure, which uses the information bottleneck method, yields significantly superior performance compared to other common document distributional clustering algorithms. Moreover, the double clustering procedure improves all the distributional clustering methods examined here.
@cite_27: Different from traditional one-sided clustering techniques, coclustering makes use of the duality between samples and features to partition them simultaneously. Most of the existing co-clustering algorithms focus on modeling the relationship between samples and features, whereas the intersample and interfeature relationships are ignored. In this paper, we propose a novel coclustering algorithm named Locally Discriminative Coclustering (LDCC) to explore the relationship between samples and features as well as the intersample and interfeature relationships. Specifically, the sample-feature relationship is modeled by a bipartite graph between samples and features. And we apply local linear regression to discovering the intrinsic discriminative structures of both sample space and feature space. For each local patch in the sample and feature spaces, a local linear function is estimated to predict the labels of the points in this patch. The intersample and interfeature relationships are thus captured by minimizing the fitting errors of all the local linear functions. In this way, LDCC groups strongly associated samples and features together, while respecting the local structures of both sample and feature spaces. Our experimental results on several benchmark data sets have demonstrated the effectiveness of the proposed method.
@cite_46: 
From the viewpoint of graph partitioning, two bipartite spectral graph partition methods were proposed in @cite_3 @cite_46 to co-cluster documents and words by finding minimum cut vertex partitions in a bipartite graph. More recently, authors in @cite_14 put forward the isoperimetric co-clustering algorithm to partition the document-word bipartite graph, which minimizes the ratio of the perimeter of the bipartite graph partition and the partition area under a well-defined graph-theoretic area. For the information theory based co-clustering, samples and features are regarded as the instances of two random variables @cite_27 , , an information bottleneck method was implemented in @cite_0 to cluster documents by using word clusters. Besides, an information-theoretic co-clustering algorithm specially designed for contingency table was introduced in @cite_42 and a more general co-clustering framework based on Bregman divergence was given in @cite_36 .