Co-clustering Problem Research Articles

A nondominated sorting genetic model for co-clustering

Co-clustering aims to cluster the rows and columns of data simultaneously and can be often formulated as a two-objective optimization problem (one objective for rows and the other for columns) and the solution is a Pareto-optimal solution set in principle. Existing methods usually convert the co-clustering problem into a single-objective optimization problem by setting a hyper-parameter λ between the two objectives. However, finding a good value of λ is not easy because of its large parameter space; also, there may exist many equally good λs. In this paper, a nondominated sorting genetic model (NSGC) is proposed to tackle the co-clustering problem, totally bypassing the trade-off parameter λ and returning to the original two-objective problem. The core of our model is to group a row objective function and a column objective function and integrate them into a genetic algorithm as the fitness functions. After this reformulation, we follow a standard genetic algorithm procedure to iteratively find the Pareto-optimal solutions. Finally, to fish out a single best solution we further design a sorting criterion according to which the Pareto-optimal solution set can be totally ordered. Extensive experiments with 16 public datasets are conducted, and the results demonstrate the superiority of our approach.

ABC

Finding a set of co-clusters in a bipartite network is a fundamental and important problem. In this paper, we present the Attributed Bipartite Co-clustering (ABC) problem which unifies two main concepts: (i) bipartite modularity optimization, and (ii) attribute cohesiveness. To the best of our knowledge, this is the first work to find co-clusters while considering the attribute cohesiveness. We prove that ABC is NP-hard and is not in APX, unless P=NP. We propose three algorithms: (1) a top-down algorithm; (2) a bottom-up algorithm; (3) a group matching algorithm. Extensive experimental results on real-world attributed bipartite networks demonstrate the efficiency and effectiveness of our algorithms.

Sparse neighbor constrained co-clustering via category consistency learning

Clustering has long been an enduring and promising task in machine learning. However, developed one-side clustering is still insufficient to explore the context of data, such as texts and genes. Hence, developing two-way clustering has drawn more attention in recent years, which tends to cluster samples and features simultaneously. This paper proposes a sparse neighbor constrained co-clustering via category consistency learning, for alleviating the misclassification of close points. Following an additional observation, samples often fall into the same category as their neighbors, as do features. Accordingly, the co-clustering problem is formulated as nonnegative matrix tri-factorization appended dual regularizers, considering coherence between data affinity and label assignment. Then, a multiplicative alternating scheme is raised for objective optimization, whose convergence and correctness are theoretically guaranteed. Furthermore, the proposed approach is validated on six datasets using three evaluation metrics, whose parameter sensitivity is analyzed as well. Finally, comprehensive experiments show that our algorithm is competitive against existing ones.

Scientific community detection via bipartite scholar/journal graph co-clustering

Abstract This paper stems from the observation that researchers in different fields tend to publish in different journals. Such a relationship between researchers and journals is quantitatively exploited to identify scientific community clusters, by casting the community detection problem into a co-clustering problem on bipartite graphs. Such an approach has the potential of leading not only to the fine- grained detection of scholar communities based on the similarity of their research activity, but also to the clustering of scientific journals based on which are the most representative of each community. The proposed methodology is purely data-driven and completely unsupervised, and does not rely on any semantics (e.g. keywords or a-priori subjective categories). Moreover, unlike “flat” data structures (e.g. collaboration graphs or citation graphs) our bipartite graph approach blends in a joint structure both the researcher's attitude and interests (i.e., freedom to select the venue where to publish) as well as the community's recognition (i.e., acceptance of the publication on a target journal); as such may perhaps inspire further scientometric evaluation strategies. Our proposed approach is applied to the Italian research system, for two broad areas (ICT and Microbiology&Genetics), and reveals some questionable aspects and community overlaps in the current Italian scientific sectors classification.

Motion Segmentation & Multiple Object Tracking by Correlation Co-Clustering.

Models for computer vision are commonly defined either w.r.t. low-level concepts such as pixels that are to be grouped, or w.r.t. high-level concepts such as semantic objects that are to be detected and tracked. Combining bottom-up grouping with top-down detection and tracking, although highly desirable, is a challenging problem. We state this joint problem as a co-clustering problem that is principled and tractable by existing algorithms. We demonstrate the effectiveness of this approach by combining bottom-up motion segmentation by grouping of point trajectories with high-level multiple object tracking by clustering of bounding boxes. We show that solving the joint problem is beneficial at the low-level, in terms of the FBMS59 motion segmentation benchmark, and at the high-level, in terms of the Multiple Object Tracking benchmarks MOT15, MOT16 and the MOT17 challenge, and is state-of-the-art in some metrics.

VIBR: Visualizing Bipartite Relations at Scale with the Minimum Description Length Principle.

Bipartite graphs model the key relations in many large scale real-world data: customers purchasing items, legislators voting for bills, people's affiliation with different social groups, faults occurring in vehicles, etc. However, it is challenging to visualize large scale bipartite graphs with tens of thousands or even more nodes or edges. In this paper, we propose a novel visual summarization technique for bipartite graphs based on the minimum description length (MDL) principle. The method simultaneously groups the two different set of nodes and constructs aggregated bipartite relations with balanced granularity and precision. It addresses the key trade-off that often occurs for visualizing large scale and noisy data: acquiring a clear and uncluttered overview while maximizing the information content in it. We formulate the visual summarization task as a co-clustering problem and propose an efficient algorithm based on locality sensitive hashing (LSH) that can easily scale to large graphs under reasonable interactive time constraints that previous related methods cannot satisfy. The method leads to the opportunity of introducing a visual analytics framework with multiple levels-of-detail to facilitate interactive data exploration. In the framework, we also introduce a compact visual design inspired by adjacency list representation of graphs as the building block for a small multiples display to compare the bipartite relations for different subsets of data. We showcase the applicability and effectiveness of our approach by applying it on synthetic data with ground truth and performing case studies on real-world datasets from two application domains including roll-call vote record analysis and vehicle fault pattern analysis. Interviews with experts in the political science community and the automotive industry further highlight the benefits of our approach.

Triadic co-clustering of users, issues and sentiments in political tweets

Social network data contains many hidden relationships. The most well known is the communities formed by users. Moreover, typical social network data, such as Twitter, can also be interpreted in terms of three-dimensional relationships; namely the users, issues discussed by the users, and terminology chosen by the users in these discussions. In this paper, we propose a new problem to generate co-clusters in these three dimensions simultaneously. There are three major differences between our problem and the standard co-clustering problem definition: a node can be a member of more than one clusters; all the nodes are not necessarily members of some cluster; and edges are signed and cluster are expected to have high density of positive signed edges, and low density of negative signed edges. We apply our method to the tweets of British politicians just before the Brexit referendum. Our motivation is to discover clusters of politicians, issues and the sentimental words politicians use to express their feelings on these issues in their tweets.

Robust co-clustering via dual local learning and high-order matrix factorization

Co-clustering is to group features and samples simultaneously and has received increasing attention in data mining and machine learning, particularly in text document categorization and gene expression. In this paper, two effective co-clustering algorithms are proposed to exploit the joint advantages of local learning and matrix factorization. First, the co-clustering problem is formulated as a form of matrix tri-factorization which embeds local structure learning and orthogonality constraints for clustering indicators. Using high-order matrix factorization, an effective algorithm is proposed for co-clustering problems and its convergence is proved. Second, symmetric co-clustering problems are studied, where the sample affinity matrix serves as the input matrix. Analogous high-order matrix factorization is used to develop an effective convergent algorithm for that problem. Finally, the two proposed algorithms are validated in eight publicly available real-world datasets from machine learning repository. Extensive experiments demonstrate that the proposed algorithms achieve competitive performance over existing state-of-the-art co-clustering methods in all tested datasets.

Mutual information, phi-squared and model-based co-clustering for contingency tables

Many of the datasets encountered in statistics are two-dimensional in nature and can be represented by a matrix. Classical clustering procedures seek to construct separately an optimal partition of rows or, sometimes, of columns. In contrast, co-clustering methods cluster the rows and the columns simultaneously and organize the data into homogeneous blocks (after suitable permutations). Methods of this kind have practical importance in a wide variety of applications such as document clustering, where data are typically organized in two-way contingency tables. Our goal is to offer coherent frameworks for understanding some existing criteria and algorithms for co-clustering contingency tables, and to propose new ones. We look at two different frameworks for the problem of co-clustering. The first involves minimizing an objective function based on measures of association and in particular on phi-squared and mutual information. The second uses a model-based co-clustering approach, and we consider two models: the block model and the latent block model. We establish connections between different approaches, criteria and algorithms, and we highlight a number of implicit assumptions in some commonly used algorithms. Our contribution is illustrated by numerical experiments on simulated and real-case datasets that show the relevance of the presented methods in the document clustering field.

Hard and fuzzy diagonal co-clustering for document-term partitioning

We propose a hard and a fuzzy diagonal co-clustering algorithms built upon the double K-means to address the problem of document-term co-clustering. At each iteration, the proposed algorithms seek a diagonal block structure of the data by minimizing a criterion based on both the variance within the class and the centroid effect. In addition to be easy-to-interpret and effective on sparse binary and continuous data, the proposed algorithms, Hard Diagonal Double K-means (DDKM) and Fuzzy Diagonal Double K-means (F-DDKM), are also faster than other state-of-the-art clustering algorithms. We evaluate our contribution using synthetic data sets, and real data sets commonly used in document clustering.

Constraint Co-Projections for Semi-Supervised Co-Clustering.

Co-clustering aims to simultaneously cluster the objects and features to explore intercorrelated patterns. However, it is usually difficult to obtain good co-clustering results by just analyzing the object-feature correlation data due to the sparsity of the data and the noise. Meanwhile, most co-clustering algorithms cannot take the prior information into consideration and may produce unmeaningful results. Semi-supervised co-clustering aims to incorporate the known prior knowledge into the co-clustering algorithm. In this paper, a new technique named constraint co-projections for semi-supervised co-clustering (CPSSCC) is presented. Constraint co-projections can not only make use of two popular techniques including pairwise constraints and constraint projections, but also simultaneously perform the object constraint projections and feature constraint projections. The two popular techniques are illustrated for semi-supervised co-clustering when some objects and features are believed to be in the same cluster a priori. Furthermore, we also prove that the co-clustering problem can be formulated as a typical eigen-problem and can be efficiently solved with the selected eigenvectors. To the best of our knowledge, constraint co-projections is first stated in this paper and this is the first work on using CPSSCC. Extensive experiments on benchmark data sets demonstrate the effectiveness of the proposed method. This paper also shows that CPSSCC has some favorable features compared with previous related co-clustering algorithms.

Co-clustering separately exchangeable network data

This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence $\mathcal{O}_P(n^{-1/4})$ corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be interpreted in this setting as an optimal piecewise-constant approximation to the generative nonparametric model. We also show for large sample sizes that the detection of co-clusters in such data indicates with high probability the existence of co-clusters of equal size and asymptotically equivalent connectivity in the underlying generative process.

A Constant-Factor Approximation Algorithm for Co-clustering

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 a lot of 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 provide constant-factor approximations to the optimum. We also show that co-clustering is NP-hard, thereby complementing our algorithmic result.