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Asymptotic theory for two-way clustering

JOURNAL OF ECONOMETRICS 2025年 249卷

作者： Yap, Luther Princeton Univ Dept Econ Princeton NJ 08544 USA

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the socalled separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that two-way clustering is a more robust version of one-way clustering, consistent with applied practice. In an application to linear regression, I show that a standard plug-in variance estimator is valid for inference.

关键词： two-way clustering Separate exchangeability

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Comorbidity Patterns and Its Impact on Health Outcomes: two-way clustering Analysis

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IEEE TRANSACTIONS ON BIG DATA 2020年第2期6卷 359-368页

作者： Ghosh, Debopriya Cabrera, Javier Adam, Tarek N. Levounis, Petros Adam, Nabil R. Rutgers State Univ Rutgers Business Sch 1 Washington Pk Newark NJ 07102 USA Rutgers State Univ Dept Stat & Biostat Newark NJ 07102 USA Rutgers New Jersey Med Sch Dept Psychiat Newark NJ 07102 USA Weill Cornell Med Ctr NYP New York NY 10065 USA Rutgers State Univ Off Chancellor 123 Washington St Newark NJ 07102 USA

Comorbidity greatly increases the complexity of managing disease in patients. Approximately 27 percent of the US population have two or more concurrent comorbid conditions. Traditional models for assessing the impact of patient demographic and comorbidity burden on patient health outcomes, represented comorbidity conditions by Charlson Comorbidity Index. In this paper, we develop a novel two-way clustering approach combining model-based and weighted K-means clustering methods for characterizing and summarizing a patient's comorbid conditions. Our two-way approach helps reduce the size of the data to a manageable size, thus being practical for big data applications. Another novel aspect of our approach is the ability to handle weighted observations. Assigning weights to observations helps reduce the size of the dataset, thus addressing the scalability challenge of algorithms when dealing with big data. Using the National Inpatient Sample database for 2008-2013, we evaluate the performance of our approach by the use of logistic regression and support vector machine models by applying them to patients whose primary diagnosis is cardiovascular disease. In addition to evaluating our proposed method using empirical test data, we use asymptotic statistics. Both evaluation methods show that the proposed approach improves the prediction of patient health outcomes;specifically, hospital length of stay.

关键词： Diseases Medical diagnostic imaging Diabetes Big data Indexes Sociology Comorbidity conditions cardiovascular disease two-way clustering weighted k-means clustering model-based clustering weighted observations

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Three-way clustering: Foundations, survey and challenges

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APPLIED SOFT COMPUTING 2024年 151卷

作者： Wang, Pingxin Yang, Xibei Ding, Weiping Zhan, Jianming Yao, Yiyu Jiangsu Univ Sci & Technol Sch Sci Zhenjiang 212003 Jiangsu Peoples R China Jiangsu Univ Sci & Technol Sch Comp Zhenjiang 212003 Jiangsu Peoples R China Nantong Univ Sch Informat Sci & Technol Nangtong 226019 Peoples R China Hubei Minzu Univ Sch Math & Stat Enshi 445000 Hubei Peoples R China Univ Regina Dept Comp Sci Regina SK S4S 0A2 Canada

clustering, as an unsupervised data mining technique, allows us to classify similar objects into the same cluster according to certain criteria. It helps us identify patterns between objects, reveal the associations between objects, and discover hidden structures. Traditional two-way clustering (2W clustering) algorithms represent one cluster by one set and only two types of relationships are considered between a sample and a cluster, namely, belonging to and not belonging to. two-way decision is not always feasible especially in situations that are characterized by uncertainty and lack of information. Guided by the principle of three-way decision (3WD) as thinking in threes, three-way clustering (3W clustering) addresses the information uncertainty problem using core and the fringe regions to character a cluster. The universe is split into three sections by these two sets, which capture three kinds of relationships between objects and a cluster, namely, belonging to, partially belonging to, and not belonging-to. Compared with 2W clustering methods, 3W clustering incorporates the fringe region to describe the uncertain relationship between objects and clusters, which provides more information about the clustering structure. This survey points out the historical developments of three-way clustering and makes an overview of the achievements in the field of three-way clustering. In addition, to reap a clearer grasp of the development and research significance of three-way clustering, we divide the existing three-way clustering approaches into two categories and present the bibliometric analysis of related approaches. Finally, we point out some challenges and future research topics in three-way clustering. It is hoped that this review can serve as a reference and provide convenience for scholars and practitioners in the field of three-way clustering.

关键词： Cluster analysis two-way clustering Three-way decision Three-way clustering

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The GH-EXIN neural network for hierarchical clustering

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NEURAL NEtwoRKS 2020年 121卷 57-73页

作者： Cirrincione, Giansalvo Ciravegna, Gabriele Barbiero, Pietro Randazzo, Vincenzo Pasero, Eros Univ South Pacific Suva Fiji Univ Picardie Jules Verne Amiens France Univ Siena DIISM Siena Italy Politecn Torino DISMA Turin Italy Politecn Torino DET Turin Italy

Hierarchical clustering is an important tool for extracting information from data in a multi-resolution way. It is more meaningful if driven by data, as in the case of divisive algorithms, which split data until no more division is allowed. However, they have the drawback of the splitting threshold setting. The neural networks can address this problem, because they basically depend on data. The growing hierarchical GH-EXIN neural network builds a hierarchical tree in an incremental (data-driven architecture) and self-organized way. It is a top-down technique which defines the horizontal growth by means of an anisotropic region of influence, based on the novel idea of neighborhood convex hull. It also reallocates data and detects outliers by using a novel approach on all the leaves, simultaneously. Its complexity is estimated and an analysis of its user-dependent parameters is given. The advantages of the proposed approach, with regard to the best existing networks, are shown and analyzed, qualitatively and quantitatively, both in benchmark synthetic problems and in a real application (image recognition from video), in order to test the performance in building hierarchical trees. Furthermore, an important and very promising application of GH-EXIN in two-way hierarchical clustering, for the analysis of gene expression data in the study of the colorectal cancer is described. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Convex hull Dynamic tree Hierarchical divisive clustering Neural network Self-organization two-way clustering

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vcemway: A one-stop solution for robust inference with multiway clustering

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STATA JOURNAL 2019年第4期19卷 900-912页

作者： Gu, Ariel Yoo, Hong, II Northumbria Univ Newcastle Business Sch Finance Newcastle Upon Tyne Tyne & Wear England Univ Durham Business Sch Econ Durham England

Most Stata commands allow cluster(varname) or vce(cluster clustvar) as an option, popularizing the use of standard errors that are robust to oneway clustering. For adjusting standard errors for multiway clustering, there is no solution that is as widely applicable. While several community-contributed packages support multiway clustering, each package is compatible only with a subset of models that Stata's ever-expanding library of commands allows the researcher to fit. We introduce a command, vcemway, that provides a one-stop solution for multiway clustering. vcemway works with any estimation command that allows cluster(varname) as an option, and it adjusts standard errors, individual significance statistics, and confidence intervals in output tables for multiway clustering in specified dimensions. The covariance matrix used in making this adjustment is stored in e(V), meaning that any subsequent call to postestimation commands that use e(V) as input (for example, test and margins) will also produce results that are robust to multiway clustering.

关键词： st0582 vcemway ivreg2 cmgreg reghdfe boottest two-way clustering multiway clustering

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two-way Regularized Fuzzy clustering of Multiple Correspondence Analysis

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MULTIVARIATE BEHAVIORAL RESEARCH 2017年第1期52卷 31-46页

作者： Kim, Sunmee Choi, Ji Yeh Hwang, Heungsun McGill Univ Montreal PQ Canada

Multiple correspondence analysis (MCA) is a useful tool for investigating the interrelationships among dummy-coded categorical variables. MCA has been combined with clustering methods to examine whether there exist heterogeneous subclusters of a population, which exhibit cluster-level heterogeneity. These combined approaches aim to classify either observations only (one-way clustering of MCA) or both observations and variable categories (two-way clustering of MCA). The latter approach is favored because its solutions are easier to interpret by providing explicitly which subgroup of observations is associated with which subset of variable categories. Nonetheless, the two-way approach has been built on hard classification that assumes observations and/or variable categories to belong to only one cluster. To relax this assumption, we propose two-way fuzzy clustering of MCA. Specifically, we combine MCA with fuzzy k-means simultaneously to classify a subgroup of observations and a subset of variable categories into a common cluster, while allowing both observations and variable categories to belong partially to multiple clusters. Importantly, we adopt regularized fuzzy k-means, thereby enabling us to decide the degree of fuzziness in cluster memberships automatically. We evaluate the performance of the proposed approach through the analysis of simulated and real data, in comparison with existing two-way clustering approaches.

关键词： Multiple correspondence analysis cluster-level heterogeneity regularized fuzzy clustering two-way clustering cross validation

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Robust Inference With Multiway clustering

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JOURNAL OF BUSINESS & ECONOMIC STATISTICS 2011年第2期29卷 238-249页

作者： Cameron, A. Colin Gelbach, Jonah B. Miller, Douglas L. Univ Calif Davis Dept Econ Davis CA 95616 USA Yale Univ Sch Law New Haven CT 06511 USA

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g., Liang and Zeger 1986;Arellano 1987) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model;a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions;and by application to studies in the empirical literature where two-way clustering is present.

关键词： Cluster-robust standard errors two-way clustering

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two-way clustering using Fuzzy ASI for Knowledge Discovery in Microarrays

Two-way Clustering using Fuzzy ASI for Knowledge Discovery i...

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IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology

作者： Shaik, J. Yeasin, M. Univ Memphis Comp Vis Pattern & Image Anal Lab Memphis TN 38152 USA

ISBN: (纸本)9781424407101

This paper presents two-way clustering of microarray data using fuzzy adaptive subspace iteration (ASI) based algorithm for knowledge discovery in microarrays. It is widely believed that each gene is involved in more than one cellular function or biological process. The proposed fuzzy ASI assigns a relevance value to each gene associated with each cluster. These functional categories are ranked based on their potential in providing maximal separation between the two tissues classes;which is an indication of differentially expressed genes (DEGs). Empirical analyses on simulated, 100 artificial microarray datasets are used to quantify the results obtained using the fuzzy-ASI algorithm. Further analyses on different microarray cancer datasets revealed several important genes that are relevant with various cancers.

关键词： fuzzy clustering two-way clustering knowledge discovery in microarrays visualization

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A new approach: Interrelated two-way clustering of gene expression data

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Statistical Methodology 2006年第1期3卷 93-102页

作者： Chandra, B. Shanker, S. Mishra, Saroj Department of Mathematics Indian Institute of Technology Delhi India Department of Biochemical Engineering and Biotechnology Indian Institute of Technology Delhi India

The paper presents a new approach to interrelated two-way clustering of gene expression data. clustering of genes has been effected using entropy and a correlation measure, whereas the samples have been clustered using the fuzzy C-means. The efficiency of this approach has been tested on two well known data sets: the colon cancer data set and the leukemia data set. Using this approach, we were able to identify the important co-regulated genes and group the samples efficiently at the same time. © 2005 Elsevier B.V. All rights reserved.

关键词： Gene expression data Microarray data two-way clustering

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Finding biclusters by random projections

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THEORETICAL COMPUTER SCIENCE 2006年第3期368卷 217-230页

作者： Lonardi, Stefano Szpankowski, Wojciech Yang, Qiaofeng Univ Calif Riverside Dept Comp Sci & Engn Riverside CA 92521 USA Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

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. (c) 2006 Elsevier B.V. All rights reserved.

关键词： biclustering two-way clustering Co-clustering bicliques textual matrices

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