Bootstrapping estimates of stability for clusters, observations and model selection

Yu, Han; Chapman, Brian E.; Florio, Arianna Di; Eischen, Ellen; Gotz, David; Jacob, Mathews; Blair, Rachael Hageman

doi:10.1007/s00180-018-0830-y

Cited by 32 publications

(64 citation statements)

References 15 publications

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“…Bootstrap procedure : Stability estimation utilizes bootstrapping to estimate the stability of clusterings [38]. However, in our setting, the nodes in a network are variables instead of subjects, therefore are typically fixed during the sampling process.…”

Section: Methodsmentioning

confidence: 99%

“…In lieu of a gold standard, different forms of cluster stability have been used as a surrogate to assess performance. Stability estimates capture how stable the clusterings are over several different representations of the data, which are derived through subsetting, cross‐validation, data noising or re‐sampling, among others [4, 12, 14, 15, 20, 22, 26, 36–38].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Yu et al [38] developed an approach to cluster stability estimation. As with other bootstrap approaches to stability, an overall estimation of stability can provide an assessment of cluster quality [12, 14].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the cluster stability framework of Yu et al [38] is extended to the problem of module detection in a graph. This approach to stability utilizes the bootstrap [13] for data re‐sampling, construction of a graph, and subsequent module detection.…”

Section: Introductionmentioning

confidence: 99%

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A framework for stability‐based module detection in correlation graphs

Tian

Blair

et al. 2021

Statistical Analysis

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Graphs can be used to represent the direct and indirect relationships between variables, and elucidate complex relationships and interdependencies. Detecting structure within a graph is a challenging problem. This problem is studied over a range of fields and is sometimes termed community detection, module detection, or graph partitioning. A popular class of algorithms for module detection relies on optimizing a function of modularity to identify the structure. In practice, graphs are often learned from the data, and thus prone to uncertainty. In these settings, the uncertainty of the network structure can become exaggerated by giving unreliable estimates of the module structure. In this work, we begin to address this challenge through the use of a nonparametric bootstrap approach to assessing the stability of module detection in a graph. Estimates of stability are presented at the level of the individual node, the inferred modules, and as an overall measure of performance for module detection in a given graph. Furthermore, bootstrap stability estimates are derived for complexity parameter selection that ultimately defines a graph from data in a way that optimizes stability. This approach is utilized in connection with correlation graphs but is generalizable to other graphs that are defined through the use of dissimilarity measures. We demonstrate our approach using a broad range of simulations and on a metabolomics dataset from the Beijing Olympics Air Pollution study. These approaches are implemented using bootcluster package that is available in the R programming language.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A framework for stability‐based module detection in correlation graphs

Tian

Blair

et al. 2021

Statistical Analysis

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“…The work of Koepke and Clarke is an exception as the stability can be computed at the levels of individual points, clusters, or overall partitions. More recently, Yu et al also proposed to measure stability at the three levels using bootstrap resampling. Another exception is made by Hennig , who proposed a measure to evaluate the stability of individual clusters.…”

Section: Introductionmentioning

confidence: 99%

Optimal transport, mean partition, and uncertainty assessment in cluster analysis

Seo

Lin

2019

Statistical Analysis

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In scientific data analysis, clusters identified computationally often substantiate existing hypotheses or motivate new ones. Yet the combinatorial nature of the clustering result, which is a partition rather than a set of parameters or a function, blurs notions of mean, and variance. This intrinsic difficulty hinders the development of methods to improve clustering by aggregation or to assess the uncertainty of clusters generated. We overcome that barrier by aligning clusters via optimal transport. Equipped with this technique, we propose a new algorithm to enhance clustering by any baseline method using bootstrap samples. Cluster alignment enables us to quantify variation in the clustering result at the levels of both overall partitions and individual clusters. Set relationships between clusters such as one‐to‐one match, split, and merge can be revealed. A covering point set for each cluster, a concept kin to the confidence interval, is proposed. The tools we have developed here will help address the crucial question of whether any cluster is an intrinsic or spurious pattern. Experimental results on both simulated and real data sets are provided. The corresponding R package OTclust is available on CRAN.

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Unsupervised and Semisupervised Learning

Pisztora

2021

Wiley StatsRef: Statistics Reference Online

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Methodologies for unsupervised and semisupervised learning are reviewed. For unsupervised learning, or clustering, the focus is on mixture‐model‐based approaches under both the classic and mode association frameworks. High‐dimensional data pose a major challenge for clustering. We thus discuss in detail variable selection and the hidden Markov model on variable blocks, which exploits a graph structure to simplify the dependence among variables. We also present topics that emerged relatively recently such as clustering distributional data under the Wasserstein metric and uncertainty assessment for cluster analysis. Semisupervised learning has attracted growing interest in the machine learning community in recent years. We review foundational approaches including self‐training, semisupervised generative models, and graphical models. We then describe in greater depth entropy minimization, consistency regularization, and mixup augmentation, methods that are utilized in state‐of‐the‐art models such as MixMatch.

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Bootstrapping estimates of stability for clusters, observations and model selection

Cited by 32 publications

References 15 publications

A framework for stability‐based module detection in correlation graphs

A framework for stability‐based module detection in correlation graphs

Optimal transport, mean partition, and uncertainty assessment in cluster analysis

Unsupervised and Semisupervised Learning

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