One key challenge encountered in single-cell data clustering is to combine clustering results of data sets acquired from multiple sources. We propose to represent the clustering result of each data set by a Gaussian mixture model (GMM) and produce an integrated result based on the notion of Wasserstein barycenter. However, the precise barycenter of GMMs, a distribution on the same sample space, is computationally infeasible to solve. Importantly, the barycenter of GMMs may not be a GMM containing a reasonable number of components. We thus propose to use the minimized aggregated Wasserstein (MAW) distance to approximate the Wasserstein metric and develop a new algorithm for computing the barycenter of GMMs under MAW. Recent theoretical advances further justify using the MAW distance as an approximation for the Wasserstein metric between GMMs. We also prove that the MAW barycenter of GMMs has the same expectation as the Wasserstein barycenter. Our proposed algorithm for clustering integration scales well with the data dimension and the number of mixture components, with complexity independent of data size. We demonstrate that the new method achieves better clustering results on several single-cell RNA-seq data sets than some other popular methods.
In the form of multidimensional arrays, tensor data have become increasingly prevalent in modern scientific studies and biomedical applications such as computational biology, brain imaging analysis, and process monitoring system. These data are intrinsically heterogeneous with complex dependencies and structure. Therefore, ad‐hoc dimension reduction methods on tensor data may lack statistical efficiency and can obscure essential findings. Model‐based clustering is a cornerstone of multivariate statistics and unsupervised learning; however, existing methods and algorithms are not designed for tensor‐variate samples. In this article, we propose a tensor envelope mixture model (TEMM) for simultaneous clustering and multiway dimension reduction of tensor data. TEMM incorporates tensor‐structure‐preserving dimension reduction into mixture modeling and drastically reduces the number of free parameters and estimative variability. An expectation‐maximization‐type algorithm is developed to obtain likelihood‐based estimators of the cluster means and covariances, which are jointly parameterized and constrained onto a series of lower dimensional subspaces known as the tensor envelopes. We demonstrate the encouraging empirical performance of the proposed method in extensive simulation studies and a real data application in comparison with existing vector and tensor clustering methods.
more » « less- NSF-PAR ID:
- 10397033
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 78
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 1067-1079
- Size(s):
- p. 1067-1079
- Sponsoring Org:
- National Science Foundation
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History: Bianca Maria Colosimo served as the senior editor for this article
Funding: This work was supported by National Science Foundation [2229245].
Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://github.com/czhou9/Code-and-Data-for-IJDS and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.x022 ).
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