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Abstract 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.
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Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise
Community detection tasks have received a lot of attention across statistics, machine learning, and information theory with work concentrating on providing theoretical guarantees for different methodological approaches to the stochastic block model. Recent work on community detection has focused on modeling the spectral embedding of a network using Gaussian mixture models (GMMs) in scaling regimes where the ability to detect community memberships improves with the size of the network. However, these regimes are not very realistic. This paper provides tractable methodology motivated by new theoretical results for networks with non-vanishing noise. We present a procedure for community detection using novel GMMs that incorporate truncation and shrinkage effects. We provide empirical validation of this new representation as well as experimental results using a large email dataset.
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- Award ID(s):
- 1750362
- PAR ID:
- 10139969
- Date Published:
- Journal Name:
- 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
- Page Range / eLocation ID:
- 699 to 703
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CAMSAP45676.2019.9022612
