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We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fréchet Inception Distance (FID). FID assumes that images featurized using the penultimate layer of Inception-v3 follow a Gaussian distribution, an assumption which cannot be violated if we wish to use FID as a metric. However, we show that Inception-v3 features of the ImageNet dataset are not Gaussian; in particular, every single marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using Inception-v3 (or another classifier) to featurize the images, estimate two GMMs, and use the restricted 2-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to imperceptible image perturbations. By modelling the non-Gaussian features obtained from Inception-v3 as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.
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Multisource Single-Cell Data Integration by MAW Barycenter for Gaussian Mixture Models
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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- Award ID(s):
- 2013905
- PAR ID:
- 10485797
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 2
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 866-877
- Size(s):
- p. 866-877
- Sponsoring Org:
- National Science Foundation
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