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Generative models based on latent variables, such as generative adversarial networks (GANs) and variationalauto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields.However, many data such as natural images usually do not populate the ambient Euclidean space but insteadreside in a lower-dimensional manifold. Thus an inappropriate choice of the latent dimension fails to uncoverthe structure of the data, possibly resulting in mismatch of latent representations and poor generativequalities. Toward addressing these problems, we propose a novel framework called the latent WassersteinGAN (LWGAN) that fuses the Wasserstein auto-encoder and the Wasserstein GAN so that the intrinsicdimension of the data manifold can be adaptively learned by a modified informative latent distribution. Weprove that there exist an encoder network and a generator network in such a way that the intrinsic dimensionof the learned encoding distribution is equal to the dimension of the data manifold. We theoreticallyestablish that our estimated intrinsic dimension is a consistent estimate of the true dimension of the datamanifold. Meanwhile, we provide an upper bound on the generalization error of LWGAN, implying that weforce the synthetic data distribution to be similar to the real data distribution from a population perspective.Comprehensive empirical experiments verify our framework and show that LWGAN is able to identify thecorrect intrinsic dimension under several scenarios, and simultaneously generate high-quality syntheticdata by sampling from the learned latent distribution. Supplementary materials for this article are availableonline, including a standardized description of the materials available for reproducing the work.
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Differentiable VQ-VAE's for Robust White Matter Streamline Encodings
Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of encoder architectures only perform dimension reduction on single streamlines as opposed to a full bundle of streamlines. This is a severe limitation of the encoder architecture that completely disregards the global geometric structure of streamlines at the expense of individual fibers. Moreover, the latent space may not be well structured which leads to doubt into their interpretability. In this paper we propose a novel Differentiable Vector Quantized Variational Autoencoder, which are engineered to ingest entire bundles of streamlines as single data-point and provides reliable trustworthy encodings that can then be later used to analyze streamlines in the latent space. Comparisons with several state of the art Autoencoders demonstrate superior performance in both encoding and synthesis.
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- Award ID(s):
- 2015577
- PAR ID:
- 10561803
- Publisher / Repository:
- IEEE International Symposium on Biomedical Imaging (ISBI)
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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