Generative adversarial networks (GANs) have shown remarkable success in the generation of data from natural data manifolds such as images. In several scenarios, it is desirable that generated data is well-clustered, especially when there is severe class imbalance. In this paper, we focus on the problem of clustering in the generated space of GANs and uncover its relationship with the characteristics of the latent space. We derive from first principles, the necessary and sufficient conditions needed to achieve faithful clustering in the GAN framework: (i) presence of a multimodal latent space with adjustable priors, (ii) existence of a latent space inversion mechanism and, (iii) imposition of the desired cluster priors on the latent space. We also identify the GAN models in the literature that partially satisfy these conditions and demonstrate the importance of all the components required, through ablative studies on multiple real-world image datasets. Additionally, we describe a procedure to construct a multimodal latent space which facilitates learning of cluster priors with sparse supervision. Codes for our implementation is available at https://github.com/NEMGAN/NEMGAN-P.

中文翻译：

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潜在结构对 GAN 聚类的影响

生成对抗网络 (GAN) 在从自然数据流形（如图像）生成数据方面取得了显着的成功。在几种情况下，希望生成的数据很好地聚类，尤其是在存在严重的类不平衡时。在本文中，我们关注 GAN 生成空间中的聚类问题，并揭示其与潜在空间特征的关系。我们从第一原则得出，在 GAN 框架中实现忠实聚类所需的必要和充分条件：（i）存在具有可调先验的多模态潜在空间，（ii）存在潜在空间反转机制，以及（iii）强加潜在空间上所需的聚类先验。我们还确定了文献中部分满足这些条件的 GAN 模型，并通过对多个真实世界图像数据集的烧蚀研究证明了所有所需组件的重要性。此外，我们描述了一种构建多模态潜在空间的过程，该过程有助于在稀疏监督下学习聚类先验。我们的实现代码可在 https://github.com/NEMGAN/NEMGAN-P 上找到。