This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the l2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features.

Problems in which abnormal or novel situations should be detected can be approached by describing the domain of the class of typical examples. These applications come from the areas of machine diagnostics, fault detection, illness identification or, in principle, refer to any problem where little knowledge is available outside the typical class. In this paper we explain why proximities are natural representations for domain descriptors and we propose a simple one-class classifier for dissimilarity representations. By the use of linear programming an efficient one-class description can be found, based on a small number of prototype objects. This classifier can be made (1) more robust by transforming the dissimilarities and (2) cheaper to compute by using a reduced representation set. Finally, a comparison to a comparable one-class classifier by Campbell and Bennett is given.

Problems in which abnormal or novel situations should be detected can be approached by describing the domain of the class of typical examples. Theseapplications come from the areas of machine diagnostics, fault detection, illness identification or, in principle, refer to any problem wherelittle knowledge is available outside the typical class. In this paper we explain why proximities are natural representations for domain descriptors and we propose a simple one-class classifier for dissimilarity representations. By the use of linear programming an efficient one-class description can be found, based on a small number of prototype objects. This classifier can be made (1) more robust by transforming the dissimilarities and(2) cheaper to compute by using a reduced representation set. Finally, a comparison to a comparable one-class classifier by Campbell and Bennett is given.