Article (Scientific journals)
PHom-GeM: Persistent Homology for Generative Models
Charlier, Jérémy Henri J.; State, Radu; Hilger, Jean
2019In The 6th Swiss Conference on Data Science
Peer reviewed
 

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Keywords :
Neural Networks; Optimal Transport; Algebraic Topology
Abstract :
[en] Generative neural network models, including Generative Adversarial Network (GAN) and Auto-Encoders (AE), are among the most popular neural network models to generate adversarial data. The GAN model is composed of a generator that produces synthetic data and of a discriminator that discriminates between the generator’s output and the true data. AE consist of an encoder which maps the model distribution to a latent manifold and of a decoder which maps the latent manifold to a reconstructed distribution. However, generative models are known to provoke chaotically scattered reconstructed distribution during their training, and consequently, incomplete generated adversarial distributions. Current distance measures fail to address this problem because they are not able to acknowledge the shape of the data manifold, i.e. its topological features, and the scale at which the manifold should be analyzed. We propose Persistent Homology for Generative Models, PHom-GeM, a new methodology to assess and measure the distribution of a generative model. PHom-GeM minimizes an objective function between the true and the reconstructed distributions and uses persistent homology, the study of the topological features of a space at different spatial resolutions, to compare the nature of the true and the generated distributions. Our experiments underline the potential of persistent homology for Wasserstein GAN in comparison to Wasserstein AE and Variational AE. The experiments are conducted on a real-world data set particularly challenging for traditional distance measures and generative neural network models. PHom-GeM is the first methodology to propose a topological distance measure, the bottleneck distance, for generative models used to compare adversarial samples in the context of credit card transactions.
Research center :
Interdisciplinary Centre for Security, Reliability and Trust (SnT) > Services and Data management research group (SEDAN)
Disciplines :
Computer science
Author, co-author :
Charlier, Jérémy Henri J. ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
State, Radu  ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Hilger, Jean ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
External co-authors :
no
Language :
English
Title :
PHom-GeM: Persistent Homology for Generative Models
Publication date :
June 2019
Journal title :
The 6th Swiss Conference on Data Science
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 15 August 2019

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