SeGMA: Semi-Supervised Gaussian Mixture Autoencoder

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Abstract
We propose a semi-supervised generative model, SeGMA, which learns a joint probability distribution of data and their classes and is implemented in a typical Wasserstein autoencoder framework. We choose a mixture of Gaussians as a target distribution in latent space, which provides a natural splitting of data into clusters. To connect Gaussian components with correct classes, we use a small amount of labeled data and a Gaussian classifier induced by the target distribution. SeGMA is optimized efficiently due to the use of the Cramer-Wold distance as a maximum mean discrepancy penalty, which yields a closed-form expression for a mixture of spherical Gaussian components and, thus, obviates the need of sampling. While SeGMA preserves all properties of its semi-supervised predecessors and achieves at least as good generative performance on standard benchmark data sets, it presents additional features: 1) interpolation between any pair of points in the latent space produces realistically looking samples; 2) combining the interpolation property with disentangling of class and style information, SeGMA is able to perform continuous style transfer from one class to another; and 3) it is possible to change the intensity of class characteristics in a data point by moving the latent representation of the data point away from specific Gaussian components.
Funding Information
  • Narodowe Centrum Nauki (2016/21/D/ST6/00980)
  • research project Bio-Inspired Artificial Neural Networks (POIR.04.04.00-00-14DE/18-00 within the Team-Net Program of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund)
  • Narodowe Centrum Nauki (2017/25/B/ST6/01271)
  • COMET Program within the K2 Center Integrated Computational Material Process and Product Engineering IC-MPPE (859480)
  • Austrian Federal Ministries for Transport Innovation and Technology BMVIT
  • Digital and Economic Affairs BMDW represented by the Austrian Research Promotion Agency FFG and the federal states of Styria Upper Austria and Tyrol
  • Austrian COMET Program---Competence Centers for Excellent Technologies---under the auspices of the Austrian Federal Ministry for Climate Action Environment Energy Mobility Innovation
  • Technology the Austrian Federal Ministry of Digital and Economic Affairs and by the State of Styria

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