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An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders.

Eleonora Grassucci1, Danilo Comminiello1, Aurelio Uncini1

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Summary
This summary is machine-generated.

This study introduces the Quaternion Variational Autoencoder (QVAE), a novel deep generative model. QVAEs effectively model quaternion data distributions, even when the data is improper, enhancing latent space entropy.

Keywords:
generative learningpropernessquaternion neural networkssecond-order circularityvariational autoencoder

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Area of Science:

  • Deep learning
  • Information theory
  • Quaternion analysis

Background:

  • Variational autoencoders (VAEs) are powerful deep generative models for various data types.
  • Quaternion domain modeling offers advanced capabilities for complex data.
  • The Quaternion Variational Autoencoder (QVAE) leverages H-proper signal statistics.

Purpose of the Study:

  • Analyze the QVAE from an information-theoretic viewpoint.
  • Evaluate the QVAE's ability to approximate both H-proper and improper quaternion distributions.
  • Investigate the impact of input signal improperness on entropy.

Main Methods:

  • Information-theoretic analysis of the QVAE.
  • Experimental evaluation on diverse quaternion signal datasets.
  • Assessment of latent space properties, including entropy and improperness.

Main Results:

  • QVAEs demonstrate effective modeling of quaternion input distributions.
  • The model learns and adapts to the improperness of quaternion data.
  • Latent space entropy is observed to increase during the modeling process.

Conclusions:

  • The proposed QVAE is capable of modeling complex quaternion data distributions.
  • Proper QVAEs provide a good approximation for improper quaternion input data.
  • QVAE analysis offers insights into information-theoretic properties of quaternion generative models.