Due to their capabilities, quaternion-valued learning methods have been applied in several applications, including spoken language understanding, color image processing, 3D audio, speech recognition, image generation, quantum mechanics, risk diversification, gait data analysis. Another fundamental property of quaternion-valued learning is the Hamilton product, which has recently favored the proliferation of convolutional neural networks in the quaternion domain. This properties have been widely exploited in shallow learning models, such as linear and nonlinear adaptive filters. The basic approach on which relies the QVAE is the learning in the quaternion domain, which results in significant advantages in the presence of multidimensional input data (mainly 3D and 4D data) showing some inter-channel correlations. Among the most recent VAE models, we focus on the quaternion-valued variational autoencoder (QVAE), which exploits the properties of quaternion algebra to improve performance, on one hand, and to significantly reduce the overall number of network parameters, on the other hand.
Recent advances on VAEs focus both on theoretical aspects, such as the improvement of the stochastic inference approach, and on architectural aspects, such as the use of different types of latent variables to learn local and global structures, the definition of hierarchical schemes, rather than the use of a multi-agent generator. This has led VAEs to be used in several fields of applications, including high-quality image generation, speech enhancement, music style transfer, data augmentation, 3D scene generation, gesture similarity analysis, text generation and sequential recommendation, among others.
The main advantages of the VAEs rely on their capability of learning smooth latent representations of the input data. Īmong such generative methods, the variational autoencoders (VAEs) have been proven to perform stochastic variational inference and learning even for large datasets and intractable posterior distributions. They have been successfully employed in a wide variety of applications, such as image-to-image translation, image fusion, face de-identification, natural language generation, data augmentation on ancient handwritten characters, MRI super-resolution, brain tumor growth prediction, generative modeling of structured-data. Generative learning models have been recently gained considerable attention due to their surprising performance in producing highly realistic signals of various types. The proposed analysis will prove that proper QVAEs can be employed with a good approximation even when the quaternion input data are improper. We conduct experiments on a substantial set of quaternion signals, for each of which the QVAE shows the ability of modelling the input distribution, while learning the improperness and increasing the entropy of the latent space.
In this paper, we analyze the QVAE under an information-theoretic perspective, studying the ability of the H-proper model to approximate improper distributions as well as the built-in H-proper ones and the loss of entropy due to the improperness of the input signal.
A novel variational autoncoder in the quaternion domain H, namely the QVAE, has been recently proposed, leveraging the augmented second order statics of H-proper signals. Variational autoencoders are deep generative models that have recently received a great deal of attention due to their ability to model the latent distribution of any kind of input such as images and audio signals, among others.
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