No abstract

No abstract

No abstract

The use of quaternion data can provide benefit in applications like robotics and image recognition, and particularly for performing transforms in 3-D space. Here, we describe a kernel adaptive algorithm for quaternions. A least mean square (LMS)-based method was used, resulting in the derivation of the quaternion kernel LMS (Quat-KLMS) algorithm. Deriving this algorithm required describing the idea of a quaternion reproducing kernel Hilbert space (RKHS), as well as kernel functions suitable with quaternions. A modified HR calculus for Hilbert spaces was used to find the gradient of cost functions defined on a quaternion RKHS. In addition, the use of widely linear (or augmented) filtering is proposed to improve performance. The benefit of the Quat-KLMS and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations.

A recent paper titled "The Complex Gaussian Kernel LMS Algorithm" published by Bouboulis and Theodoridis introduced a complex version of the Gaussian kernel LMS (KLMS) algorithm. In this paper, we extend the concepts of complex and complexified RKHS spaces to develop suitable complex Kernel based adaptive algorithms using the Affine projection algorithm (KAPA) method. We apply the complex Gaussian kernel here, as well as develop APA-based algorithms using other suitable complex kernels. We evaluate the performance of the new algorithms using practical simulation applications. The complex KAPA algorithms are seen to outperform their LMS-based counterparts, particularly for applications where convergence rate is important.

No abstract

Autoencoders are a self-supervised learning system where, during training, the output is an approximation of the input. Typically, autoencoders have three parts: Encoder (which produces a compressed latent space representation of the input data), the Latent Space (which retains the knowledge in the input data with reduced dimensionality but preserves maximum information) and the Decoder (which reconstructs the input data from the compressed latent space). Autoencoders have found wide applications in dimensionality reduction, object detection, image classification, and image denoising applications. Variational Autoencoders (VAEs) can be regarded as enhanced Autoencoders where a Bayesian approach is used to learn the probability distribution of the input data. VAEs have found wide applications in generating data for speech, images, and text. In this paper, we present a general comprehensive overview of variational autoencoders. We discuss problems with the VAEs and present several variants of the VAEs that attempt to provide solutions to the problems. We present applications of variational autoencoders for finance (a new and emerging field of application), speech/audio source separation, and biosignal applications. Experimental results are presented for an example of speech source separation to illustrate the powerful application of variants of VAE: VAE, β-VAE, and ITL-AE. We conclude the paper with a summary, and we identify possible areas of research in improving performance of VAEs in particular and deep generative models in general, of which VAEs and generative adversarial networks (GANs) are examples.

No abstract