Quaternion-valued recurrent projection neural networks on unit quaternions

Neural Networks for Quaternion-valued Function Approximation

In the paper a new structure of Multi-Layer Perceptron, able to deal with quaternion-valued signal, is proposed. A learning algorithm for the proposed Quaternion MLP (QMLP) is also derived. Such a neural network allows to interpolate functions of quaternion variable with a smaller number of connections with respect to the corresponding real valued MLP. INTRODUCTION In the last few years, neural...

Quaternion Valued Neural Networks and Nonlinear Adaptive Filters

A class of locally analytic transcendental functions suitable for nonlinear adaptive filtering and neural network filtering is proposed. Since the stringent standard analyticity conditions prevent full exploitation of nonlinear quaternionic models, we make use of local analyticity conditions to provide a framework for a generic extension of nonlinear learning algorithms from the real and comple...

Scaled Conjugate Gradient Learning for Quaternion-Valued Neural Networks

A class of quaternion valued affine projection algorithms

The strictly linear quaternion valued affine projection algorithm (QAPA) and its widely linear counterpart (WLQAPA) are introduced, in order to provide fast converging stochastic gradient learning in the quaternion domain, for the processing of both second order circular (proper) and second order noncircular (improper) signals. This is achieved based on the recent advances in augmented quaterni...

Minimal Gated Unit for Recurrent Neural Networks

Recently recurrent neural networks (RNN) has been very successful in handling sequence data. However, understanding RNN and finding the best practices for RNN is a difficult task, partly because there are many competing and complex hidden units (such as LSTM and GRU). We propose a gated unit for RNN, named as Minimal Gated Unit (MGU), since it only contains one gate, which is a minimal design a...