Abstract
Quaternions have found applications in various machine learning algorithms, however these algorithms usually do not exploit the complete available second order statistics of quaternions. To this end, we present the so-called quaternion'augmented'statistics to show how to make use of the complete second order statistical information available within the quaternion domain H. Next, as a case study, the widely linear model, which operates on the quaternion augmented statistics, is employed to enhance the performance of the Quaternion Least Mean Square algorithm. Simulations on time series prediction of both chaotic and non-stationary real world data support the approach.