Augmented complex matrix factorisation

A novel framework for the factorisation of complex-valued data is derived using recent developments in complex statistics. Unlike existing factorisation tools the algorithms can cater for noncircularity of the input a necessary feature in applications for modelling real-world data. It is furthermore shown how the framework can be constrained to incorporate nonnegativity, helping generate results which allow a more realistic interpretation. Simulations illustrate the usefulness and enhanced accuracy for modelling synthetic data and a mixture of acoustic stimuli.