New methods of complex matrix factorization for single-channel source separation and analysis

Throughout the day, people are constantly bombarded by a variety of sounds. Humans with normal hearing are able to easily and automatically cut through the noise to focus on the sources of interest, a phenomenon known as the "cocktail party effect.'' This ability, while easy for humans, is typically very challenging for computers. In this dissertation, we will focus on the task of single-channel source separation via matrix factorization, a state-of-the-art family of algorithms. In this work, we present three primary contributions. First, we explore how cost function and parameter choice affect source separation performance, as well as discuss the advantages and disadvantages of each matrix factorization model. Second, we propose a new model, complex matrix factorization with intra-source additivity, that has significant advantages over the current state-of-the-art matrix factorization models. Third, we propose the complex probabilistic latent component analysis algorithm, which can be used to transform complex-valued data into nonnegative data in such a way that the underlying structure in the complex data is preserved. We also show how these new methods can be applied to single-channel source separation and compare them with the current state-of-the-art methods.