Unsupervised signal separation: a study on the applicability of Generative Adversarial Networks and on nonlinear models based on the Choquet Integral

Abstract

Blind source separation (BSS) refers to the task of recovering a set of source signals in an unsupervised fashion, that is, by only considering a set of mixtures of these sources. This field, which has been extensively studied in signal processing and fields related to data analysis, encompasses a wide range of applications, from the separation of biomedical signals to feature extraction in the context of machine learning. In this project, we address a challenging problem in BSS: the case of nonlinear mixtures. Our main aim is to develop BSS methods for novel mixing models. In a first moment, we shall investigate mixing models based on the Choquet integral. Our motivation comes from the fact that the parameters of the Choquet integral allow one to quantify the contributions of each attribute individually as well as of coalitions of them; such a feature has been pursued in the search for interpretable nonlinear models. In a second moment, we shall study the applicability of generative adversarial networks (GAN) in BSS. These networks have been applied in the context of unsupervised learning and provide a high degree of flexibility, which can be useful in BSS problems. We will assess the proposed methods by considering real applications in two different domains: separation of chemical signals and image separation. Moreover, we shall apply our proposal in the problem of searching disentangled representations of data, an emerging topic in the field of machine learning. (AU)