Fault diagnosis of a railway device using semi-supervised independent factor analysis with mixing constraints

Independent factor analysis (IFA) defines a generative model for observed data that are assumed to be linear mixtures of some unknown non-Gaussian, mutually independent latent variables (also called sources or independent components). The probability density function of each individual latent variable is modelled by a mixture of Gaussians. Learning in the context of this model is usually performed within an unsupervised framework in which only unlabelled samples are used. Both the mixing matrix and the parameters of latent variable densities are learned from the observed data. This paper investigates the possibility of estimating an IFA model in a noiseless setting when two kinds of prior information are incorporated, namely constraints on the mixing process and partial knowledge on the cluster membership of some training samples. Semi-supervised or partially supervised learning frameworks can thus be handled. The investigation of these two kinds of prior information was motivated by a real-world application concerning the fault diagnosis of railway track circuits. Simulated data, resulting from both these applications, are provided to demonstrate the capacity of our approach to enhance estimation accuracy and remove the indeterminacy commonly encountered in unsupervised IFA, such as source permutations.