Unifying factor analysis techniques, this paper introduces independent factor analysis (IFA) for source separation. Generalizing FA, PCA, and ICA, IFA handles noisy data and mixing scenarios where mixtures differ from sources. IFA is a two-step process: first, source densities, mixing matrix, and noise covariance are estimated by maximum likelihood using an expectation-maximization (EM) algorithm. Then, sources are reconstructed using an optimal nonlinear estimator. Each source is described by a mixture of gaussians, allowing analytical probabilistic calculations. A variational approximation handles cases with many sources. IFA can model multidimensional data and serve as a tool for nonlinear signal encoding. Beyond blind separation, IFA provides a means for learning arbitrary source densities, offering advantages over ICA and potential applications in data modeling and signal processing.
As a publication in Neural Computation, this paper aligns with the journal's focus on computational methods in neural systems and machine learning. By presenting the IFA algorithm, it contributes to research on source separation, signal processing, and data modeling, fitting the journal's scope.