ADIS - A robust pursuit algorithm for probabilistic, constrained and non-square blind source separation with application to fMRI

In this article, we develop an algorithm for probabilistic and constrained projection pursuit. Our algorithm called ADIS (automated decomposition into sources) accepts arbitrary non-linear contrast functions and constraints from the user and performs non-square blind source separation (BSS). In the first stage, we estimate the latent dimensionality using a combination of bootstrap and cross validation techniques. In the second stage, we apply our state-of-the-art optimization algorithm to perform BSS. We validate the latent dimensionality estimation procedure via simulations on sources with different kurtosis excess properties. Our optimization algorithm is benchmarked via standard benchmarks from GAMS performance library. We develop two different algorithmic frameworks for improving the quality of local solution for BSS. Our algorithm also outputs extensive convergence diagnostics that validate the convergence to an optimal solution for each extracted component. The quality of extracted sources from ADIS is compared to other well known algorithms such as Fixed Point ICA (FPICA), efficient Fast ICA (EFICA), Joint Approximate Diagonalization (JADE) and others using the ICALAB toolbox for algorithm comparison. In several cases, ADIS outperforms these algorithms. Finally we apply our algorithm to a standard functional MRI data-set as a case study.