  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.
