Generalised Fastica for Independent Subspace Analysis

Independent subspace analysis (ISA) was developed as an extension of independent component analysis (ICA) when statistical independences are assumed to exist between groups of components rather than between individual components. Due to the superiority of FastICA against other linear ICA algorithms, an intuitive analogy, the so-called FastISA algorithm, has been proposed to solve the problem of ISA. Experimental evidences so far have shown the capability of FastISA, regardless of any independence criterion. Since standard FastICA can be viewed as a special case of an approximate Newton ICA method and moreover can be generalised as a scalar shifted fixed point algorithm, in this work, we propose two new classes of ISA algorithms, an approximate Newton-like ISA method and a matrix shifted fixed point ISA algorithm on the Grabmann manifold. As an aside, FastISA is a special case in the class of matrix shifted fixed point ISA algorithms. Performances of the proposed algorithms are investigated by numerical experiments.