FastICA and SOBI are two widely-known algorithms for Independent Components Analysis (ICA). EFICA and WASOBI are enhanced versions thereof (respectively), asymptotically optimal under certain conditions. EFICA can only exploit non-Gaussianity of the sources, disregarding any time-structure, whereas WASOBI only exploits time-structure, ignoring the sources’ statistical distributions. However, realistic mixtures are often composed of sources which exhibit both non-Gaussianity and diverse time-structure, rendering EFICA and WASOBI severely suboptimal. Algorithms COMBI and MULTI-COMBI offer novel schemes for combining EFICA and WASOBI, enabling to fuse the strengths of both techniques. Tested for separating Gaussian and non-Gaussian autoregressive sources, the algorithms are shown to outperform competing algorithms aimed at similar mixtures.
Some important facts:
- EFICA cannot separate sources that do not have any spatial-structure, e.g. any gaussian sources. WASOBI cannot separate sources with the same spectra or sources that do not exhibit any time-structure. More precisely, at most one of the original signals is allowed not to fulfill the estimability conditions for the corresponding method.
- WASOBI and EFICA are optimal within the frame of corresponding models of signals. Therefore, their proper fusion may yield promising performance when the original data possess both spatial and time structure.
- Their theoretical performances, in terms of interference-to-signal ratio, are known and are easily applicable. Therefore, computationally expensive bootstrap methods are not required when estimating separation accuracy, which is necessary for hybrid algorithm control.
- MULTI-COMBI is an enhanced version of COMBI mitigating its limited ability to reveal multidimensional components in the mixing. A typical example of multidimensional component that is well identifiable by WASOBI but cannot be further separated into original signals therewith, is a subspace of independent non-Gaussian signals with the same spectra (see the simulation example below).