Global Convergence of FastICA: Theoretical Analysis and Practical Considerations

摘要

FastICA is now a popular algorithm for independent component analysis (ICA) based on negentropy. However the convergence of FastICA has not been comprehensively studied. This paper provides the global convergence analysis of FastICA and some practical considerations on algorithmic implementations. The exhaustive equilibria are obtained from the iteration first. Then the global convergence property is given on the 2-channel system with cubic nonlinearity function, and the results can also be generalized to the multi-channel system. In addition, two practical considerations, e.g. the convergence threshold for demixing matrix and independence restriction for sources, are evaluated and the influence on the separation solutions is illustrated respectively.