Independent component ordering in ICA time series analysis

Independent component analysis (ICA) has provided a new tool to analyze time series, which also gives rise to a question - how to order independent components? In the literature, some methods (Back and Trappenberg, Proceedings of International Joint Conference on Neural Networks, Vol. 2, 1999, pp. 989-992; Hyvärinen, Neural Computing Surveys 2 (1999) 94; Back and Weigend, Int. J. Neural Systems 8(4) (1997) 473) have been suggested to decide the order based on each individual component without considering their interactions on the observed series. In this paper, we propose an alternative approach to order the components according to their joint contributions in data reconstruction, which naturally leads the component ordering to a typical combinatorial optimization problem, whereby the underlying optimum ordering can be found in an exhaustive way. To save computing costs, we also present a fast approximate search algorithm. The accompanying experiments have shown the outperformance of this new approach in comparison with an existing method.