The MSE reconstruction criterion for independent component ordering in ICA timeseries analysis

It has been shown that the dominant independent components obtained by independent component analysis (ICA) can reveal more underlying structure of the series than principal component analysis (Back and Weigend 1997). To find those dominant components, all the independent components are listed in an appropriate order and then a subset of components is selected according to the order. In Back and Weigend (1997), the order is determined based on the L1 norm of each individual component without considering their interactive contribution to the observed time series. In this paper, we propose to order the components according to their contribution in the mean square error (MSE) between the observed time series and the reconstruction from these components, which leads to a typical combinational optimization problem. To avoid exhaustive search, we use an sub-optimum algorithm called Testing-and-Acceptance (TnA) to find the order. Experiments on foreign exchange rates have shown that the TnA approach outperforms the L1 norm method.