Evaluating Model Misspecification in Independent Component Analysis

Abstract

Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.

Keywords: Convolutive Mixing; Independent Component Analysis; Model Misspecification.

Figure 1

Convolutive Mixture of Temporally Independent Sources: The temporal dependence test result of each observed chanel X_j is reported in (a). The first two chanels show clear temporal dependence with lag 1. Matrices of the absolute correlation between the true sources and estimated sources obtained by four ICA algorithms. The errors of diagonal elements and offdiagonal elements are reported in (b) and (c), respectively. The timelagICA performs better than other methods.

Figure 2

Convolutive Mixture of Temporally Independent Sources: The temporal dependence test result of each observed chanel X_j is reported in (a). All variables had significant temporal dependence with lag 1. Matrices of the absolute correlation between the true sources and estimated sources by four ICA algorithms were computed. The errors of diagonal elements and offdiagonal elements are reported in (b) and (c), respectively.

Figure 3

Multivariate AR mixture: The temporal dependence test result of each observed chanel X_j is reported in (a). First two varialbes do not have temporal dependence except two and five simulation runs at 0.05 significance level, respectively. The errors of diagonal elements and offdiagonal elements of the absolute correlation matrices are reported in (b) and (c), respectively.

Figure 4

Instantaneous Mixture of Autocorrelated Sources: The temporal dependence test result of each observed chanel X_j is reported in (a). All varialbes have significant temporal dependence. The errors of diagonal elements and offdiagonal elements of the absolute correlation matrices are reported in (b) and (c), respectively. The cICA-YW performed the best.

Figure 5

Instantaneous Mixtures: As we found from the previous simulation studies, cICA-YW performs the best, while other methods do not separate the sources well.

Figure 6

Convoluted Mixtures: timelagICA and cICA-YW do not separate sources well, while JADE and fastICA performed relatively better.

Figure 7

Spatial maps. We reordered the topography according to the clustering patterns of the correlations of the estimated sources.