A New Index for Measuring Inconsistencies in Independent Component Analysis Using Multi-sensor Data

In separation of source signals from signal mixtures and involving multiple sensors, an emerging useful method has been Independent Component Analysis (ICA). We examine one of the challenges of ICA – instability or inconsistency. The context of the study is ICA involving multiple sensors (time series data). Instability is said to occur when the independent components vary, each time when ICA is conducted. There is no solution to this, but there are performance indexes as attempts to quantify the problem. State-of-the-art software packages mention of the stability issue but there is no unanimity in the choice of performance indexes; the Icasso stability index and the Amari performance index are the most frequently used. Our contribution is that we propose a new index. The differentiating feature of this index is that it makes it possible for a proper comparison to be made upon repeated ICA on the same input because the new index works on the dispersion (range) of the fourth cumulants considering global maximum and minimum. Further, we test statistical significance. Future work in ICA may benefit from more consistent results and reporting of statistical significance.