Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

Abstract

Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper. This simple technique consists of performing exact line search optimization of the kurtosis contrast function. The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial. This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration. Among other practical benefits, RobustICA can avoid prewhitening and deals with real- and complex-valued mixtures of possibly noncircular sources alike. The absence of prewhitening improves asymptotic performance. The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records. These features are demonstrated by a comparative numerical analysis on synthetic data. RobustICA's capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique.

Analysis of complex-valued functional magnetic resonance imaging data: are we just going through a “phase”?

“…As expected, in the presence of noncircular sources, the performance of those algorithms suffer. There are now a number of powerful solutions available for complex ICA for the general case where sources can be either circular or noncircular, e.g., [36,38,41,43,44,80] as well as those that adapt to different source distributions using general models such as complex generalized Gaussian distributions [43,81], or more flexible models through efficient entropy estimation techniques as in ICA by entropy bound minimization (ICA-EBM) [70].…”

Application of Single Channel Blind Separation Algorithm Based on EEMD-PCA-RobustICA in Bearing Fault Diagnosis

“…RobustICA uses the independent component analysis algorithm based on kur-tosis and optimal step length to search the global optimal step by using the sentinel as the control function, find the solution matrix W , and calculate the approximate value of the original signal [7].…”

Independent Component Analysis in ECG Signal Processing

“…ECG based diagnostics applications in which ICA has been utilized include, e.g., classification of ECG beats (Chou & Yu, 2007;Huang, et al, 2010), analysis of parameterized ECG signals (Chawla, 2007;Tanskanen et al, 2006aTanskanen et al, , 2006b, heart rate variability analysis (Zhangyong et al, 2005), arrhythmia estimation (Castells et al, 2005;Jiang et al, 2006;Llinares & Igual, 2009), and atrial fibrillation extraction and analysis (Rieta et al, 2004;Stridh & Sörnmo, 2001;Zarzoso & Comon, 2010). A nice diagram of an atrial source separation system has been presented by Castells et al (2005).…”