Independent Vector Analysis: Identification Conditions and Performance Bounds

• Published in: IEEE transactions on signal processing Vol. 62; no. 17; pp. 4399 - 4410
• Main Authors: Anderson, Matthew, Geng-Shen Fu, Phlypo, Ronald, Adali, Tulay
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-09-2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Blind source separation; Correlation; Covariance matrices; Cramér-Rao bound; Demixing; Engineering Sciences; Entropy; Formulations; identification conditions; independent vector analysis; Linear programming; Lower bounds; Mutual information; Nonlinearity; Signal and Image processing; Signal processing; Tin; Transaction processing; Vector analysis; Vectors
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2333554

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been a subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is identification of dependent sources between datasets. Thus, we provide additional conditions for when the arbitrary ordering of the estimated sources can be common across datasets. Performance bounds in terms of the Cramér-Rao lower bound are also provided for demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.