Dimension reduction as a deflation method in ICA

• Published in: IEEE signal processing letters Vol. 13; no. 1; pp. 45 - 48
• Main Authors: Kun Zhang, Kun Zhang, Lai-Wan Chan, Lai-Wan Chan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2006; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Closed-form solution; Computation; Constraint optimization; Convergence; Councils; Decorrelation; dimension-reduction; Entropy; Gram-Schmidt-like decorrelation; Independent component analysis; independent component analysis (ICA); Mathematical analysis; Mutual information; one-unit objective function; Optimization; Optimization methods; Reduction; Signal processing algorithms; Vectors (mathematics); Weight reduction
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2005.860541

In independent component analysis (ICA), when using the one-unit contrast function optimization approach to estimate independent components one by one, the constraint of uncorrelatedness between independent components prevents the algorithm from converging to the previously found components. A popular way to achieve uncorrelatedness is the Gram-Schmidt-like decorrelation scheme. In fact, uncorrelatedness between independent components can be achieved by reducing the degree of freedom in the unknown parameter set of the de-mixing matrix. In this letter, we propose to exploit the dimension-reduction technique to exactly enforce uncorrelatedness between difference independent components. The advantage of this method is that dimension reduction of the observations and de-mixing weight vectors makes the computation complexity lower and produces a faster convergence. Hence, our method results in a faster algorithm in computation of ICA.