Abstract
By utilizing a priori information available as reference, constrained independent component analysis (cICA) or independent component analysis with reference (ICA-R) achieves some advantages over other methods. However, ICA-R is very time-consuming; moreover, it is very difficult to determine its threshold parameter, once the value is improperly chosen the algorithm will fail to converge. In order to overcome these drawbacks, a very simple blind source extraction method, whose optimization function is simply the closeness measure between the desired output and its corresponding reference in ICA-R, is proposed in this paper. Experiments with synthesized data and real-world electrocardiograph data confirm its validity and superiority.
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Notes
P = (p1, p2, …,p m ) is called a canonical basis vector, if p i = 1 and p l = 0,∀l ≠ i [1].
Since s i ’ are mutually independent and we assume E{s 2 i } = 1, we have E{ss T} = I. \(\tilde{\bf{x}}\) is whitened, so we have \( E\{{\tilde{\bf{x}}\tilde{\bf{x}}}^{T} \} = \left({{\bf{VA}}} \right)E\{{\bf{ss}}^{T} \} \left({{\bf{VA}}} \right)^{T} = \left({{\bf{VA}}} \right)\left({{\bf{VA}}} \right)^{T} = {\bf{I}}. \) Hence, VA is orthogonal. Due to ||w|| = 1 and VA being a unitary matrix, we can get ||p|| = ||w T VA|| = ||w T|| = 1. This is why any p in Table 1 is near to a canonical basis vector.
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Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable and constructive comments, which greatly improved the manuscript’s readability. This work was supported by NSFC under Grant No. 60736009.
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Li, C., Liao, G. A reference-based blind source extraction algorithm. Neural Comput & Applic 19, 299–303 (2010). https://doi.org/10.1007/s00521-009-0303-x
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DOI: https://doi.org/10.1007/s00521-009-0303-x