Effective blind separation of skewed sources

Martı́n-Clemente, Rubén; Hornillo-Mellado, Susana

doi:10.1016/j.sigpro.2006.03.021

Cited by 1 publication

(4 citation statements)

References 6 publications

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“…When i ≠ j ,

\begin{matrix} right leftthickmathspace.5em \\ E (z s_{i} s_{j}) & = E ({false\sum}_{l = 1}^{n} {bold-italicu}^{normalT} {bold-italicu}_{l} s_{l} s_{i} s_{j}) \\ = E ({bold-italicu}^{normalT} {bold-italicu}_{i} s_{i}^{2} s_{j}) + E ({bold-italicu}^{normalT} {bold-italicu}_{j} s_{i} s_{j}^{2}) + E ({false\sum}_{l = 1, l \neq i, j}^{n} {bold-italicu}^{normalT} {bold-italicu}_{l} s_{l} s_{i} s_{j}) = 0. \end{matrix}

Taking all E ( zs i s j ) into (3), we obtain

\begin{matrix} right leftthickmathspace.5em \\ bold-italicC & = (c_{i j} false)_{n \times n} = bold-italicU bold-italicD {bold-italicU}^{normalT}, \\ normaland bold-italicD & = normaldiag ({bold-italicu}^{normalT} {bold-italicu}_{1} γ_{1}, {bold-italicu}^{normalT} {bold-italicu}_{2} γ_{2}, \dots, {bold-italicu}^{normalT} {bold-italicu}_{n} γ_{n}) \end{matrix}

The proof is completed. □ Remark 1: Equation (2) is introduced by Martin‐Clemente and Hornillo‐Mellado in [2], but it is not proved in the paper.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…The proof is completed. □ Remark 1: Equation 2is introduced by Martin-Clemente and Hornillo-Mellado in [2], but it is not proved in the paper.…”

Section: Introductionmentioning

confidence: 96%

“…Proposed algorithm: Skewness of a random variable X is defined as γ = c/σ 3/2 , where c = E(X 3 ) and s 2 = E(X 2 ) − (E(X)) 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Proof: Based on Proposition 1, for any unite norm vector u, if the weight is taken as u T v = u T Us, we can obtain the equation in (2).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Simple technique to determine the Givens‐rotation matrix in the two‐source ICA problem for skewed sources

2016

Electron. lett.

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The estimation of the Givens-rotation matrix or the Jacobi angle has always been a fundamental problem in independent component analysis. To estimate the angle, many approaches which use the optimal means and statistics of observation data have been presented during the past few decades. It is showed in this Letter that as long as one of two sources is asymmetrical, the Givens-rotation matrix can be solved from two weighted covariance matrices constructed by observations. Simulations illustrate the effectiveness of the approach.

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“…When i ≠ j ,