Joint Diagonalisation Via Weighted Generalised Eigenvalue Decomposition

Jun Liu; Jingli Li

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Joint Diagonalisation Via Weighted Generalised Eigenvalue Decomposition

机译：通过加权广义特征值分解进行联合对角化

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摘要

In this correspondence, we propose a new approach for joint diagonalisation of multiple matrices. The proposed algorithm performs generalised eigenvalue decomposition (GEVD) of two weighted matrices, and then optimises the weighting factors so that an upper bound of the mean square error (MSE) of the estimates of the mixing matrix is minimised. The proposed scheme can solve the potential problem in the initialisation step of several existing joint diagonalisation algorithms in the presence of repeated eigenvalues. The simulation results indicate that weighted diagonalisation offers competitive performance for joint diagonalisation.

机译：在这种对应关系中，我们提出了一种将多个矩阵联合对角化的新方法。该算法对两个加权矩阵进行广义特征值分解（GEVD），然后优化加权因子，以使混合矩阵估计值的均方误差（MSE）的上限最小。所提出的方案可以在存在重复特征值的情况下解决几种现有的联合对角化算法的初始化步骤中的潜在问题。仿真结果表明，加权对角化为联合对角化提供了竞争性能。

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来源
《International Journal of Information Technology,Communications and Convergence》 |2011年第3期|p.318-330|共13页
作者
Jun Liu; Jingli Li;
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作者单位

LinkQuest Inc., San Diego, CA 92121, USA;

TopWorx, Louisville, KY 40213, USA;

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正文语种 eng
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关键词
joint diagonalisation; generalised eigenvalue decomposition; GEVD; mean square error; MSE; weighted diagonalisation; WD;

机译：联合对角化;广义特征值分解;GEVD;均方误差;MSE;加权对角化;WD;

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Joint Diagonalisation Via Weighted Generalised Eigenvalue Decomposition

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