Algorithms on the Stiefel manifold for joint diagonalisation
Algorithms on the Stiefel manifold for joint diagonalisation
复制标题
用于联合对角化的 Stiefel 流形算法
DOI：
10.1109/icassp.2002.5744893
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Hori
中科院分区：
文献类型：
--
作者：
M. Nikpour;J. Manton;G. Hori
本文提出了一种新颖的方法来解决统一关节对角线化问题。我们将问题作为对单位矩阵的多种形式的优化问题，并获得最陡峭的下降和牛顿算法。两种算法都与众所周知的特征 - 元素（JADE）算法的关节对角线化相同的溶液。但是，如果适当初始化的话，我们的牛顿算法几乎立即达到二次收敛率，而玉（在某些情况下）可以以二次速率开始融合到溶液之前（在某些情况下）进行30次扫描。模拟说明我们最陡峭的下降算法可用于找到牛顿算法的合适起点，然后以二次速率来完善我们的估计值。这两个阶段的算法总体上所需的迭代次数要比翡翠少，而每次迭代的成本与Jade相同。因此，我们的方法为玉提供了一种新颖的替代品。
This paper presents a novel approach to the unitary joint diagonalisation problem. We approach the problem as an optimisation problem over the manifold of unitary matrices and obtain steepest descent and Newton algorithms. Both algorithms converge to the same solution as the well known Joint Approximate Diagonalisation of Eigen-matrices (JADE) algorithm. However, our Newton algorithm achieves a quadratic convergence rate almost immediately if suitably initialised, whereas JADE can (in some cases) take up to 30 sweeps before it starts converging to the solution at a quadratic rate. Simulations illustrate that our steepest descent algorithm can be used to find a suitable starting point for our Newton algorithm which then refines our estimate at a quadratic rate. This two stage algorithm requires less iterations overall than JADE, with the cost per iteration being the same as JADE. Our methods, therefore, offer a novel alternative to JADE.