Independent component analysis based on higher-order statistics only
Independent component analysis based on higher-order statistics only
复制标题
仅基于高阶统计的独立成分分析
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
J. Vandewalle
中科院分区：
文献类型：
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作者：
L. D. Lathauwer;B. Moor;J. Vandewalle
用于独立分量分析（或盲源分离）的大多数常规技术采用二阶统计量来对观测数据进行去相关。预白化步骤使得这些算法对加性高斯噪声的存在敏感。提出了一种仅限高阶的方法。的识别问题接近（线性和多线性）代数框架：我们的推导开始观察，解决方案可以从高阶累积量张量的正则分解（CANDECOMP）。接下来，它表明，CANDECOMP组件遵循从同时对角化，通过同余变换，一组矩阵。在正交未知数方面的一个重新制定导致同时舒尔分解，这是解决了一个Givens型迭代。该技术可以被认为是流行的JADE算法的高阶等价物。
Most conventional techniques for independent component analysis (or blind source separation) resort to second-order statistics to decorrelate the observed data. The prewhitening step makes these algorithms sensitive to the presence of additive Gaussian noise. A higher-order-only technique is presented. The identification problem is approached in a (linear and multilinear) algebraic framework: our derivation starts with the observation that the solution can be obtained from the canonical decomposition (CANDECOMP) of a higher-order cumulant tensor. Next, it is demonstrated that the CANDECOMP components follow from the simultaneous diagonalization, by congruence transformation, of a set of matrices. A reformulation in terms of orthogonal unknowns leads to a simultaneous Schur decomposition, which is solved by a Givens-type iteration. The technique can be considered as the higher-order-only equivalent of the popular JADE-algorithm.