Independent component analysis in the presence of Gaussian noise by maximizing joint likelihood
Independent component analysis in the presence of Gaussian noise by maximizing joint likelihood
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DOI：
10.1016/s0925-2312(98)00049-6
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发表时间：
1998-11-01
期刊：
影响因子：
6
通讯作者：
Hyvarinen, A
中科院分区：
文献类型：
--
作者：
Hyvarinen, A
考虑了高斯噪声下独立分量分析数据模型的估计问题。我们表明，联合最大似然估计的独立成分和混合矩阵导致一个目标函数已经提出了Olshausen和字段使用不同的推导。由于目标函数的复杂性，我们引入近似，大大简化了优化问题。我们表明，噪声的存在意味着观察到的数据和独立分量的估计之间的关系是非线性的，并显示如何近似这种非线性。特别地，在超高斯（稀疏）数据的情况下，非线性可以通过简单的收缩操作来近似。使用这些近似，我们提出了一个有效的算法近似最大化的可能性。在超高斯分量的情况下，这可以通过简单的竞争学习来近似，并且在亚高斯分量的情况下，通过反竞争学习来近似。(C)1998 Elsevier Science B.V.保留所有权利。
We consider the estimation of the data model of independent component analysis when Gaussian noise is present. We show that the joint maximum likelihood estimation of the independent components and the mixing matrix leads to an objective function already proposed by Olshausen and Field using a different derivation. Due to the complicated nature of the objective function, we introduce approximations that greatly simplify the optimization problem. We show that the presence of noise implies that the relation between the observed data and the estimates of the independent components is non-linear, and show how to approximate this non-linearity. In particular, the non-linearity may be approximated by a simple shrinkage operation in the case of super-Gaussian (sparse) data. Using these approximations, we propose an efficient algorithm for approximate maximization of the likelihood. In the case of super-Gaussian components, this may be approximated by simple competitive learning, and in the case of sub-Gaussian components, by anti-competitive learning. (C) 1998 Elsevier Science B.V. All rights reserved.