A Unifying Objective Function of Independent Component Analysis for Ordering Sources by Non-Gaussianity
A Unifying Objective Function of Independent Component Analysis for Ordering Sources by Non-Gaussianity
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DOI：
10.1109/tnnls.2018.2806959
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发表时间：
2018-11-01
影响因子：
10.4
通讯作者：
Yamaguchi, Kazunori
中科院分区：
文献类型：
--
作者：
Matsuda, Yoshitatsu;Yamaguchi, Kazunori
独立分量分析（伊卡）是一种应用广泛的解决盲分离问题的方法。伊卡假设源是相互独立的，并通过最大化它们的非高斯性作为目标函数来提取它们。存在两种类型的源的非高斯性（具有正峰度的超高斯型和具有负峰度的亚高斯型）。在本文中，我们提出了一个新的目标函数自然地统一的两种类型的非高斯性，这是通过应用高斯近似的源分布在二阶多项式特征空间。所提出的目标函数[称为自适应伊卡函数（AIF）]是一种简单的形式，作为加权四阶统计量的总和，其中权重由当前的峰自适应估计。AIF的第一个实际优点是它可以按照非高斯准则的降序顺序逐个提取源。它可以解决排列二义性问题。第二个更重要的优点是，它可以估计的数量的非高斯源的赤池信息准则，而不管其分布的具体形式。为了充分利用AIF的上述优点，我们对快速伊卡进行了扩展，构造了一种新的算法--排序伊卡。实验结果表明，排序伊卡在人工和真实的数据集上都能正确估计出非高斯源的个数。
The independent component analysis (ICA) is a widely used method for solving blind separation problems. The ICA assumes that the sources are independent of each other and extracts them by maximizing their non-Gaussianity as the objective function. There are the two types of non-Gaussianity of the sources (the super-Gaussian type with the positive kurtosis and the sub-Gaussian one with the negative kurtosis). In this paper, we propose a new objective function unifying the two types of non-Gaussianity naturally, which is derived by applying the Gaussian approximation to the distribution of sources in the second-order polynomial feature space. The proposed objective function [called the adaptive ICA function (AIF)] is a simple form given as a summation of weighted fourth-order statistics, where the weights are adaptively estimated by the current kurtoses. The first practical advantage of the AIF is that it can extract the sources one by one in the descending order of the criterion of non-Gaussianity. It can solve the permutation ambiguity problem. The second and more important advantage is that it can estimate the number of non-Gaussian sources by the Akaike information criterion irrespective of the specific form of their distributions. In order to utilize the above-mentioned advantages of the AIF, we construct a new algorithm named the ordering ICA by extending the fast ICA. Experimental results verify that the ordering ICA can estimate the number of non-Gaussian sources correctly in both artificial and real data sets.