IVA using complex multivariate GGD: application to fMRI analysis
IVA using complex multivariate GGD: application to fMRI analysis
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DOI：
10.1007/s11045-019-00685-0
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发表时间：
2019-10
影响因子：
2.5
通讯作者：
Rami Mowakeaa;Zois Boukouvalas;Qunfang Long;T. Adalı
中科院分区：
文献类型：
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作者：
Rami Mowakeaa;Zois Boukouvalas;Qunfang Long;T. Adalı
复值随机现象在科学和工程中的例子比比皆是，联合盲源分离（JBSS）提供了一种有效的方法来分析多集数据。因此，需要灵活的JBSS算法，用于在复杂域中进行有效的数据驱动特征提取。独立向量分析（IVA）是独立分量分析到多变量源的突出的最近扩展，即，但其有效性取决于所使用的源模型与真实潜在分布的匹配程度以及所采用的优化算法。复杂多元广义高斯分布（CMGGD）是一个简单而有效的参数化分布族，它可以解释完整的二阶和高阶统计量，包括非圆性，这是一个经常为了方便而忽略的属性。在本文中，我们结婚IVA和CMGGD派生，IVA-CMGGD，与一些数值优化实现，包括最速下降，拟牛顿方法Broyden-Fletcher-Goldfarb-Shanno（BFGS），和它的有限内存兄弟有限内存BFGS都在复域。我们证明了我们的算法对模拟数据的性能，以及14个主题的真实世界的复值功能磁共振成像数据集对一些竞争的算法。
Examples of complex-valued random phenomena in science and engineering are abound, and joint blind source separation (JBSS) provides an effective way to analyze multiset data. Thus there is a need for flexible JBSS algorithms for efficient data-driven feature extraction in the complex domain. Independent vector analysis (IVA) is a prominent recent extension of independent component analysis to multivariate sources, i.e., to perform JBSS, but its effectiveness is determined by how well the source models used match the true latent distributions and the optimization algorithm employed. The complex multivariate generalized Gaussian distribution (CMGGD) is a simple, yet effective parameterized family of distributions that account for full second- and higher-order statistics including noncircularity, a property that has been often omitted for convenience. In this paper, we marry IVA and CMGGD to derive, IVA-CMGGD, with a number of numerical optimization implementations including steepest descent, the quasi-Newton method Broyden–Fletcher–Goldfarb–Shanno (BFGS), and its limited-memory sibling limited-memory BFGS all in the complex-domain. We demonstrate the performance of our algorithm on simulated data as well as a 14-subject real-world complex-valued functional magnetic resonance imaging dataset against a number of competing algorithms.