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.

中文翻译：

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使用复杂多元 GGD 的 IVA：在 fMRI 分析中的应用

科学和工程中复值随机现象的例子比比皆是，联合盲源分离（JBSS）提供了一种分析多集数据的有效方法。因此，需要灵活的 JBSS 算法来在复杂域中进行高效的数据驱动特征提取。独立向量分析 (IVA) 是独立分量分析对多变量源（即执行 JBSS）的突出最近扩展，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和所采用的优化算法。复杂的多元广义高斯分布 (CMGGD) 是一个简单而有效的参数化分布族，它解释了完整的二阶和更高阶统计信息，包括非圆度、为方便起见，经常省略的属性。在本文中，我们将 IVA 和 CMGGD 结合起来推导出 IVA-CMGGD，其中包含许多数值优化实现，包括最速下降、拟牛顿法 Broyden-Fletcher-Goldfarb-Shanno (BFGS) 及其有限内存的兄弟有限-memory BFGS 都在复杂域中。我们展示了我们的算法在模拟数据以及 14 个主题的真实世界复值功能磁共振成像数据集上与许多竞争算法相比的性能。