JADE for Tensor-Valued Observations
JADE for Tensor-Valued Observations
复制标题
DOI：
10.1080/10618600.2017.1407324
复制
发表时间：
2018-01-01
影响因子：
2.4
通讯作者：
Oja, Hannu
中科院分区：
文献类型：
--
作者：
Virta, Joni;Li, Bing;Oja, Hannu
独立成分分析是现代数据分析的标准工具，存在许多不同的应用方法。然而，当数据由比向量更高阶的结构组成时，即矩阵或张量（例如，图像或视频），标准方法很快失去有效性，无法处理大量的噪声。最近，提出了经典的四阶盲识别（FOBI）的扩展，特别适用于张量值观测，并证明其优于矢量版本的张量数据。在本文中，我们扩展了另一种流行的独立分量分析方法，特征矩阵的联合近似对角化（JADE），用于张量观测。除了理论背景之外，我们还提供了所提出的估计器的渐近性质，并使用模拟和实际数据来证明其实用性和优越性。补充材料包括定理的证明和运行模拟的代码以及实际数据示例可以在网上获得。
Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely, matrices or tensors (e.g., images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth-order blind identification (FOBI) specially suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this article, we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background, we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors. Supplementary material including the proofs of the theorems and the codes for running the simulations and the real data example are available online.