JADE for Tensor-Valued Observations

ABSTRACT

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.

KEYWORDS:

• Independent component analysis
• Kurtosis
• Limiting normality
• Minimum distance index
• Multilinear algebra

Additional information

Funding

The work of Virta and Oja was supported by the Academy of Finland Grant 268703. The work of Li was supported in part by the National Science Foundation Grants DMS-1407537 and DMS-1713078. The work of Nordhausen was partly supported by the Academy of Finland Grant 268703 and CRoNoS COST Action IC1408.