2016/03/17 by Joni Virta, Bing Li, Klaus Nordhausen +1
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #Component (thermodynamics) #Estimator #Extension (predicate logic) #Identification (biology) #JADE (particle detector) #Mathematical proof #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #math.ST #msc:62G20 #msc:62H10 #msc:62H12 #stat.TH
paper · pdf · doi:10.1080/10618600.2017.1407324
published as Journal of Computational and Graphical Statistics, 2018, Vol. 27, pp. 628-637 · 10 pages, 3 figures
arxiv created 2016/03/17 · openalex created_date 2016/06/24 · openalex publication_date 2017/11/27 · arxiv updated 2019/05/07 · openalex updated_date 2026/08/06
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.