In the realm of data analysis, the exploration of independent component analysis (ICA) for tensor-valued data represents a burgeoning area of research. Unlike traditional scalar or vector data, tensor-valued data capture complex relationships and structures across multiple dimensions. Independent component analysis offers a powerful framework for decomposing tensor-valued data into statistically independent components, revealing underlying patterns and dependencies that may remain obscured in raw data representations. This paper delves into the application of ICA techniques specifically tailored for tensor-valued data, exploring theoretical foundations, algorithmic implementations, and practical considerations. Through a comprehensive review and analysis, we elucidate the potential of ICA in uncovering hidden structures and sources of variability within tensor-valued datasets across diverse domains.

Independent component analysis, tensor-valued data, multidimensional data analysis

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