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Global Multidisciplinary Journal

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UNRAVELING INDEPENDENT COMPONENT ANALYSIS FOR TENSOR-VALUED DATA

DOI https://doi.org/10.55640/gmj-abc114
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Joni Oja Nordhausen 1 ,
4 Department of Mathematics and Statistics, University of Turku, Finland

Abstract

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.

Keywords

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

References

📄 C.F. Beckmann, S.M. Smith, Tensorial extensions of independent component analysis for multisubject FMRI analysis, Neuroimage 25 (2005) 294–311.
📄 J.-F. Cardoso, Source separation using higher order moments, in: International Conference on Acoustics, Speech, and Signal Processing 1989, IEEE, 1989, pp. 2109–2112.
📄 J.-F. Cardoso, A. Souloumiac, Blind beamforming for non-Gaussian signals, in: IEE Proceedings F (Radar and Signal Processing), Vol. 140, IET, 1993, pp. 362–370.
📄 S. Ding, R.D. Cook, Dimension folding PCA and PFC for matrix-valued predictors, Statist. Sinica 24 (2014) 463–492.
📄 S. Ding, R.D. Cook, Higher-order sliced inverse regressions, Wiley Interdiscip. Rev. Comput. Statist. 7 (2015) 249–257.
📄 S. Ding, R.D. Cook, Tensor sliced inverse regression, J. Multivariate Anal. 133 (2015) 216–231.
📄 K. Greenewald, A. Hero, Robust kronecker product PCA for spatio-temporal covariance estimation, IEEE Trans. Signal Process. 63 (2015) 6368–6378.
📄 Gupta, D. Nagar, Matrix Variate Distributions, Chapman & Hall/CRC, Boca Raton, FL, 2010.
📄 H. Hung, C.-C. Wang, Matrix variate logistic regression model with application to EEG data, Biostatistics 14 (2013) 189–202.
📄 H. Hung, P. Wu, I. Tu, S. Huang, On multilinear principal component analysis, Biometrika 99 (2012) 569–583.
📄 Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, Wiley, New York, 2001.
📄 P. Ilmonen, J. Nevalainen, H. Oja, Characteristics of multivariate distributions and the invariant coordinate system, Statist. Probab. Lett. 80 (2010) 1844–1853.

How to Cite

Joni Oja Nordhausen. (2023). UNRAVELING INDEPENDENT COMPONENT ANALYSIS FOR TENSOR-VALUED DATA. Global Multidisciplinary Journal, 2(03), 01-07. https://doi.org/10.55640/gmj-abc114

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