Robust Multilinear Principal Component Analysis

M. Hirari

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F. Centofanti

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M. Hubert

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and S. Van Aelst

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Section of Statistics and Data Science, Department of Mathematics, KU Leuven, Belgium;
[Mehdi.Hirari@kuleuven.be, Fabio.Centofanti@kuleuven.be, Mia.Hubert@kuleuven.be,
Stefan.VanAelst@kuleuven.be]

Keywords: Tensor data, Multiway data, Outlier Detection, Cellwise Outliers

Multilinear Principal Component Analysis (MPCA) is an important dimension reduction method for tensor data, and can be seen as a generalisation of PCA for multivariate data [Lu et al., 2008]. Since classical MPCA is sensitive to outliers, we propose a robust MPCA method. It can handle casewise outliers, which are entire tensors that deviate from the majority of the tensors. Our method is also resistant to cellwise outliers and it can cope with missing entries. A single loss function is proposed to reduce the influence of casewise and cellwise outliers, minimized through an Iteratively Reweighted Least Squares (IRLS) algorithm. The method is assessed through simulations and applied to two real datasets. A comparison is made with the proposals in [Inoue et al., 2009] that are either robust to casewise outliers or to cellwise outliers.

References

Inoue et al. [2009] Kohei Inoue, Kenji Hara, and Kiichi Urahama. Robust multilinear principal component analysis. In 2009 IEEE 12th International Conference on Computer Vision, pages 591–597, 2009.
Lu et al. [2008] Haiping Lu, Konstantinos N. Plataniotis, and Anastasios N. Venetsanopoulos. MPCA: Multilinear principal component analysis of tensor objects. IEEE transactions on Neural Networks, 19(1):18–39, 2008.