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Robust Principal Tensor Component Analysis

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Tensor Computation for Data Analysis

Abstract

As a fundamental and popular tool for data analysis and dimensionality reduction, principal component analysis (PCA) plays an important role in a wide range of disciplines. Due to PCA’s sensitivity to sparse noise, robust PCA formulates a data matrix as the superposition of a low-rank component and a sparse component. When dealing with the ubiquitous multidimensional data, matrix transformation operation is inevitable, which will cause the loss of structure information. Therefore, robust principal tensor component analysis (RPTCA) is proposed, which separates the low-rank and the sparse tensor from the whole tensor by exploring the multidimensional structure properties.

In this chapter, various RPTCA methods for different tensor ranks and sparse tensor constraints are outlined. Especially, approaches based on tensor singular value decomposition (t-SVD) and its extensions are mainly discussed. The classic alternating direction method of multipliers (ADMM) is used for solving the RPTCA problem easily and efficiently. Finally, we present several related practical applications such as background extraction, video rain streaks removal, and infrared small target detection.

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Notes

  1. 1.

    http://vision.ucsd.edu/content/yale-face-database.

  2. 2.

    http://trace.eas.asu.edu/yuv/.

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Authors and Affiliations

  1. University of Electronic Science and Technology of China (UESTC), Chengdu, China

    Yipeng Liu, Jiani Liu, Zhen Long & Ce Zhu

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  1. Yipeng Liu
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  4. Ce Zhu
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Liu, Y., Liu, J., Long, Z., Zhu, C. (2022). Robust Principal Tensor Component Analysis. In: Tensor Computation for Data Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-74386-4_6

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  • DOI: https://doi.org/10.1007/978-3-030-74386-4_6

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