Enhanced Multilinear PCA for Efficient Image Analysis and Dimensionality Reduction: Unlocking the Potential of Complex Image Data

Tianyu Sun, Lang He, Xi Fang () and Liang Xie
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Tianyu Sun: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China
Lang He: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China
Xi Fang: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China
Liang Xie: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China

Mathematics, 2025, vol. 13, issue 3, 1-16

Abstract: This paper presents an Enhanced Multilinear Principal Component Analysis (EMPCA) algorithm, an improved variant of the traditional Multilinear Principal Component Analysis (MPCA) tailored for efficient dimensionality reduction in high-dimensional data, particularly in image analysis tasks. EMPCA integrates random singular value decomposition to reduce computational complexity while maintaining data integrity. Additionally, it innovatively combines the dimensionality reduction method with the Mask R-CNN algorithm, enhancing the accuracy of image segmentation. Leveraging tensors, EMPCA achieves dimensionality reduction that specifically benefits image classification, face recognition, and image segmentation. The experimental results demonstrate a 17.7% reduction in computation time compared to conventional methods, without compromising accuracy. In image classification and face recognition experiments, EMPCA significantly enhances classifier efficiency, achieving comparable or superior accuracy to algorithms such as Support Vector Machines (SVMs). Additionally, EMPCA preprocessing exploits latent information within tensor structures, leading to improved segmentation performance. The proposed EMPCA algorithm holds promise for reducing image analysis runtimes and advancing rapid image processing techniques.

Keywords: tensor; multilinear principal component analysis; random singular value decomposition; image analysis; dimensionality reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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