Applications of singular value decomposition in data reduction

Wengyao Jiang

doi:10.1117/12.2648696

27 September 2022 Applications of singular value decomposition in data reduction

Wengyao Jiang

Proceedings Volume 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022); 123450J (2022) https://doi.org/10.1117/12.2648696
Event: 2022 International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 2022, Qingdao, China

Abstract

The singular value decomposition (SVD) is broadly used in the dimensional reduction due to its universality for all matrices. We have deduced the mathematical formula of the SVD and logical thinking of SVD truncation. Dimensional reduction just uses the SVD truncation to select N biggest singular values. We have experimentally found that image compression used by SVD could greatly save memory without losing too much accuracy. The effectiveness of SVD could be directly shown in image recognition with complex data hierarchy. We also combined SVD with another useful dimensional reduction method named Principle Component Analysis (PCA). Our analysis indicates that the accuracy of both SVD and PCA could be guaranteed when processing a large number of data. Taken together with the data science and machine learning, SVD appears to be a fundamental tool of data processing. Our results establish a basic understanding of SVD in the application of dimensional reduction.

Citation Download Citation

Wengyao Jiang "Applications of singular value decomposition in data reduction", Proc. SPIE 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 123450J (27 September 2022); https://doi.org/10.1117/12.2648696

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