Author(s)

Zhang Yuyao ¹

Affiliation(s)

¹ Jinan Foreign Language School International Center, 3399 Jinyu Avenue, Licheng District, Jinan, Shandong Province, China

Corresponding Author

Zhang Yuyao

ABSTRACT

This study focuses on geometric patterns in Islamic art, employing mathematical methods such as Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) to explore the quantitative rules in terms of structural features and style classification. Initially, by preprocessing the images and representing them in a matrix format, SVD is used to extract major geometric characteristics, including energy distribution, pattern repetitiveness, and visual complexity. Subsequently, PCA and clustering analysis reveal the similarities and differences among various patterns. The experimental results indicate that the first few principal components effectively encapsulate the overall structure and local features of the patterns, while the clustering results identify three main types of decorative styles: structure-concentrated, balanced-transition, and complex-detailed.

KEYWORDS

Geometric Patterns, Singular Value Decomposition, Principal Component Analysis

CITE THIS PAPER

Zhang Yuyao, Research on Islamic Traditional Artistic Patterns Based on Singular Value Decomposition. Transactions on Computational and Applied Mathematics (2025) Vol. 5: 28-36. DOI: http://dx.doi.org/10.23977/tracam.2025.050104.

REFERENCES

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