Vol. 6 No. 2 (2025)

Standard Journal Issues

Enhanced algorithm based on Chio-like Method for Non-Square Determinant Calculations for application in CBVR

Published 2025-08-01

  • Besnik Duriqi
    • ,
  • Halil Snopçe
    • ,
  • Armend Salihu
    • ,
  • Artan Luma
    • ,
  • Majlinda Fetaji

Besnik Duriqi
Computer Science, South East European University (SEEU), North Macedonia

Halil Snopçe
Computer Science, South East European University (SEEU), North Macedonia

Armend Salihu
Computer Science, UNI Universum International College, Kosovo

Artan Luma
Computer Science, South East European University (SEEU), North Macedonia

Majlinda Fetaji
Computer Science, South East European University (SEEU), North Macedonia

Abstract

In this paper, we propose an enhanced algorithm based on the Chio-like method for calculating non-square determinants, optimized for content-based video retrieval (CBVR) systems. The algorithm accelerates the computation of determinant kernels used for similarity score generation, which is critical for efficient video indexing and retrieval. While the classical Chio-like method reduces the determinant order by one at each step, our improved approach reduces the order by four, providing notable computational benefits. Although the asymptotic time complexity remains the same, considering the fact that the resulting determinant is decreased by four orders compared to one and two orders, respectively, from existing Chio-like methods, the proposed method demonstrates clear practical performance improvements. The computer implementation of the proposed algorithm in MATLAB shows an average execution time reduction of approximately 24.5% compared to the standard Chio-like method and 3.2% compared to its modified version. These enhancements make the method well-suited for large-scale or real-time CBVR applications, where fast and accurate similarity evaluation is essential.

Keywords

Non-square determinants, Chio’s-like, Algorithm optimization, Execution time, Kernels, Similarity score, CBVR

PDF

References

  1. [1] A., Kaur, T., & Kaur, S. (2024). Content-Based Video and Image
  2. Retrieval in the Modern Era: Apprehensions and Scope. In Latest
  3. Trends in Engineering and Technology (pp. 141-145). CRC Press. URL:
  4. https://www.taylorfrancis.com/chapters/edit/10.1201/9781032665443-
  5. 20/content-based-video-image-retrieval-modern-era-apprehensions- scope-amarjeet-kaur-taranjeet-kaur-sarabpreet-kaur
  6. [2] Zhang, J., Wu, Y., Hao, F., Liu, X., Li, M., Zhou, D., & Zheng, W.
  7. (2024). Double similarities weighted multi-instance learning kernel and
  8. its application. Expert Systems with Applications, 238, 121900. URL: https://doi.org/10.1016/j.eswa.2023.121900
  9. [3] Kang, Z., Peng, C., & Cheng, Q. (2017). Kernel-driven similarity Learning. Neurocomputing, 267, 210-219. URL:
  10. https://doi.org/10.1016/j.neucom.2017.06.005
  11. [4] Gwashavanhu, B. K., Oberholster, A. J., & Heyns, S. P. (2024). A comparative study of principal component analysis and kernel principal component analysis for photogrammetric shape-based turbine blade damage analysis. Engineering Structures, 318, 118712. [4] P.H. Gosselin, M. Cord, S. URL: https://doi.org/10.1016/j.engstruct.2024.118712
  12. [5] Bach, F. (2022). Information theory with kernel methods. IEEE Transactions on Information Theory, 69(2), 752-775. URL: 10.1109/TIT.2022.3211077
  13. [6] Batlle, P., Darcy, M., Hosseini, B., & Owhadi, H. (2024). Kernel methods are competitive for operator learning. Journal of Computational Physics, 496, 112549. URL: https://doi.org/10.1016/j.jcp.2023.112549
  14. [7] Rasekhinezhad, H., Abbasbandy, S., Allahviranloo, T., & Baboliand, E. (2024). Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems. International Journal of Dynamics and Control, 12(8), 2795-2802. URL: https://doi.org/10.1007/s40435-024-01397-5
  15. [8] Ghojogh, B., Ghodsi, A., Karray, F., & Crowley, M. (2021). Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr" om Method, and Use of Kernels in Machine Learning: Tutorial and Survey. arXiv preprint arXiv:2106.08443. URL:
  16. https://doi.org/10.48550/arXiv.2106.08443
  17. [9] Liu, X., Zhang, Z., Igathinathane, C., Flores, P., Zhang, M., Li, H., ... & Kim, H. J. (2024). Infield corn kernel detection using image processing, machine learning, and deep learning methodologies under natural lighting. Expert Systems with Applications, 238, 122278. URL: https://doi.org/10.1016/j.eswa.2023.122278
  18. [10] Croughan, M. K., Paganin, D. M., Alloo, S. J., Ahlers, J. N., How, Y. Y., Harker, S. A., & Morgan, K. S. (2024). Correcting directional dark field x-ray imaging artefacts using position dependent image deblurring and attenuation removal. Scientific Reports, 14(1), 17807. URL: https://doi.org/10.1038/s41598-024-68659-2
  19. [11] Arora, P., Mehta, R., & Ahuja, R. (2024). An integration of meta-heuristic approach utilizing kernel principal component analysis for multimodal medical image registration. Cluster Computing, 27(5), 6223-6246. URL: https://doi.org/10.1007/s10586-024-04281-1
  20. [12] Dai, M., Raffiee, A. H., Jain, A., & Correa, J. (2024). Evaluating Transferability in Retrieval Tasks: An Approach Using MMD and Kernel Methods. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 22390-22400). URL: 10.1109/CVPR52733.2024.02113
  21. [13] Yi, Q., He, Y., Wang, J., Song, X., Qian, S., Yuan, X., ... & Shi, T. (2025). Score: Story coherence and retrieval enhancement for ai narratives. arXiv preprint arXiv:2503.23512. URL:
  22. https://doi.org/10.48550/arXiv.2503.23512
  23. [14] Cullis, E.C. (1913). Matrices and determinoids. Cambridge: Cambridge: University Press. URL: https://doi.org/10.2307/3603184
  24. [15] Radic, M. (1966). Definition of Determinant of Rectangular Matrix, Glasnik Matematicki, 17-22. URL:
  25. https://web.math.pmf.unizg.hr/glasnik/Vol/vol01no1.html
  26. [16] Salihu, A., & Marevci, F. (2021). Chio’s-like method for calculating the rectangular (non-square) determinants: Computer algorithm interpretation and comparison. European Journal of Pure and Applied Mathematics, 14(2), 431-450. URL:
  27. https://doi.org/10.29020/nybg.ejpam.v14i2.3920
  28. [17] Salihu, A., Snopce, H., Luma, A., & Ajdari, J. (2023). MODIFIED CHIOS-LIKE METHOD FOR RECTANGULAR DETERMINANT CALCULATIONS. Advanced Mathematical Models & Applications, 8(3). URL:
  29. https://jomardpublishing.com/UploadFiles/Files/journals/AMMAV1N1/V8N3/Salihu_et_al.pdf
  30. [18] Salihu, A., & Marevci, F. (2019). Determinants order decrease/increase for k orders, interpretation with computer algorithms and comparison. Computer Science, 9(2), 501-518. URL:
  31. https://future-in-tech.net/14.2/R-Marecvi-Salihu.pdf
  32. [19] Makarewicz, A., & Pikuta, P. (2020). Cullis-Radi? determinant of a rectangular matrix which has a number of identical columns. Annales Universitatis Mariae Curie-Sklodowska, sectio A–Mathematica, 74(2), 41-60. URL:
  33. https://bibliotekanauki.pl/articles/1395917.pdf
  34. [20] Makarewicz, A., Pikuta, P., & Sza?kowski, D. (2014). Properties of the determinant of a rectangular matrix. Annales Universitatis Mariae Curie-Sk?odowska, sectio A–Mathematica, 68(1). URL:
  35. https://bibliotekanauki.pl/articles/747308.pdf

Downloads

Download data is not yet available.

Similar Articles

21-30 of 34

You may also start an advanced similarity search for this article.