International Journal of Discrete Mathematics

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Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem

Received: Feb. 01, 2019    Accepted: Mar. 12, 2019    Published: Mar. 30, 2019
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Abstract

It is of paramount importance to establish an identity of citizenry to curb criminalities. Principal Component Analysis (PCA) which is one of the foremost methods for feature extraction and feature selection is adopted for identification and authentication of people. The computational time used by PCA is too much and Chinese Remainder Theorem was employed to reduce its computational time. TOAM database was setup which contained 120 facial images of 40 persons frontal faces with 3 images of each individual. 80 images were used for training while 40 were used for testing. Training time and testing time were used as performance metrics to determine the effect of CRT on PCA in terms of computational time. The experimenal results indicated an average training time of 13.5128 seconds and average testing time of 1.5475 second for PCA while PCA-CRT average training time is 13.2387 seconds and average testing time of 1.5185 seconds. Column chart was used to show the graphical relationship between PCA and PCA-CRT Training time and testing time. The research revealed that CRT reduce PCA computational time.

DOI 10.11648/j.dmath.20190401.11
Published in International Journal of Discrete Mathematics ( Volume 4, Issue 1, June 2019 )
Page(s) 1-7
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Dimensionality Reduction, Chinese Remainder Theorem, Eigenface, Training Time, Database

References
[1] Aleix M. M. and Avinash C. K. (2001). IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, No.2, pp. 228-233, 2001 PCA versus LD A.
[2] Gassenbauer , V., Krivánek, J., Bouatouch, K., Bouville, C. and Ribardière, M. (2011). Improving Performance and Accuracy of Local PCA. Computer Graphics Forum. The Eurographics Association and Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
[3] Gbolagade, K. A. (2010). Effective Reverse Conversion in Residue Number System Processors. PhD Thesis. The Netherlands.
[4] Jolliffe I. T and Cadima J. (2016). Principal component analysis: a review and recent developments. Phil. Trans. R. Soc. A 374: 20150202. http://dx.doi.org/10.1098/rsta.2015.0202.
[5] Kirby, M. and Sirovich, L. (1990) Application of the Karhunen-Loeve procedure for the characterization of human faces. IEEE Transaction on Pattern and Machine Intelligence, 12(1), 103-108.
[6] Martinez, A. M. and Kak, A. C. (2001): PCA versus LDA. IEEE Trans. on Pattern Analysis and Machine Intelligence, 23(2): pp. 228-233.
[7] Phillips, S. J. (2002). Acceleration of K-means and related clustering algorithms. In Algorithm Engineering and Experiments (ALENEX), pp. 166–177.
[8] Ross A. (2007). “An Introduction to Multibiometrics”. 15th European Signal Processing Conference (EUSIPCO), Poznan, Poland.
[9] Salih, G., Kadriye Ö. and Abdullah, Ç. (2016). CUDA Based Speed Optimization of the PCA Algorithm. TEM Journal Volume 5 / Number 2 / 152–159.
[10] Soderstrand, M. A., Jenkins, W. K., Jullien, G. A. and Taylor, F. J.(1986). Residue Number System Arithmetic: Modern Applications in Digital Signal Processing. IEEE press, Piscataway, NJ, USA.
[11] Symeonidis, et al. (2010): What are the advantages of kernel PCA over standard PCA retrieved from https://stats.stackexchange.com/questions/94463/what-are-the-advantages-of-kernel-PCA-over-standard-PCA
[12] Szabo, N. and Tanaka, R. (1967). Residue Arithmetic and its Application to Computer Technology. MC-Graw-Hill, New York.
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    Madandola Tajudeen Niyi, Gbolagade Kazeem Alagbe. (2019). Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem. International Journal of Discrete Mathematics, 4(1), 1-7. https://doi.org/10.11648/j.dmath.20190401.11

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    ACS Style

    Madandola Tajudeen Niyi; Gbolagade Kazeem Alagbe. Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem. Int. J. Discrete Math. 2019, 4(1), 1-7. doi: 10.11648/j.dmath.20190401.11

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    AMA Style

    Madandola Tajudeen Niyi, Gbolagade Kazeem Alagbe. Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem. Int J Discrete Math. 2019;4(1):1-7. doi: 10.11648/j.dmath.20190401.11

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  • @article{10.11648/j.dmath.20190401.11,
      author = {Madandola Tajudeen Niyi and Gbolagade Kazeem Alagbe},
      title = {Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem},
      journal = {International Journal of Discrete Mathematics},
      volume = {4},
      number = {1},
      pages = {1-7},
      doi = {10.11648/j.dmath.20190401.11},
      url = {https://doi.org/10.11648/j.dmath.20190401.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.dmath.20190401.11},
      abstract = {It is of paramount importance to establish an identity of citizenry to curb criminalities. Principal Component Analysis (PCA) which is one of the foremost methods for feature extraction and feature selection is adopted for identification and authentication of people. The computational time used by PCA is too much and Chinese Remainder Theorem was employed to reduce its computational time. TOAM database was setup which contained 120 facial images of 40 persons frontal faces with 3 images of each individual. 80 images were used for training while 40 were used for testing. Training time and testing time were used as performance metrics to determine the effect of CRT on PCA in terms of computational time. The experimenal results indicated an average training time of 13.5128 seconds and average testing time of 1.5475 second for PCA while PCA-CRT average training time is 13.2387 seconds and average testing time of 1.5185 seconds. Column chart was used to show the graphical relationship between PCA and PCA-CRT Training time and testing time. The research revealed that CRT reduce PCA computational time.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Reducing Computational Time of Principal Component Analysis with Chinese Remainder Theorem
    AU  - Madandola Tajudeen Niyi
    AU  - Gbolagade Kazeem Alagbe
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    DO  - 10.11648/j.dmath.20190401.11
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 1
    EP  - 7
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20190401.11
    AB  - It is of paramount importance to establish an identity of citizenry to curb criminalities. Principal Component Analysis (PCA) which is one of the foremost methods for feature extraction and feature selection is adopted for identification and authentication of people. The computational time used by PCA is too much and Chinese Remainder Theorem was employed to reduce its computational time. TOAM database was setup which contained 120 facial images of 40 persons frontal faces with 3 images of each individual. 80 images were used for training while 40 were used for testing. Training time and testing time were used as performance metrics to determine the effect of CRT on PCA in terms of computational time. The experimenal results indicated an average training time of 13.5128 seconds and average testing time of 1.5475 second for PCA while PCA-CRT average training time is 13.2387 seconds and average testing time of 1.5185 seconds. Column chart was used to show the graphical relationship between PCA and PCA-CRT Training time and testing time. The research revealed that CRT reduce PCA computational time.
    VL  - 4
    IS  - 1
    ER  - 

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Author Information
  • Department of Computer Science, Kwara State College of Education, Oro, Nigeria

  • Department of Computer Science, Kwara State University, Malete, Nigeria

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