Skip to main content
SpringerLink
Log in

Spherical coordinate-based kernel principal component analysis

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

This paper proposes a spherical coordinate-based kernel principal component analysis (PCA). Here, the kernel function is the nonlinear transform from the Cartesian coordinate system to the spherical coordinate system. In particular, first, the vectors represented in the Cartesian coordinate system are expressed as those represented in the spherical coordinate system. Then, certain rotational angles or the radii of the vector are set to their corresponding mean values. Finally, the processed vectors represented in the spherical coordinate system are expressed back in the Cartesian coordinate system. As the degrees of the freedoms of the processed vectors represented in the spherical coordinate system are reduced, the dimension of the manifold of the processed vectors represented in the Cartesian coordinate system is also reduced. Moreover, since the conversion between the vectors represented in the Cartesian coordinate system and those represented in the spherical coordinate system only involves some elements in the vectors, the required computational power for the conversion is low. Computer numerical simulation results show that the mean squares reconstruction error via the spherical coordinate-based kernel PCA is lower than that via the conventional PCA. Also, the required computational power is significantly reduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Yildiz, K.: Dimensionality reduction-based feature extraction and classification on fleece fabric images. Signal Image Video Process. 11, 317–323 (2017)

    Article  Google Scholar 

  2. Routray, S., Ray, A.K., Mishra, C.: An efficient image denoising method based on principal component analysis with learned patch groups. Signal Image Video Process. 1, 1–8 (2019)

    Google Scholar 

  3. Thomaz, C.E., Giraldi, G.A.: PCA-based magnification method for revealing small signals in video. Signal Image Video Process. 12, 1293–1299 (2018)

    Article  Google Scholar 

  4. Sharma, A., Paliwal, K.K.: Fast principal component analysis using fixed-point algorithm. Pattern Recognit. Lett. 28, 1151–1155 (2007)

    Article  Google Scholar 

  5. Karamizadeh, S., Abdullah, S.M., Manaf, A.A., Zamani, M.: An overview of principal component analysis. J. Signal Inf. Process. 4, 173–175 (2013)

    Google Scholar 

  6. Dong, S., Hu, R.M., Tu, W.P., Zheng, X., Jiang, J.J., Wang, S.: Enhanced principal component using polar coordinated PCA for stereo audio coding. In: IEEE International Conference on Multimedia and Expo, pp. 628–633 (2012)

  7. Dong, S., Hu, R.M., Tu, W.P., Cheng, X.C., Zheng, X.: High efficiency stereo audio compression method using polar coordinate principle component analysis for wireless communications. Inf. Theory Coding 10, 98–111 (2013)

    Google Scholar 

  8. Campos, L.M.B.C., Cunha, F.S.R.P.: On hypersherical Legendre polynomials and higher dimensional multipole expansions. J. Inequal. Spec. Funct. 1–28 (2012)

  9. Martinez, D.R., Bond, R.A., Vai, M.M.: High Performance Embedded Computing Handbook: A Systems Perspective, pp. 5–7. CRC Press Taylor and Francis Group, Boca Raton (2008)

    Book  Google Scholar 

  10. Tao, Q., Wu, G., Wang, J.: Learning linear PCA with convex semi-definite programming. Pattern Recognit. 40(10), 2633–2640 (2007)

    Article  Google Scholar 

  11. Balcerowska, G., Siuda, R.: Inelastic background subtraction from a set of angle-dependent XPS spectra using PCA and polynomial approximation. Vacuum 54(1–4), 195–199 (1999)

    Article  Google Scholar 

  12. Xiao, Y., Wang, H., Xu, W.: Model selection of Gaussian kernel PCA for novelty detection. Chemom. Intell. Lab. Syst. 136, 164–172 (2014)

    Article  Google Scholar 

  13. Lu, M., Huang, J.Z., Qian, X.: Sparse exponential family principal component analysis. Pattern Recognit. 60, 681–691 (2016)

    Article  Google Scholar 

  14. Yang, W., Sun, C., Zhang, L., Ricanek, K.: Laplacian bidirectional PCA for face recognition. Neurocomputing 74(1–3), 487–493 (2010)

    Article  Google Scholar 

Download references

Funding

This paper was supported partly by the National Nature Science Foundation of China (No. U1701266, No. 61372173 and No. 61671163), the Team Project of the Education Ministry of the Guangdong Province (No. 2017KCXTD011), the Guangdong Higher Education Engineering Technology Research Center for Big Data on Manufacturing Knowledge Patent (No. 501130144), the Guangdong Province Intellectual Property Key Laboratory Project (No. 2018B030322016) and Hong Kong Innovation and Technology Commission, Enterprise Support Scheme (No. S/E/070/17).

Author information

Authors and Affiliations

  1. School of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China

    Yitong Guo & Bingo Wing-Kuen Ling

Authors
  1. Yitong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bingo Wing-Kuen Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bingo Wing-Kuen Ling.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, Y., Ling, B.WK. Spherical coordinate-based kernel principal component analysis. SIViP 15, 511–518 (2021). https://doi.org/10.1007/s11760-020-01771-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-020-01771-8

Keywords

Search

Navigation