Advertisement

Incomplete-Data Oriented Dimension Reduction via Instance Factoring PCA Framework

  • Ernest Domanaanmwi Ganaa
  • Timothy Apasiba Abeo
  • Sumet Mehta
  • Heping Song
  • Xiang-Jun ShenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11903)

Abstract

In this paper, we propose an instance factoring PCA (IFPCA) framework for dimension reduction in incomplete datasets. The advantage of IFPCA over the traditional PCA is that, a penalty is imposed on the instance space via a scaling-factor to suppress the effect of outliers in pursuing projections. We geometrically use two scaling-factor strategies, total distance and cosine similarity metrics. Both strategies can learn the relationship between each data point and the principal projection in the feature space. In this way, better low-rank projections are obtained through scaling the data iteratively to suppress the impact of noise in the training set. Extensive experiments on COIL-20, ORL and USPS datasets prove the superiority of the proposed framework over state-of-the-art dimensionality reduction methods such as LSDA, gLPCA, RPCA-OM, PCA, LPP and RCDA.

Keywords

Principal component analysis Instance factoring Incomplete-data Dimensionality reduction Manifold learning 

Notes

Acknowledgments

This work was funded in part by the National Natural Science Foundation of China(No. 61572240) and Natural Science Foundation of Jiangsu Province (No. BK20170558).

References

  1. 1.
    Deng, C., He, X., Zhou, K., Han, J., Bao, H.: Locality sensitive discriminant analysis (2007)Google Scholar
  2. 2.
    Teoh, A.B.J., Han, P.Y.: Face recognition based on neighbourhood discriminant preserving embedding. In: International Conference on Control, Automation, Robotics and Vision, pp. 428–433 (2009)Google Scholar
  3. 3.
    Feng, G., Hu, D., Zhou, Z.: A direct locality preserving projections (DLPP) algorithm for image recognition. Neural Process. Lett. 27(3), 247–255 (2008)CrossRefGoogle Scholar
  4. 4.
    Chen, J., Ye, J., Li, Q.: Integrating global and local structures: a least squares framework for dimensionality reduction. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)Google Scholar
  5. 5.
    Yang, M.H.: Face recognition using extended isomap. In: International Conference on Image Processing (2002)Google Scholar
  6. 6.
    Wiriyathammabhum, P., Kijsirikul, B.: Robust principal component analysis using statistical estimators. arXiv preprint arXiv:1207.0403 (2012)
  7. 7.
    Jolliffe, I.T., Cadima, J.: Principal component analysis: a review and recent developments. Philos. Trans. Roy. Soc. A Math. Phys. Eng. Sci. 374(2065), 20150202 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Roweis, S.T.: EM algorithms for PCA and SPCA. In: Advances in Neural Information Processing Systems, pp. 626–632 (1998)Google Scholar
  9. 9.
    Kriegel, H.-P., Kröger, P., Schubert, E., Zimek, A.: A general framework for increasing the robustness of PCA-based correlation clustering algorithms. In: Ludäscher, B., Mamoulis, N. (eds.) SSDBM 2008. LNCS, vol. 5069, pp. 418–435. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-69497-7_27CrossRefGoogle Scholar
  10. 10.
    Vaswani, N., Bouwmans, T., Javed, S., Narayanamurthy, P.: Robust PCA, subspace learning, and tracking. IEEE Signal Process. Mag. 35, 32–55 (2018)CrossRefGoogle Scholar
  11. 11.
    Jiang, B., Ding, C., Luo, B., Tang, J.: Graph-Laplacian PCA: closed-form solution and robustness. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3492–3498 (2013)Google Scholar
  12. 12.
    Nie, F., Yuan, J., Huang, H.: Optimal mean robust principal component analysis. In: International Conference on Machine Learning, pp. 1062–1070 (2014)Google Scholar
  13. 13.
    Abeo, T.A., Shen, X.J., Gou, J.P., Mao, Q.R., Bao, B.K., Li, S.: Dictionary-induced least squares framework for multi-view dimensionality reduction with multi-manifold embeddings. IET Comput. Vision 13(2), 97–108 (2019)CrossRefGoogle Scholar
  14. 14.
    Yang, W., Shi, Y., Gao, Y., Wang, L., Yang, M.: Incomplete-data oriented multiview dimension reduction via sparse low-rank representation. IEEE Trans. Neural Netw. Learn. Syst. 29, 6276–6291 (2018)CrossRefGoogle Scholar
  15. 15.
    Li, C., Liu, J., Liu, Y., Xu, C., Liu, Q., Lu, H.: Ordinal preserving projection: a novel dimensionality reduction method for image ranking. In: Proceedings of the 2nd ACM International Conference on Multimedia Retrieval, p. 17. ACM (2012)Google Scholar
  16. 16.
    Wall, M.E., Rechtsteiner, A., Rocha, L.M.: Singular value decomposition and principal component analysis. In: Berrar, D.P., Dubitzky, W., Granzow, M. (eds.) A Practical Approach to Microarray Data Analysis, vol. 5, pp. 91–109. Springer, Boston (2003).  https://doi.org/10.1007/0-306-47815-3_5CrossRefGoogle Scholar
  17. 17.
    Vidal, R., Ma, Y., Sastry, S.S.: Generalized Principal Component Analysis. IAM, vol. 40. Springer, New York (2016).  https://doi.org/10.1007/978-0-387-87811-9CrossRefzbMATHGoogle Scholar
  18. 18.
    Huang, K.K., Dai, D.Q., Ren, C.X.: Regularized coplanar discriminant analysis for dimensionality reduction. Pattern Recogn. 62(Complete), 87–98 (2017)CrossRefGoogle Scholar
  19. 19.
    Alom, M.Z., Josue, T., Rahman, M.N., Mitchell, W., Yakopcic, C., Taha, T.M.: Deep versus wide convolutional neural networks for object recognition on neuromorphic system. arXiv preprint arXiv:1802.02608 (2018)
  20. 20.
    Jiang, R., Al-Maadeed, S., Bouridane, A., Crookes, D., Celebi, M.E.: Face recognition in the scrambled domain via salience-aware ensembles of many kernels. IEEE Trans. Inf. Forensics Secur. 11(8), 1807–1817 (2016)CrossRefGoogle Scholar
  21. 21.
    Proedrou, K., Nouretdinov, I., Vovk, V., Gammerman, A.: Transductive confidence machines for pattern recognition. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) ECML 2002. LNCS (LNAI), vol. 2430, pp. 381–390. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-36755-1_32CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ernest Domanaanmwi Ganaa
    • 1
    • 3
  • Timothy Apasiba Abeo
    • 1
    • 4
  • Sumet Mehta
    • 1
  • Heping Song
    • 1
  • Xiang-Jun Shen
    • 1
    • 2
    Email author
  1. 1.School of Computer Science and Communication EngineeringJiangSu UniversityZhenjiangChina
  2. 2.Jingkou New-Generation Information Technology Industry InstituteJiangSu UniversityZhenjiangChina
  3. 3.School of Applied Science and TechnologyWa PolytechnicWaGhana
  4. 4.School of Applied ScienceTamale Technical UniversityTamaleGhana

Personalised recommendations