Orthogonal Neighborhood Preserving Projection using L1-norm Minimization

Purvi A. Koringa, Suman K. Mitra


Subspace analysis or dimensionality reduction techniques are becoming very popular for many computer vision tasks including face recognition or in general image recognition. Most of such techniques deal with optimizing a cost function using L2-norm. However, recently, due to capability of handling outliers, optimizing such cost function using L1-norm is drawing the attention of researchers. Present work is the first attempt towards the same goal where Orthogonal Neighbourhood Preserving Projection (ONPP) technique is optimized using L1-norm. In particular the relation of ONPP and PCA is established in the light of L2-norm and then ONPP is optimized using an already proposed mechanism of L1-PCA. Extensive experiments are performed on synthetic as well as real data. It has been observed that L1-ONPP outperforms its counterpart L2-ONPP.


  1. Baccini, A., Besse, P., and De Falguerolles, A. (1996). A l1-norm pca and a heuristic approach.
  2. Chang, H. and Yeung, D.-Y. (2006). Robust locally linear embedding. Pattern recognition, 39(6):1053-1065.
  3. Ding, C., Zhou, D., He, X., and Zha, H. (2006). R 1- pca: rotational invariant l 1-norm principal component analysis for robust subspace factorization. In Proceedings of the 23rd international conference on Machine learning, pages 281-288. ACM.
  4. Fisher, R. A. (1999). UCI repository of machine learning databases - iris data set.
  5. He, X., Cai, D., Yan, S., and Zhang, H. J. (2005). Neighborhood preserving embedding. In Tenth IEEE International Conference on Computer Vision, ICCV 2005., volume 2, pages 1208-1213. IEEE.
  6. He, X. and Niyogi, P. (2004). Locality preserving projections. In Advances in Neural Information Processing Systems, pages 153-160.
  7. Ke, Q. and Kanade, T. (2005). Robust l 1 norm factorization in the presence of outliers and missing data by alternative convex programming. In Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on, volume 1, pages 739- 746. IEEE.
  8. Kokiopoulou, E. and Saad, Y. (2007). Orthogonal neighborhood preserving projections: A projection-based dimensionality reduction technique. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(12):2143-2156.
  9. Koringa, P., Shikkenawis, G., Mitra, S. K., and Parulkar, S. (2015). Modified orthogonal neighborhood preserving projection for face recognition. In Pattern Recognition and Machine Intelligence, pages 225- 235. Springer.
  10. Kwak, N. (2008). Principal component analysis based on l1-norm maximization. IEEE transactions on pattern analysis and machine intelligence, 30(9):1672-1680.
  11. Lu, J., Plataniotis, K. N., and Venetsanopoulos, A. N. (2003). Face recognition using lda-based algorithms. Neural Networks, IEEE Transactions on, 14(1):195- 200.
  12. Roweis, S. T. and Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500):2323-2326.
  13. Shikkenawis, G. and Mitra, S. K. (2012). Improving the locality preserving projection for dimensionality reduction. In Third International Conference on Emerging Applications of Information Technology (EAIT), 2012, pages 161-164. IEEE.
  14. Turk, M. and Pentland, A. (1991). Eigenfaces for recognition. Journal of Cognitive Neuroscience, 3(1):71-86.

Paper Citation

in Harvard Style

A. Koringa P. and K. Mitra S. (2017). Orthogonal Neighborhood Preserving Projection using L1-norm Minimization . In Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-222-6, pages 165-172. DOI: 10.5220/0006196101650172

in Bibtex Style

author={Purvi A. Koringa and Suman K. Mitra},
title={Orthogonal Neighborhood Preserving Projection using L1-norm Minimization},
booktitle={Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

in EndNote Style

JO - Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - Orthogonal Neighborhood Preserving Projection using L1-norm Minimization
SN - 978-989-758-222-6
AU - A. Koringa P.
AU - K. Mitra S.
PY - 2017
SP - 165
EP - 172
DO - 10.5220/0006196101650172