Abstract
This paper attempts to develop a novel Non-negative Matrix Factorization (NMF) algorithm to improve traditional NMF approach. Based on gradient descent method, we appropriately choose a larger step-length than that of traditional NMF and obtain efficient NMF update rules with fast convergence rate and high performance. The step-length is determined by solving some inequalities, which are established according to the requirements on step-length and non-negativity constraints. The proposed algorithm is successfully applied to face recognition. The rates of both convergence and recognition are utilized to evaluate the effectiveness of our method. Compared with traditional NMF algorithm on ORL and FERET databases, experimental results demonstrate that the proposed NMF method has superior performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
He, X.F., Niyogi, P.: Locality preserving projections. In: Thrun, S., Saul, L.K., Schölkopf, B. (eds.) NIPS, vol. 16, pp. 153–160. MIT Press, Cambridge (2004)
Yang, J., Zhang, D., Yang, J.Y., Niu, B.: Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(4), 650–664 (2007)
Turk, M., Pentland, A.: Eigenfaces for Recognition. J. Cogn. Neurosci. 3(1), 71–86 (1991)
Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)
Lee, D.D., Seung, H.S.: Learning the Parts of Objects by Non-negative Matrix Factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Leen, T.K., Dietterich, T.G., Tresp, V. (eds.) NIPS, vol. 13, pp. 556–562. MIT Press, Cambridge (2000)
Li, L.X., Wu, L., Zhang, H.S.: Nonnegative Matrix Factorization: A Comprehensive Review. IEEE Transactions on Neural Networks and Learning Systems 25(6), 1336–1353 (2013)
Wang, Y.X., Zhang, Y.J., Wu, F.X.: A Fast Algorithm for Nonnegative Matrix Factorization and Its Convergence. IEEE Transactions on Knowledge and Data Engineering 25(10), 1855–1863 (2014)
Korattikara, A., Boyles, L., Welling, M., Kim, J., Park, H.: Statistical optimization of non-negative matrix factorization. In: 14th International Conference on Artificial Intelligence and Statistics, pp. 128–136. Microtome Publishing, Brookline (2011)
Mizutani, T.: Ellipsoidal Rounding for Nonnegative Matrix Factorization Under Noisy Separability. Journal of Machine Learning Research 15, 1011–1039 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Li, Y., Chen, W., Pan, B., Zhao, Y., Chen, B. (2015). An Efficient Non-negative Matrix Factorization with Its Application to Face Recognition. In: Yang, J., Yang, J., Sun, Z., Shan, S., Zheng, W., Feng, J. (eds) Biometric Recognition. CCBR 2015. Lecture Notes in Computer Science(), vol 9428. Springer, Cham. https://doi.org/10.1007/978-3-319-25417-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-25417-3_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25416-6
Online ISBN: 978-3-319-25417-3
eBook Packages: Computer ScienceComputer Science (R0)