Abstract
The existing Kernel Nonnegative Matrix Factorization (KNMF) cannot ensure the non-negativity of the mapped data in the kernel feature space. This is called the nonnegative in-compatible problem of KNMF. To tackle this problem, this paper presents a new methodology to construct Nonnegative Compatible Kernel (NC-Kernel) for face recognition. We obtain a Nonnegative Nonlinear Mapping (NN-Mapping) by using the techniques of symmetric NMF and nonnegative interpolation strategy. The symmetric function generated by the NN-Mapping is proven to be a nonnegative compatible Mercer kernel function. We apply the NC-Kernel to the Kernel Principle Component Analysis (KPCA) and KNMF for face recognition. The ORL and Pain Expression face databases are selected for evaluations. Experimental results indicate our NC-Kernel based methods outperform some RBF or polynomial kernel based algorithms.
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.
Similar content being viewed by others
References
Turk, M., Pentland, A.: Eigenfaces for Recognition. Journal of Cognitive Neurosicence 3, 71–86 (1991)
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. NIPS 13, 556–562 (2001)
Lin, C.J.: Projected Gradients for Non-Negative Matrix Factorization. Neural Computation 19, 2756–2779 (2007)
Kotsia, I., Zafeiriou, S., Pitas, I.: A Novel Discriminant Non-Negative Matrix Factorization Algorithm with Applications to Facial Image Characterization Problems. IEEE Transactions on Information Forensics and Security 2, 588–595 (2007)
Buciu, I., Nikolaidis, N., Pitas, I.: Non-Negative Matrix Factorization in Polynomial Feature Space. IEEE Transactions on Neural Networks 19, 1090–1100 (2007)
Zafeiriou, S., Petrou, M.: Nonlinear Non-Negative Component Analysis Algorithms. IEEE Transactions on Image Processing 19, 1050–1066 (2010)
Pan, B.B., Lai, H.L., Chen, W.S.: Nonlinear Nonnegative Matrix Factorization Based on Mercer Kernel Construction. Pattern Recognition 44(10–11), 2800–2810 (2011)
Shi, M., Yi, Q., Lv, J.: Symmetric Nonnegative Matrix Factorization with Beta-Divergences. IEEE Signal Processing Letters 19, 539–542 (2012)
Schölkopf, B., Smola, A.J.: Learning with Kernels-Support Vector Machine, Regularization, Optimization, and Beyond. The MIT Press, Cambridge, MA (2002)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)
Zhu, F., Honeine, P., Kallas, M.: Kernel Nonnegative Matrix Factorization without the Curse of the Pre-Image. arXiv preprint, arXiv:1407.4420 (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
Zhao, Y., Chen, W., Pan, B., Chen, B. (2015). Non-negative Compatible Kernel Construction for 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-25417-3_3
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)