Dimensionality reduction methods have commonly been used as principled ways to understand high-dimensional data. In this paper, a novel non-linear method named supervised data-dependent kernel sparsity preserving projection (SDKSPP) is proposed for dimensionality reduction. SDKSPP is a non-linear extension of sparsity preserving projection, it adopts a data-dependent kernel (DK) instead of standard kernels to achieve performance improvements. Different from previous dimensionality reduction methods based on DK, SDKSPP can simultaneously optimize the coefficients in DK and explore the manifold structure, i.e., the sparse reconstructive relationship of data. The manifold structure in the feature space is shared in the label space so that the information of labels can be utilized to help optimizing the coefficients in DK and improving the discriminative ability. After the optimal sparse reconstructive relationship is obtained, a transform matrix that can preserve this relationship is calculated to project the mapped data into a low-dimensional space. The effectiveness of the proposed method is tested and compared on nine popular databases.
This is a preview of subscription content, log in to check access.
This work is partially supported by the National Natural Science Foundation of China (No. 61573088, No. 61573087 and No. 61433004).
Turk MA, Pentland AP (1991) Face recognition using eigenfaces. In: International conference on computer research and development, CVPR. IEEE, pp 302–306Google Scholar
Belhumeur PN, Hespanha JP, Kriengman DJ (1997) Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720CrossRefGoogle Scholar
Tenenbaum JB, De SV, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319CrossRefGoogle Scholar
Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290 (5500):2323CrossRefGoogle Scholar
Qiao L, Chen S, Tan X (2010) Sparsity preserving projections with applications to face recognition. Pattern Recogn 43(1):331– 341CrossRefGoogle Scholar
Zhang J, Wang J, Cai X (2017) Sparse locality preserving discriminative projections for face recognition. Neurocomputing 260:321–330CrossRefGoogle Scholar
Lou S, Zhao X, Chuang Y, Zhang S (2016) Graph Regularized Sparsity Discriminant Analysis for face recognition. Neurocomputing 173(P2):290–297CrossRefGoogle Scholar
Zhang P, You X, Ou W, Chen CLP, Cheung YM (2016) Sparse discriminative multi-manifold embedding for one-sample face identification. Pattern Recogn 52(C):249–259CrossRefGoogle Scholar
Gao S, Tsang WH, Chia LT (2010) Kernel Sparse Representation for Image Classification and Face Recognition. In: European Conference on Computer Vision, ECCV, pp 1–14Google Scholar
Lin C, Wang B, Zhao X, Pang M (2013) Optimizing kernel PCA using sparse representation-based classifier for MSTAR SAR image target recognition. Mathematical Problems in Engineering 2013(6)707–724Google Scholar
Lee MMS, Keerthi SS, Ong CJ, Decoste D (2004) An efficient method for computing leave-one-out error in support vector machines with Gaussian kernels. IEEE Trans Neural Netw 15(3):750–757CrossRefGoogle Scholar
Cristianini N, Kandola J, Elisseeff A, Shawe-Taylor J (2002) On Kernel-Target alignment. Adv Neural Inform Process Syst 179(5):367–373Google Scholar
Lanckriet GRG, Cristianini N, Bartlett P, Ghaoui LE, Jordan MI (2004) Learning the kernel matrix with Semi-Definite programming. J Mach Learn Res 5(Jan):27–72zbMATHGoogle Scholar
Smola AJ, Schölkopf B, Müller KR (1998) The connection between regularization operators and support vector kernels. Neural Netw 11(4):637–649CrossRefGoogle Scholar
Wang D, Zhang M, Cai Z et al (2016) Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning. Opt Commun 369:199–208CrossRefGoogle Scholar
Wen J, Fang X, Cui J et al (2018) Robust sparse linear discriminant analysis. IEEE Trans Circ Syst Video Technol PP(99):1–13Google Scholar
Martínez A M, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Intell 23(2):228–233CrossRefGoogle Scholar
Samaria FS, Harter AC (1994) Parameterisation of a stochastic model for human face identification. In: Proceedings of the Second IEEE Workshop on Applications of Computer Vision. IEEE, pp 138–142Google Scholar