Abstract
In this paper, a multiple sub-manifold learning method oriented classification is presented via sparse representation, which is named maximum variance sparse mapping. Based on the assumption that data with the same label locate on a sub-manifold and different class data reside in the corresponding sub-manifolds, the proposed algorithm can construct an objective function which aims to project the original data into a subspace with maximum sub-manifold distance and minimum manifold locality. Moreover, instead of setting the weights between any two points directly or obtaining those by a square optimal problem, the optimal weights in this new algorithm can be approached using L1 minimization. The proposed algorithm is efficient, which can be validated by experiments on some benchmark databases.
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References
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)
Bengio, Y., Paiement, J.-F., Vincent, P.: Out-of-sample extensions for LLE, Isomap, MDS, eigenmaps, and spectral clustering, Technical Report 1238, Universit’ e deMontreal (2003)
Yan, S., Xu, D., Zhang, B., Zhang, H.-J.: Graph Embedding: A General Framework for Dimensionality Reduction. IEEE Trans. Pattern Analysis and Machine Intelligence 29(1), 40–51 (2007)
He, X., Yang, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face Recognition Using Laplacianfaces. IEEE Trans. Pattern Analysis and Machine Intelligence 27(3), 328–340 (2005)
He, X., Niyogi, P.: Locality preserving projections. In: Neural Information Processing Systems, NIPS 2003, Vancouver, Canada, vol. 16 (2003)
Cai, D., He, X., Han, J., Zhang, H.: Orthogonal Laplacianfaces for Face Recognition. IEEE Trans. on Image Processing 15(11), 3609–3614 (2006)
Yang, J., Zhang, D., Yang, J.Y., Niu, B.: Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Application to Face and Palm Biometrics. IEEE Trans. Pattern Analysis and Machine Intelligence 29(4), 650–664 (2007)
Deng, W., Hu, J., Guo, J., Zhang, H., Zhang, C.: Comments on Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Application to Face and Palm Biometrics. IEEE Trans. Pattern Analysis and Machine Intelligence (accepted)
Li, B., Wang, C., Huang, D.-S.: Supervised feature extraction based on orthogonal discriminant projection. Neurocomputing 73(1-3), 191–196 (2009)
Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. J. Mach. Learning Res. 4, 119–155 (2003)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Wright, J., Yang, A., Sastry, S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)
Li, B., Huang, D.-S., Wang, C., Liu, K.-H.: Feature extraction using constrained maximum variance mapping. Pattern Recognition 41(11), 3287–3294 (2008)
Tibshirani, R.: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society 58(1), 267–288 (1996)
Drori, I., Donoho, D.: Solution of L1 minimization problems by LARS/Homotopy methods. In: ICASSP, vol. 3, pp. 636–639 (2006)
Qiao, L., Chen, S., Tan, X.: Sparsity preserving projections with applications to face recognition. Pattern Recognition 43(1), 331–341 (2010)
Brunet, J.P., Tamayo, P., Golun, T.R., Mesirov, J.P.: Metagenes and Molecular Pattern Discovery Using Matrix Factorization. Proc. Natl. Acad. Sci. 101, 4164–4416 (2004)
Pomeroy, S.L., Tamayo, P., et al.: Prediction of Central Nervous System Embryonal Tumour Outcome Based on Gene Expression. Nature 415, 436–442 (2002)
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Li, B., Liu, J., Dong, W. (2011). Maximum Variance Sparse Mapping. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21090-7_1
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DOI: https://doi.org/10.1007/978-3-642-21090-7_1
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