Abstract
Manifold learning is developed to find the observed data’s low dimension embeddings in high dimensional data space. As a type of effective nonlinear dimension reduction method, it has been widely applied to data mining, pattern recognition and machine learning. However, most existing manifold learning algorithms work in a “batch” mode and cannot effectively process data collected sequentially (or data streams). In order to explore the intrinsic low dimensional manifold structures in data streams on-line or incrementally, in this paper we propose a new manifold Learning algorithm based on Incremental Tangent Space Alignment, LITSA for short. By constructing data points’ local tangent spaces to preserve local coordinates incrementally, we can accurately obtain the low dimensional global coordinates. Experiments on both synthetic and real datasets show that the proposed algorithm can achieve a more accurate low-dimensional representation of the data than state-of-the-art incremental algorithms.
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References
Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Zhang, Z.Y., Zha, H.Y.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2004)
Law, M.H.C., Jain, A.K.: Incremental nonlinear dimensionality reduction by manifold learning. IEEE Trans. Pattern Anal. Mach. Intell. 28, 377–391 (2006)
Jia, P., Yin, J., et al.: Incremental Laplacian eigenmaps by preserving adjacent information between data points. Pattern Recogn. Lett. 30, 1457–1463 (2009)
Kouropteva, O., Okun, O., et al.: Incremental locally linear embedding. Pattern Recogn. 38, 1764–1767 (2005)
Abdel-Mannan, O., Ben Hamza, A., et al.: Incremental line tangent space alignment algorithm. In: Proceedings of Canadian Conference on Electrical and Computer Engineering (CCECE), pp. 1329–1332. IEEE (2007)
Liu, X., Yin, J., Feng, Z., Dong, J.: Incremental manifold learning via tangent space alignment. In: Schwenker, F., Marinai, S. (eds.) ANNPR 2006. LNCS, vol. 4087, pp. 107–121. Springer, Heidelberg (2006). doi:10.1007/11829898_10
Zhao, D.F., Yang, L.: Incremental isometric embedding of high-dimensional data using connected neighborhood graphs. IEEE Trans. Pattern Anal. Mach. Intell. 31, 86–98 (2009)
Abdel-Mannan, O., Ben Hamza, A., et al.: Incremental Hessian locally linear embedding algorithm. In: Proceedings of 9th International Symposium on Signal Processing and Its Applications (ISSPA), pp. 1–4. IEEE (2007)
Min, W.L., Lu, L., He, X.F.: Locality pursuit embedding. Pattern Recogn. 37(4), 781–788 (2004)
Ling, G, Han, P., et al.: Face recognition via semi-supervised discriminant local analysis. In: Proceedings of International Conference on Signal and Image Processing Applications (ICSIPA), pp. 292–297. IEEE (2015)
Li, B., Du, J., Zhang, X.: Feature extraction using maximum nonparametric margin projection. Neurocomputing 188, 225–232 (2016)
Han, P., Yin, O., Ling, G.: Semi-supervised generic descriptor in face recognition. In: Proceedings of International Colloquium on Signal Processing and Its Applications (CSPA), pp. 21–25. IEEE (2015)
Xu, Y., Huang, H., et al.: Semi-supervised local fisher discriminant analysis for speaker verification. Adv. Inf. Sci. Serv. Sci. 6, 1–11 (2014)
Artac, M., Jogan, M., Leonardis, A.: Incremental PCA for on-line visual learning and recognition. In: Proceedings of International Conference on Pattern Recognition (ICPR), pp. 781–784. IEEE (2002)
Zhao, H., Yuen, P.C., Kwok, J.T.: A novel incremental principal component analysis and its application for face recognition. IEEE Trans. Syst. 36(4), 873–886 (2006)
Li, Y.M.: On incremental and robust subspace learning. Pattern Recogn. 37(7), 1509–1518 (2004)
Weng, J.Y., Zhang, Y.L., Hwang, W.S.: Candid covariance-free incremental principal component analysis. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 1034–1040 (2003)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (2012)
Acknowledgements
This work is supported by National Natural Science Foundation of China under Grants No. 41471371 and the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No. 15KJB520022.
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Tan, C., Ji, G. (2016). A Manifold Learning Algorithm Based on Incremental Tangent Space Alignment. In: Sun, X., Liu, A., Chao, HC., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2016. Lecture Notes in Computer Science(), vol 10040. Springer, Cham. https://doi.org/10.1007/978-3-319-48674-1_48
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DOI: https://doi.org/10.1007/978-3-319-48674-1_48
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