Abstract
Each manifold learning algorithm has its own advantages and applicable situations. And it is an important question that how to select out the best one as the result. To this end, a manifold learning fusion algorithm is proposed to select out the best one from multiple results yielded by different manifold learning algorithms according to an equation of criterion. Moreover, a kind of local optimal technique is used to optimize the embedded result. By combining the advantages of classical manifold learning algorithms that preserve some properties effectively and the better preservation to distance and angle, our algorithm can yield a more satisfactory result to almost all kind of manifolds. The effectiveness and stability of our algorithm are further confirmed by some experiments.
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References
Jolliffe, I.T.: Principal Component Analysis. Springer (1986)
Fisher, R.A.: The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics 7, 179–188 (1936)
He, X., Niyogi, P.: Locality Preserving Projections. In: Advances in Neural Information Processing Systems, pp. 37–44. MIT Press, Cambridge (2003)
He, X., Cai, D., Yan, S., Zhang, H.: Neighborhood Preserving Embedding. Computer Vision, 1208–1213 (2005)
Kokiopoulou, E., Saad, Y.: Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique. Pattern Analysis and Machine Intelligence 29(12), 2143–2156 (2007)
Zhang, T., Yang, J., Zhao, D., Ge, X.: Linear Local Tangent Space Alignment and Application to Face Recognition. Neurocomputing 70, 1547–1553 (2007)
Goldberg, Y., Zakai, A., Kushnir, D., Ritov, Y.: Manifold Learning: The Price of Normalization. Machine Learning Research 9, 1909–1939 (2008)
Rosman, G., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding. Computer Vision 89, 56–68 (2010)
Lin, T., Zha, H.B.: Riemannian Manifold Learning. Pattern Analysis and Machine Intelligence 30(5), 796–809 (2008)
Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(5000), 2219–2323 (2000)
Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290(5000), 2323–2326 (2000)
Donoho, D.L., Grimes, C.: Hessian eigenmaps: Locally Linear Embedding Techniques for High-dimensional Data. Proceedings of the National Academy of Sciences 100(10), 5591–5599 (2003)
Zhang, Z.Y., Zha, H.Y.: Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SLAM Journal of Scientific Computing 26(1), 313–338 (2004)
Belkin, M., Niyogi, P.: Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation 15, 1373–1396 (2002)
Weinberger, K.Q., Sha, F., Saul, L.K.: Learning a Kernal Matrix for Nonlinear Dimensionality Reduction. In: Proc. 21st ICML, pp. 839–846 (2004)
Coifman, R.R., Lafon, S.: Diffusion Maps. Applied and Computational Harmonic Ayalysis 21, 5–30 (2006)
Sha, F., Saul, L.K.: Analysis and Extension of Spectral Methods for Nonlinear Dimensionality Reduction. In: Proc. 22nd Int’l Conf. Machine Learning, pp. 785–792 (2005)
Gashler, M., Ventura, D., Martinez, T.: Manifold Learning by Graduated Optimization. System, Man, and Cybernetics-Part B: Bybernetics 41(6), 1458–1470 (2011)
Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks, vol. IV, pp. 1942–1948 (2005)
Mani Data set, http://www.math.ucla.edu/~wittman/mani/index.html
Frey Faces Data Set, http://www.cs.nyu.edu/~roweis/data.html
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Gu, Y., Zhang, D., Ma, Z., Niu, G. (2014). A Manifold Learning Fusion Algorithm Based on Distance and Angle Preservation. In: Li, S., Liu, C., Wang, Y. (eds) Pattern Recognition. CCPR 2014. Communications in Computer and Information Science, vol 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45646-0_4
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DOI: https://doi.org/10.1007/978-3-662-45646-0_4
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