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A regularized approach for unsupervised multi-view multi-manifold learning

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Abstract

In this paper, we focus on the fundamental problem of efficiently selecting uniform class-consistent neighbors from all available views for graph-based multi-view multi-manifold learning methods in an unsupervised manner. We define each class of objects with continuous varying of pose angle as a relatively independent object manifold. The ideal neighborhood set is unknown, and selecting an appropriate neighborhood is not an easy task if we have multiple manifolds that have some intersections. Our approach concentrated on choosing the comprehensive form of each object manifold. We propose a TV-regularized least square problem to represent each object in a weighted sum of its class-consistent neighbors under different views. The goal of the proposed method is to make a distinction between some class-consistent view-inconsistent objects and class-inconsistent view-consistent objects that may be very close and also select a significant subset of the class-consistent view-inconsistent neighbors. The results we achieve show the superiority of proposed neighborhood graph construction when applied to manifold learning methods. The proposed approach works as extensions for the current graph-based manifold learning methods, such as Isomap, LLE, and LE, to handle multiple manifolds. Neighborhood selection and recognition accuracy experiments on several benchmark multi-view data sets have verified the excellent performance of our novel approach.

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References

  1. Madathil, B., George, S.N.: A novel dictionary-based approach for missing sample recovery of signals in manifold. SIViP 11(2), 283–290 (2016)

    Article  Google Scholar 

  2. Hu, M.W., Sun, Z., Zhao, S.: Kernel collaboration representation-based manifold regularized model for unconstrained face recognition. SIViP 12(5), 925–932 (2018)

    Article  Google Scholar 

  3. Aeini, F., Moghadam, A.M.E., Mahmoudi, F.: Supervised hierarchical neighborhood graph construction for manifold learning. SIViP 12(4), 799–807 (2018)

    Article  Google Scholar 

  4. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensional reduction and data representation. Neural Comput. 15, 1373–1396 (2000)

    Article  MATH  Google Scholar 

  5. Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM J. Sci. Comput. 26(1), 313–338 (2002)

    Article  MATH  Google Scholar 

  6. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  7. Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)

    Article  Google Scholar 

  8. Vlachos, M., Domeniconi, C., Gunopulos, D., Kollios, G., Koudas, N.: Non-linear dimensionality reduction techniques for classification and visualization. In: Proceedings of ACM Int. Conf. Knowl. Discovery Data Mining, pp. 645–651. ACM New York NY. USA (2002)

  9. Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Neural Information Processing Systems, pp. 585–591 (2002)

  10. Sakarya, U.: Semi-supervised dimension reduction approaches integrating global and local pattern information. SIViP (2018). https://doi.org/10.1007/s11760-018-1342-5

    Google Scholar 

  11. Hettiarachchi, R., Peters, J.F.: Multi-manifold LLE learning in pattern recognition. Pattern Recogn. 48(9), 2947–2960 (2015)

    Article  MATH  Google Scholar 

  12. Lee, C.-S., Elgammal, A., Torki, M.: Learning representations from multiple manifolds. Pattern Recogn. 50, 74–87 (2016)

    Article  Google Scholar 

  13. Fan, M., Zhang, X., Qiao, H., Zhang, B.: Efficient isometric multi-manifold learning based on the self-organizing method. Inf. Sci. 345, 325–339 (2016)

    Article  Google Scholar 

  14. Yang, B., Xiang, M., Zhang, Y.: Multi-manifold discriminant Isomap for visualization and classification. Pattern Recogn. 55, 215–230 (2016)

    Article  Google Scholar 

  15. Li, B., Li, J., Zhang, X.-P.: Nonparametric discriminant multi-manifold learning for dimensionality reduction. Neurocomputing 152(25), 121–126 (2015)

    Article  Google Scholar 

  16. Li, J., Wu, Y., Zhao, J., Lu, K.: Multi-manifold sparse graph embedding for multi-modal image classification. Neurocomputing 173(3), 501–510 (2016)

    Article  Google Scholar 

  17. Sun, S.: A survey of multi-view machine learning. Neural Comput. Appl. 23, 2031–2038 (2013)

    Article  Google Scholar 

  18. Li, Y., Shi, X., Du, C., Liu, Y., Wen, Y.: Manifold regularized multi-view feature selection for social image annotation. Neurocomputing 204(5), 135–141 (2016)

    Article  Google Scholar 

  19. Nane, S.A., Nayar, S.K., Murase, H.: Columbia Object Image Librarry (COIL-20). Department of Computer Science, Columbia University, New York (1996)

    Google Scholar 

  20. Gao, W., Cao, B., Shan, S.: The CAS-PEAL large-scale chinese face database and baseline evaluations. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 38(1), 149–161 (2008)

    Article  Google Scholar 

  21. Geng, X., Zhan, D.C., Zhou, Z.H.: Supervised nonlinear dimensionality reduction for visualization and classification. IEEE Trans. Syst. Man Cybern. Part B Syst. Hum. 35(6), 1098–1107 (2005)

    Article  Google Scholar 

  22. Aeini, F., Moghadam, A.M.E., Mahmoudi, F.: Non linear dimensional reduction method based on supervised neighborhood graph. In: 7th International Symposium on Telecommunications (IST’2014). IEEE: Tehran, Iran, pp. 35–40 (2014)

  23. Ridder, D.D., Kouropteva, O., Okun, O., Pietikäinen, M., Duin, R.P.W.: Supervised locally linear embedding. In: Artificial Neural Networks and Neural Information Processing-ICANN/ICONIP 2003, pp. 333–341. Springer (2003)

  24. Raducanu, B., Dornaika, F.: A supervised non-linear dimensionality reduction approach for manifold learning. Pattern Recognit. 45, 2432–2444 (2012)

    Article  MATH  Google Scholar 

  25. Zhang, Z., Chow, T.W.S., Zhao, M.: M-Isomap: orthogonal constrained marginal isomap for nonlinear dimensionality reduction. IEEE Trans. Cybern. 43(1), 180–191 (2013)

    Article  Google Scholar 

  26. Boyd, S., Parikh, N., Chu, E., Peleat, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–125 (2010)

    Article  MATH  Google Scholar 

  27. Barbero, A.l., Sra, S.: Fast algorithms for total-variation based optimization. Max–Planck–Institut f ¨ur biologische Kybernetik (2010)

  28. Thomaz, C.E., Giraldi, G.A.: A new ranking method for principal components analysis and its application to face image analysis. Image Vis. Comput. 28(6), 902–913 (2010)

    Article  Google Scholar 

  29. Samaria, F., Harter, A.: Parameterisation of a stochastic model for human face identification. In: Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota FL (1994)

  30. Zhang, Y., Ye, D., Liu, Y.: Robust locally linear embedding algorithm for machinery fault diagnosis. Neurocomputing 273(17), 323–332 (2018)

    Article  Google Scholar 

  31. Maaten, L.J.P.V.D., Postma, E.O., Herik, H.J.V.D.: Dimensionality reduction: a comparative review. Mach. Learn. Res. 10(1-41), 66–71 (2009)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer and Information Technology Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Faraein Aeini & Amir Masoud Eftekhari Moghadam

  2. Data Scientist Advanced Analytics Department, General Motors, Warren, MI, USA

    Fariborz Mahmoudi

Authors
  1. Faraein Aeini
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  2. Amir Masoud Eftekhari Moghadam
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  3. Fariborz Mahmoudi
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Correspondence to Amir Masoud Eftekhari Moghadam.

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Aeini, F., Eftekhari Moghadam, A.M. & Mahmoudi, F. A regularized approach for unsupervised multi-view multi-manifold learning. SIViP 13, 253–261 (2019). https://doi.org/10.1007/s11760-018-1352-3

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