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Simultaneous p- and s-orders minmax robust locality preserving projection

  • 1221: Deep Learning for Image/Video Compression and Visual Quality Assessment
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Abstract

This paper proposes a new method of locality preserving projection (LPP), which replaces the squared L2-norm minimization and maximization distances in the objective of conventional LPPW. The proposed method is termed as Simultaneous p- and s-orders Minmax Robust Locality Preserving Projection (psRLPP), which is robust to outlier samples. Then, we design an efficient iterative algorithm to solve the objective problem of psRLPP. At each iteration, our method ends with solving a trace ratio problem rather inexact ratio trace problem. We also conduct some insightful analysis on the existence of local minimum and the convergence of the proposed algorithm. These characteristics make our psRLPP more intuitive and powerful than the most up-to-date method, robust LPP via p-order minimization (RLPP) which considers only the p-order minimization of the L2-norm distance and requires transforming the original trace ratio problem in each iteration into an inexact ratio problem in the solving of projection vectors. Theoretical insights and effectiveness of our method is further supported by promising experimental results for clustering.

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References

  1. Adil D, Kyng R, Peng R, Sachdeva S (2019) Iterative Refinement for Lp-norm Regression. Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms

  2. Belkin M, Niyogi P (2003) Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Comput 15(6):1373–1396

    Article  MATH  Google Scholar 

  3. Cai D, He X, Han J (2007) Semi-supervised discriminant analysis. In Proc IEEE Int Conf Comput Vis, Rio de Janeiro, Brazil, pp. 1–7

  4. Dornaika F, Traboulsi YE (2016) Learning Flexible Graph-Based Semi-Supervised Embedding. IEEE Transactions on Cybernetics 46(1):206–218

    Article  Google Scholar 

  5. Fu L, Li Z, Ye Q et al (2020) Learning robust discriminant subspace based on joint L2, p- and L2, s-Norm distance metrics. IEEE Transactions on Neural Networks and Learning Systems (Early Access)

  6. Geusebroek JM, Burghouts GJ, Smeulders AWM (2005) The Amsterdam Library of Object Images. Int J Comput Vision 61(1):103–112

    Article  Google Scholar 

  7. Graham DB, Allinson NM (1998) Characterizing virtual eigensignatures for general purpose face recognition. NATO ASI Series F pp.446–456

  8. Handwritten Digit Dataset. (online), http://www.cs.nyu.edu/_roweis/data.html.

  9. He X, Yan S, Hu Y, Niyogi P, Zhang H (2005) “Face Recognition Using Laplacianfaces”, IEEE Trans. Pattern Analysis and Machine Intelligence 27(3):328–340

    Article  Google Scholar 

  10. Houben S, Stallkamp J, Salmen J et al (2013) “Detection of traffic signs in real-world images: the german traffic sign detection benchmark. In Proc Int Conf Neural Netw pp1–8

  11. Jia Y, Nie F, Zhang C (2009) Trace Ratio Problem Revisited. IEEE Transactions on Neural Networks and Learning Systems 20(4):729–735

    Article  Google Scholar 

  12. Jolliffe I (2005) Principal component analysis. Wiley Online Library

  13. Kwak N (2008) Principal component analysis based on L1-norm maximization. IEEE Trans Pattern Anal Mach Intell 30(9):1672–1680

    Article  Google Scholar 

  14. Kwak N (2014) Principal Component Analysis by Lp-norm Maximization. IEEE Trans Cybern 44(5):594–609

    Article  Google Scholar 

  15. Lai Z, Xu Y, Yang J et al (2017) Rotational Invariant Dimensionality Reduction Algorithms. IEEE Trans Cybern 47(11):3733–3746

    Article  Google Scholar 

  16. Lu G, Zhong L, Zhong J (2010) Face recognition using discriminant locality preserving projections based on maximum margin criterion. Pattern Recognit 43(10):3572–3579

    Article  MATH  Google Scholar 

  17. Lu J, Tan Y (2011) Improved discriminant locality preserving projections for face and palmprint recognition. Neurocomputing 74(18):3760–3767

    Article  Google Scholar 

  18. Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans PatternAnal Mach Intell 23(2):228–233

    Article  Google Scholar 

  19. Nene SA, Nayar SK, Murase H (1996) Columbia Object Image Library (COIL-20). Columbia Univ. New York, Tech Rep CUCS-005–96

  20. Nie F, Huang H, Ding C, Luo DJ, Wang H (2011) Robust principal component analysis with non-greedy L1-norm maximization. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence

  21. Nie FP, Wang Z, Wang R et al (2021) Towards Robust Discriminative Projections Learning via Non-greedy L2,1-Norm MinMax. IEEE Trans Pattern Anal Mach Intell 41(6):2086–2100

    Article  Google Scholar 

  22. Roweis ST, Saul LK (2000) Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290:2323–2326

    Article  Google Scholar 

  23. Sugiyama M (2007) Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. J Mach Learn Res 8:1027–1061

    MATH  Google Scholar 

  24. Tenenbaum JB, Silva VD, Langford JC (2001) A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(2000):2319–2323

    Google Scholar 

  25. Wang H, Nie F, Huang H (2015) Learning robust locality preserving, projection via p-order minimization. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence pp. 3059–3065.

  26. Yu G, Zhang G, Domeniconi C, Yu Z, You J (2012) Semi-supervised classification based on random subspace dimensionality reduction. Pattern Recognit 45(3):1119–1135

    Article  MATH  Google Scholar 

  27. Yale. Face Database. (Online), available from: /http://cvc.yale.edu/projects/yalefaces/yalefaces.htmlS.

  28. Ye Q, Yang J, Liu F et al (2018) L1-Norm Distance Linear Discriminant Analysis Based on an Effective Iterative Algorithm. IEEE Transactions on Circuits Systems and Video Technology 28(1):114–129

    Article  Google Scholar 

  29. Ye Q, Zhao H, Li Z et al (2018) L1-norm Distance Minimization Based Fast Robust Twin Support Vector k-plane clustering. IEEE Transactions on Neural Networks and Learning Systems 29(9):4494–4503

    Article  Google Scholar 

  30. Yan He, Ye Q, Zhang T et al (2018) Least squares twin bounded support vector machines based on L1-norm distance metric for classification. Pattern Recogn 74:434–447

    Article  Google Scholar 

  31. Ye Q, Fu L, Zhang Z et al (2018) Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis. Neural Netw 105:393–404

    Article  MATH  Google Scholar 

  32. Ye Q, Li Z, Fu L et al (2019) Nonpeaked Discriminant Analysis. IEEE Transactions on Neural Networks and Learning Systems 30(12):3818–3832

    Article  MathSciNet  Google Scholar 

  33. Zhang H, Qian J, Zhang B, Yang J et al (2020) Low-Rank Matrix Recovery via Modified Schatten-p Norm Minimization with Convergence Guarantees. IEEE Trans Image Process 29:3132–3142

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhou GY, Xu GQ, Hao JY et al (2019) Generalized Centered 2-D Principal Component Analysis. IEEE Trans Cybern pp.1–12 (Early Access)

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Acknowledgements

The authors extend their appreciation to the Natural Science Foundation of the Jiangsu Higher Education Institute of China (20KJB413001), talent research start-up fund project (YKJ201922), the Innovative Training Program for College Students of Jiangsu Province (Grant No. 201911276014Z), and the Deanship of Scientific Research at King Saud University for funding this work through research group no. RG-1441-331. This work was also supported by Startup Foundation for Introducing Talent of Nan-jing University of Information Science and Technology (Grant No.2019r030).

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Authors and Affiliations

  1. Nanjing University of Information Science and Technology, Nanjing, China

    Biao Song

  2. Nanjing Institute of Technology, Nanjing, China

    Yuan Tian

  3. King Saud University, Riyadh, Saudi Arabia

    Najla Al-Nabhan

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  1. Biao Song
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  2. Yuan Tian
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  3. Najla Al-Nabhan
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Correspondence to Yuan Tian.

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Song, B., Tian, Y. & Al-Nabhan, N. Simultaneous p- and s-orders minmax robust locality preserving projection. Multimed Tools Appl 81, 42513–42526 (2022). https://doi.org/10.1007/s11042-021-11393-y

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