Abstract
Linear dimensionality reduction techniques have been applied widely in data classification and recognition to extract low-dimensional features. The methods exploit a simple linear function to transform high dimensional data into a low dimensional subspace while preserving the statistical or geometrical characteristics of high dimensional datasets. The neighborhood relationship is one of the most important geometrical characteristics. The original dimensionality reduction algorithms usually set neighborhood parameters manually when defining neighborhood relationships. However, the methods based on collaborative representation select the neighbors automatically. A supervised dimensionality reduction method proposed in this paper is named Collaborative Representation based Discriminant Local Preserving Projection (CR-DLPP). First, it uses collaborative representation to select potential neighbors automatically for samples reconstruction. Then, a similarity matrix is built by calculating the Gaussian distance between the reconstructed samples. Finally, the Maximum Margin Criterion (MMC) is adopted to design an objective function, and the optimal projection matrix is obtained via eigenvalue decomposition. The results of extensive experiments on several benchmark datasets show that CR-DLPP can achieve better performance than several other typical linear dimensionality reduction methods.
Similar content being viewed by others
References
Wei Y, Xia W, Lin M et al (2016) HCP: a flexible CNN framework for multi-label image classification. IEEE Trans Softw Eng 38:1901–1907
Hannun A, Case C, Casper J et al (2014) Deep speech: scaling up end-to-end speech recognition. arXiv 1412.5567.
Karpathy A, Toderici G, Shetty S et al (2014) Large-scale video classification with convolutional neural networks. Proceedings of the IEEE conference on computer vision and pattern recognition. 1725–1732
Ayesha S, Hanif MK, Talib R (2020) Overview and comparative study of dimensionality reduction techniques for high dimensional data. Inform Fusion 59:44–58. https://doi.org/10.1016/j.inffus.2020.01.005
Ringnér M (2008) What is principal component analysis? Nat Biotechnol 26:303–304
Ahmadkhani S, Adibi P (2016) Face recognition using supervised probabilistic principal component analysis mixture model in dimensionality reduction without loss framework. IET Comput Vis 10:193–201
Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 7:711–720
Tharwat A, Gaber T, Ibrahim A et al (2017) Linear discriminant analysis: a detailed tutorial. AI Commun 30:169–190
Chen L, Liao H, Ko M et al (2000) A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognit 33:1713–1726
Li H, Jiang T, Zhang K (2006) Efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 17:157–165
Liu J, Chen S, Tan X et al (2007) Comments on ‘‘Efficient and robust feature extraction by maximum margin criterion”. IEEE Trans Neural Netw 18:1862–1864
Howland P, Wang J, Park H (2006) Solving the small sample size problem in face recognition using generalized discriminant analysis. Pattern Recognit 39:277–287
He X, Yan S, Hu Y et al (2003) Learning a locality preserving subspace for visual recognition. Proceeding of ninth IEEE international conference on computer vision. 385–392
He X, Niyogi P (2004) Locality preserving projections. In: Advances in Neural Information Processing Systems, pp 153–160
Wang H, Che S, Hu Z, Zheng W (2008) Locaility-preserved maximum information projection. IEEE Trans Neural Netw 19:571–585
Yu W, Teng X, Liu C (2006) Face recognition using discriminant locality preserving projections. Image Vis Comput 24:239–248
Yang L, Gong W, Gu X et al (2008) Null space discriminant locality preserving projections for face recognition. Neurocomputing 71:3644–3649
Ruisheng R, Ren Y, Zhang S, Fang B (2021) A novel discriminant locality preserving projections method. J Math Imaging Vis 63:541–554
Ran R, Feng J, Zhang S, Fang B (2020) A general matrix function dimensionality reduction framework and extension for manifold learning. IEEE Trans Cybern 99:1–12
Yan S, Xu D, Zhang B et al (2006) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29:40–51
Goyal P, Ferrara E (2018) Graph embedding techniques. Appl Perform: A Surv Knowl-Based Syst 151:78–94
Gou J, Xue Y, Ma H et al (2020) Double graphs-based discriminant projections for dimensionality reduction. Neural Comput Appl 32:17533–17550
Wang S, Ding C, Hsu C, Yang F (2020) Dimensionality reduction via preserving local information. Futur Gener Comput Syst 108:967–975
Gou J, Yang Y, Yi Z et al (2020) Discriminative globality and locality preserving graph embedding for dimensionality reduction. Expert Syst Appl 144:113079
Wright J, Yang AY, Ganesh A et al (2008) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31:210–227
Wang Y, Tang Y, Li L et al (2019) Block sparse representation for pattern classification: theory, extensions and applications. Pattern Recognit 88:198–209
Zhang Z, Xu Y, Yang J et al (2015) A survey of sparse representation: algorithms and applications. IEEE Access 3:490–530
Zhang L, Yang M, Feng X et al. (2012) Collaborative representation based classification for face recognition. arXiv:1204.2358.
Cai S, Zhang L, Zuo W (2016) A probabilistic collaborative representation based approach for pattern classification, Proceedings of the IEEE conference on computer vision and pattern recognition. 2950–2959.
Gou J, Hou B, Qu W et al (2018) Several robust extensions of collaborative representation for image classification. Neurocomputing. https://doi.org/10.1016/j.neucom.2018.06.089
Deng W, Hu J, Guo J (2018) Face recognition via collaborative representation: its discriminant nature and superposed representation. IEEE Trans Pattern Anal Mach Intell 40:2513–2521
Qiao L, Chen S, Tan X (2010) Sparsity preserving projections with applications to face recognition. Pattern Recognit 43:331–341
Gui J, Sun Z, Jia W et al (2012) Discriminant sparse neighborhood preserving embedding for face recognition. Pattern Recognit 45:2884–2893
Liao M, Gu X (2020) Face recognition approach by subspace extended sparse representation and discriminative feature learning. Neurocomputing 373:35–49
Gou J, Du L, Cheng K et al. (2016) Discriminative sparsity preserving graph embedding. Proceeding of 2016 IEEE congress on evolutionary computation (CEC).
Zhang L, Yang M, Feng X (2011) Sparse representation or collaborative representation: which helps face recognition. Proceedings of IEEE conference on computer vision (ICCV) 471–478.
Zhang W, Wang Z, Sun C (2015) A collaborative representation based projections method for feature extraction. Pattern Recognit 48:20–27
Hua J, Wang H, Ren M, Huang H (2016) Dimension reduction using collaborative representation reconstruction based projections. Neurocomputing 193:1–6
Wang L, Li M, Ji H, Li D (2019) When collaborative representation meets subspace projection: a novel supervised framework of graph construction augmented by anti-collaborative representation. Neurocomputing 328:157–170
Pless R, Souvenir R (2009) A survey of manifold learning for images. IPSJ Trans Comput Vis Appl 1:83–94
Huang P, Li T, Gao G et al (2018) Collaborative representation based local discriminant projection for feature extraction. Digit Signal Process 76:84–93
Gou J, Yang Y, Liu Y et al (2020) Collaborative representation-based locality preserving projections for image classification. J Eng 13:310–315
Wang G, Gong L, Pang Y et al (2020) Dimensionality reduction using discriminant collaborative locality preserving projections. Neural Process Lett 51:611–638
Wang G, Shi N (2020) Collaborative representation-based discriminant neighborhood projections for face recognition. Neural Comput Appl 32:5815–5832
Yuan M, Feng D, Liu W, Xiao C (2016) Collaborative representation discriminant embedding for image classification. J Vis Commun Image Represent 41:212–224
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge
Magnus JR, Neudecker H (1999) Matrix differential calculus with applications in statistics and econometrics. Revised ed. Wiley, Chichester
Georghiades AS, Belhumeur PN, Kriegman D (2001) From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23:643–660
Phillips PJ, Moon H, Rizvi SA et al (2000) The FERET evaluation methodology for face recognition algorithms. IEEE Trans Pattern Anal Mach Intell 22:1090–1104
Sim T, Baker S, Bsat M (2003) The CMU pose, illumination, and expression database. IEEE Trans Pattern Anal Mach Intell 25:1615–1618
Nene SA, Nayar SK, Murase H (1996) Technical report CUCS-005–96, Columbia object image library (COIL-20).
Guyon I, Gunn SR, Ben-Hur A, Dror G (2004) Result analysis of the NIPS 2003 Feature Selection Challenge. In: Advances in neural information processing systems, pp 545–552
Bouzas D, Arvanitopoulos N, Tefas A (2015) Graph embedded nonparametric mutual information for supervised dimensionality reduction. IEEE Trans Neural Netw Learn Syst 26:951–963
Lu Y, Lai Z, Xu Y et al (2016) Low-rank preserving projections. IEEE Trans Cybern 46:1900–1913
Liu Z, Wang J, Liu G, Zhang L (2019) Discriminative low-rank preserving projection for dimensionality reduction. Appl Soft Comput 85:105768
Acknowledgements
The authors would like to convey their thanks and appreciation to the National Natural Science Foundation of China [grant number 61971470] for supporting the work.
Funding
This work was supported by the National Natural Science Foundation of China [grant number 61971470].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Su, T., Feng, D. & Hu, H. Collaborative Representation Based Discriminant Local Preserving Projection. Neural Process Lett 54, 3999–4026 (2022). https://doi.org/10.1007/s11063-022-10798-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-022-10798-6