Abstract
Face clustering aims to group the face images without any label information into clusters, and has recently attracted considerable attention in machine learning and data mining. Many graph based clustering methods have been proposed and among which sparse representation (SR) and low-rank representation (LRR) are two representative methods for affinity graph construction. The clustering result may be inaccurate if the affinity graph is constructed with low quality. In this paper, we propose a novel face clustering method via learning a sparsity preserving low-rank graph (LSPLRG), where the initial affinity graph is derived on the sparse coefficients without any a priori graph or similarity matrix. In addition, an adaptive weighted matrix is imposed on the data reconstruction errors to enhance the role of important features, while a constraint on the representation matrix is to reduce the redundant features. By integrating the local distance regularization term into LRR, LSPLRG could exploit the global and local structures of data simultaneously. These appealing properties allow LSPLRG to well capture the intrinsic structure of data, and thus has potential to improve clustering performance. Experiments conducted on several face image databases demonstrate the effectiveness and robustness of LSPLRG compared with several state-of-the-art subspace clustering methods.
Similar content being viewed by others
References
Basri R, Jacobs DW (2003) Lambertian reflectance and linear subspaces. IEEE Trans Patt Anal Mach Intell 25(2):218–233
Benhur A, Horn D, Siegelmann H, Vapnik V (2002) Support vector clustering. J Mach Learn Res 2(2):125–137
Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122
Brukstein A, D Donoho M (2009) Elad, from sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev 51(1):34–81
Cai D, He X, Han J (2005) Document clustering using locality preserving indexing. IEEE Trans Know Data Eng 17(12):1624–1637
Cai D, He X, Han J, Huang TS (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Patt Anal Mach Intell 33(8):1548–1560
Candes EJ, Recht B (2009) Exact matrix completion via convex optimization. Found Comput Math 9(6):717–772
Chen S, Donoho DL, Saunders MA (2001) Atomic decomposition by basis pursuit. Siam Rev 43(1):129–159
Chen J, Yang J (2014) Robust subspace segmentation via low-rank representation. IEEE Trans Syst Man, Cybern 44(8):1432–1445
Donoho D (2006) For most large underdetermined systems of linear equations the minimal ℓ1-norm solution is also the sparsest solution. Commun Pure Appl Math 59 (6):797–829
Dornaika F, Kejani M, Bosaghzadeh A (2017) Graph construction using adaptive local hybrid coding scheme. Neural Netw 91–101
Eckstein J, Bertsekas DP (1992) On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math Program 55(3):293–318
Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781
Fan D, Zhang S, Wu Y, Liu Y, Cheng M, Ren B, Rosin PL (2019) Scoot: a perceptual metric for facial sketches. Int Conf Comput Vision 5612–5622
Fang X, Xu Y, Li X, Lai Z, Wong WK (2016) Robust semi-supervised subspace clustering via non-negative low-rank representation. IEEE Trans on Syst Man, Cybern 46(8):1828–1838
Glowinski R, Tallec PL (1989) Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. Math Comput 58(197)
Khan S, Hussain A, Usman M (2018) Reliable facial expression recognition for multi-scale images using weber local binary image based cosine transform features. Multimed Tools Appl 77(1):1133–1165
Khan S, Hussain A, Usman M, Nazir M, Riaz N, Mirza A (2014) Robust face recognition using computationally efficient features. J Intell Fuzzy Syst 27(6):3131–3143
Khan S, Ishtiaq M, Nazir M, Shaheen M (2018) Face recognition under varying expressions and illumination using particle swarm optimization. J Comput Sci 94–100
Khan S, Usman M, Riaz N (2015) Face recognition via optimized features fusion. J Intell Fuzzy Syst 28(4):1819–1828
Lin Z, Chen M, Ma Y (2011) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank Matrices. Neural Inform Process Sys 1–20
Liu G, Li P (2016) Low-rank matrix completion in the presence of high coherence. IEEE Trans Signal Process 64(21):5623–5633
Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Patt Analy Mach Intell 35(1):171–184
Lu C, Feng J, Lin Z, Mei T, Yan S (2019) Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell 41 (2):487–501
Luxburg UV (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416
Macqueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth berkeleysymposium on mathematical statistics and probability, pp 281–297
Munir A, Hussain A, Khan S, Nadeem M, Arshid S (2018) Illumination invariant facial expression recognition using selected merged binary patterns for real world images. Optik 1016–1025
Ng A, Jordan M, Weiss Y (2002) On spectral clustering: analysis and an algorithm. Neural Inform Process Syst 849–856
Nie F, Wang X, Jordan M, Huang H (2016) The constrained laplacian rank algorithm for graph-based clustering. In: Proceedings of the thirtieth aaai conference on artificial intelligence, pp 1969–1976
Qiao L, Chen S, Tan X (2010) Sparsity preserving projections with applications to face recognition. Pattern Recognit 43(1):331–341
Rao S, Tron R, Vidal R, Ma Y (2010) Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Trans Patt Anal Mach Intell 32(10):1832–1845
Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905
Vidal R (2011) Subspace clustering. IEEE Signal Process Mag 28 (2):52–68
Wang Q, Lin J, Yuan Y (2016) Salient band selection for hyperspectral image classification via manifold ranking. IEEE Trans Neural Netw 27 (6):1279–1289
Wen J, Han N, Fang X, Fei L, Yan K, Zhan S (2018) Low-rank preserving projection via graph regularized reconstruction. IEEE Trans on Syst Man, and Cybern 1–13
Wen J, Zhang B, Xu Y, Yang J, Han N (2018) Adaptive weighted nonnegative low-rank representation. Pattern Recognit 81:326–340
Xu L, Neufeld J, Larson B, Schuurmans D (2005) Maximum margin clustering. Neural Inform Process Syst 1537–1544
Xu R, Wunsch D (2005) Survey of clustering algorithms. IEEE Trans Neural Netw 16(3):645–678
Yang J, Yuan X (2012) Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization. Math Comput 82(281):301–329
Yao X, Han J, Zhang D, Nie F (2017) Revisiting co-saliency detection: a novel approach based on two-stage multi-view spectral rotation co-clustering. IEEE Trans Image Process 26(7):3196–3209
Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans Pat Anal Mach Intell 38(3):504–517
Zhang C, Hu Q, Fu H, Zhu P, Cao X (2017) Latent multi-view subspace clustering. Comput Vision Pattern Recognit 4333–4341
Zhang X, Xu C, Sun X, Baciu G (2016) Schatten-q regularizer constrained low rank subspace clustering model. Neurocomputing. 182:36–47
Zhao J, Hou Q, Ren B, Cheng M, Rosin P (2018) FLIC: fast linear iterative clustering with active search. Nat Conf Artif Intell 4(4):333–348
Zhao J, Liu J, Fan D, Cao Y, Yang J, Cheng M (2019) EGNEt: Edge guidance network for salient object detection. Int Conf Comput Vision 8779–8788
Zheng M, Bu J, Chen C, Wang C, Zhang L, Qiu G, Cai D (2011) Graph regularized sparse coding for image representation. IEEE Trans Image Process 20(5):1327–1336
Zheng J, Yang P, Chen S, Shen G, Wang W (2017) Iterative re-constrained group sparse face recognition with adaptive weights learning. IEEE Trans Image Process 26(5):2408–2423
Zhou T, Zhang C, Gong C, Bhaskar H, Yang J (2020) Multiview latent space learning with feature redundancy minimization. IEEE Trans on Syst Man, Cybern 50(4):1655–1668
Zhou T, Zhang C, Peng X, Bhaskar H, Yang J (2019) Dual shared-specific multiview subspace clustering. IEEE Trans Syst Man, Cybern 1–14
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant no. 61572393, 71701021 and 41601437, the Basic Science Research of Shaanxi province under Grant no. 2018JQ1038, the Fundamental Research Funds for the Central Universities in Chang’an University under Grant no. 300102120201, and the Special Fund for Basic Scientific Research of Central Colleges in Chang’an University under Grant no. 310812163504.
Author information
Authors and Affiliations
Corresponding author
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
Wang, C., Zhang, J., Song, X. et al. Face clustering via learning a sparsity preserving low-rank graph. Multimed Tools Appl 79, 29179–29198 (2020). https://doi.org/10.1007/s11042-020-09392-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-020-09392-6