Abstract
In this paper, we present a novel approach for classification named Probabilistic Semi-supervised Random Subspace Sparse Representation (P-RSSR). In many random subspaces based methods, all features have the same probability to be selected to compose the random subspace. However, in the real world, especially in images, some regions or features are important for classification and some are not. In the proposed P-RSSR, firstly, we calculate the distribution probability of the image and determine which feature is selected to compose the random subspace. Then, we use Sparse Representation (SR) to construct graphs to characterize the distribution of samples in random subspaces, and train classifiers under the framework of Manifold Regularization (MR) in these random subspaces. Finally, we fuse the results in all random subspaces and obtain the classified results through majority vote. Experimental results on face image datasets have demonstrated the effectiveness of the proposed P-RSSR.
Similar content being viewed by others
References
A leksandar D, Qiu D (2010) Automatic hard thresholding for sparse signal reconstruction from NDE measurements. Rev Progress Quant Nondestruct Eval 29(1211):806–813
Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neurocomputing 15(6):1373–1396
Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434
Cai D, He XF, Han JW (2007) Semi-supervised discriminant analysis. IEEE international conference on computer vision 1–7
Cevikalp H, Verbeek J, Jurie F, Klaser A (2008) Semi-supervised dimensionality reduction using pairwise equivalence constraints. Conf Comput Vis Imaging Comput Graph Theory Appl 1:489–496
Chen K, Wang SH (2011) Semi-supervised learning via regularized boosting working on multiple semi-supervised assumptions. IEEE Trans Pattern Anal Mach Intell 33(1):129–143
Cui JS, Liu Y, Xu YD, Zhao HJ, Zha HB (2013) Tracking generic human motion via fusion of low-and high-dimensional approaches. IEEE Trans Syst Man Cybern: Syst 43(4):996–1002
Ding M, Fan G (2015) Multilayer joint gait-pose manifolds for human gait motion modeling. IEEE Trans Cybern 45(11):2413–2424
Drori I, Donoho DL (2006) Solution of L1 minimization problems by LARS/homotopy methods. IEEE international conference on acoustics, speech and signal processing 636–639
Fan MY, Gu NN, Qiao H, Zhang B (2011) Sparse regularization for semi-supervised classification. Pattern Recogn 44(8):1777–1784
Fan MY, Zhang XQ, Lin ZC, Zhang ZF, Bao HJ (2014) A regularized approach for geodesic-based semisupervised multimanifold learning. IEEE Trans Image Process 23(5):2133–2147
Girosi F (1998) An equivalence between sparse approximation and support vector machines. Neurocomputing 10(6):1455–1480
Han J, Yue J, Zhang Y, Bai LF (2014) Kernel maximum likelihood scaled locally linear embedding for night vision images. Opt Laser Technol 56(1):290–298
He XF, Yan SC, Hu YX, Niuogi P, Zhang HJ (2005) Face recognition using laplacian faces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340
Ho TK (1998) The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell 20(8):832–844
Jenatton R, Mairal J, Obozinski G, Bach G (2010) Proximal methods for sparse hierarchical dictionary learning. International conference on machine learning 487–494
Kim KI, Kwon Y (2010) Single-image super-resolution using sparse regression and natural image prior. IEEE Trans Pattern Anal Mach Intell 32:1127–1133
Lai ZH, Wan MH, Jin Z, Yang J (2011) Sparse two dimensional local discriminant projections for feature extraction. Neurocomputing 74(4):629–637
Lai ZH, Wong WK, Jin Z, Yang J, Xu Y (2012) Sparse approximation to the eigensubspace for discrimination. IEEE Trans Neural Netw Learn Syst 23(12):1948–1960
Lawrence ND (2004) Gaussian process latent variable models for visualisation of high dimensional data. Adv Neural Inf Proces Syst:329–336
Lawrence N (2005) Probabilistic non-linear principal component analysis with Gaussian process latent variable models. J Mach Learn Res 6(Nov):1783–1816
Lee KC, Ho J, Kriegman DJ (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 27(5):684–698
Li B, Huang DS, Wang C, Liu KH (2008) Feature extraction using constrained maximum variance mapping. Pattern Recogn 41(11):3287–3294
Liu Y, Zhang X, Cui JS, Wu C, Hamid Aghajan, Zha HB (2010) Visual analysis of child-adult interactive behaviors in video sequences. International conference on virtual systems and multimedia. IEEE 26–33
Liu Y, Cui JS, Zhao HJ, Zha HB (2012) Fusion of low-and high-dimensional approaches by trackers sampling for generic human motion tracking. 21st international conference on pattern recognition pattern recognition 898–901
Liu L, Zhang HX, Hu XJ, Sun FF (2014) Semi-supervised image classification learning based on random feature subspace. Chinese conference on pattern recognition 237–242
Liu Y, Nie L, Han L, Zhang LM, DS Rosenblum (2015) Action2Activity: recognizing complex activities from sensor data. Int Conf Artif Intell 1617-1623
Liu Y, Zheng Y, Liang Y, Liu SM, DS Rosenblum (2016) Urban water quality prediction based on multi-task multi-view learning. Proceedings of the twenty-fifth international joint conference on artificial intelligence 2576–2582
Liu L, Cheng L, Liu Y, Jia YP, DS Rosenblum (2016) Recognizing complex activities by a probabilistic interval-based model. Proceedings of the Thirtieth AAAI Conf Artif Intell 30:1266–1272
Liu Y, Nie L, Liu L, Rosenblum DS (2016) From action to activity: sensor-based activity recognition. Neurocomputing 181:108–115
Liu Y, Liang Y, Liu S, David SR, Zheng Y (2016) Predicting urban water quality with ubiquitous data. https://arxiv.org/abs/1610.09462v1
Liu Y, Zhang LM, Nie LQ, Yan Y, David SR (2016) Fortune teller: predicting your career path. Proceedings of the thirtieth AAAI Conference on Artificial Intelligence 201–207. AAAI Press, Phoenix
Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2008) Supervised dictionary learning. Conf Neural Info Process Systems 21:1–8
Mairal J, Jenatton R, Obozinski G, Bach F (2010) Network flow algorithms for structured sparsity. Conf Neural Info Process Syst 23:1558–1566
Mallapragada PK, Jin R, Jain AK, Liu Y (2009) Semiboost: boosting for semi-supervised learning. IEEE Trans Pattern Anal Mach Intell 31(11):2000–2014
Martinez AM, Benavente R (1998) The AR face database. CVC Tech Rep 24
Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Intell 23(2):228–233
Preoţiuc-Pietro D, Liu Y, Hopkins DJ, Ungar Lyle (2017) Beyond binary labels: political ideology prediction of Twitter users. Proceedings of the 55th annual meeting of the association for computational linguistics 1:729–740
Protter M, Elad M (2009) Image sequence denoising via sparse and redundant representations. IEEE Trans Image Process 18(18):27–35
Qiao LS, Chen SC, Tan XY (2010) Sparsity preserving discriminant analysis for single training image face recognition. Pattern Recogn Lett 31:422–429
Ramirez I, Sprechmann P, Sapiro G (2010) Classification and clustering via dictionary learning with structured incoherence and shared features. IEEE Conf Comput Vis Pattern Recognit 3501–3508. IEEE, San Francisco
Roweis ST, Saul LK (2000) Nonlinear dimension reduction by locally linear embedding. Science 290(5):2323–2326
Samaria F, Harter A (1994) Parameterisation of a stochastic model for human face identification. Proceedings of the second IEEE workshop on applications of computer vision 138–142. IEEE, Sarasota
Scholkopf B, Herbrich R, Smola AJ (2000) A generalized Representer theorem. Conf Comput Learn Theory 42(3):416–426
Shiozaki A (1986) Edge extraction using entropy operator. Comput Vis Graph Image Proc 36(4):1–9
Sim T, Baker S, Bsat M (2003) The CMU pose illumination and expression database. IEEE Trans Pattern Anal Mach Intell 25(12):1615–1618
Tenenbaum JB, Silva VD, Langform JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5000):2319–2323
Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J R Stat Soc 58(1):267–288
Wang JM, Fleet DJ, Hertzmann A (2008) Gaussian process dynamical models for human motion. IEEE Trans Pattern Anal Mach Intell 30(2):283–298
Wechsler H, Phillips PJ, Bruce V, Fogelman F, Huang TS (1998) Face recognition: from theory to applications. NATO ASI Series F, Comput Syst Sci 163:446–456
Wold S, Esbensen K, Geladi P (1987) Principal component analysis. Chemom Intell Lab Syst 2(1):37–52
Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2009) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227
Wu F, Wang WH, Yang Y, Zhuang YT, Nie FP (2010) Classification by semi-supervised discriminative regularization. Neurocomputing 73(10):1641–1651
Yang JC, Wright J, Huang T, Ma Y (2008) Image super-resolution as sparse representation of raw image patches. IEEE Conf Comput Vis Pattern Recognit: 1–8. IEEE, Anchorage
Yang WK, Sun CY, Zhang L (2011) A multi-manifold discriminant analysis method for image feature extraction. Pattern Recogn 44(8):1649–1657
Yu GX, Zhang G, Domeniconi C, Yu ZW, You J (2012) Semi-supervised classification based on random subspace dimensionality reduction. Pattern Recogn 45(3):1119–1135
Yu GX, Zhang G, Yu ZW, Domeniconi C, You J, Han GQ (2012) Semi-supervised ensemble classification in subspaces. Appl Soft Comput 12(5):1511–1522
Yu GX, Zhang GJ, Zhang ZL, Yu ZW, Lin D (2015) Semi-supervised classification based on subspace sparse representation. Knowl Inf Syst 43(1):81–101
Zhao MB, Chow TWS, Zhou W, Zhang Z, Li B (2014) Automatic image annotation via compact graph based semi-supervised learning. Knowl-Based Syst 76:148–165
Zhao MB, Zhan C, Wu Z, Tang P (2015) Semi-supervised image classification based on local and global regression. IEEE Signal Process Lett 22(10):1666–1670
Zhu X (2005) Semi-supervised learning literature survey. Computer Science, University of Wisconsin-Madison 2(3):4–63
Zhu XJ, Ghahramani ZB, Lafferty JD (2003) Semi-supervised learning using Gaussian fields and harmonic functions. Int Conf Mach Learn 3:912–919
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 61727802, 61501235), the National Defense Pre-Research Field Foundation of China (6140450010316BQ02001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, Z., Bai, L., Zhang, Y. et al. Probabilistic semi-supervised random subspace sparse representation for classification. Multimed Tools Appl 77, 23245–23271 (2018). https://doi.org/10.1007/s11042-017-5567-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-017-5567-z