Abstract
Nonnegative matrix factorization has been widely applied recently. The nonnegativity constraints result in parts-based, sparse representations which can be more robust than global, non-sparse features. However, existing techniques could not accurately dominate the sparseness. To address this issue, we present a unified criterion, called Nonnegative Matrix Factorization by Joint Locality-constrained and ℓ 2,1-norm Regularization(NMF2L), which is designed to simultaneously perform nonnegative matrix factorization and locality constraint as well as to obtain the row sparsity. We reformulate the nonnegative local coordinate factorization problem and use ℓ 2,1-norm on the coefficient matrix to obtain row sparsity, which results in selecting relevant features. An efficient updating rule is proposed, and its convergence is theoretically guaranteed. Experiments on benchmark face datasets demonstrate the effectiveness of our presented method in comparison to the state-of-the-art methods.
Similar content being viewed by others
References
Belhumeur PN, Hespanha JP, Kriegman D et al (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press
Bradley PS, Mangasarian OL (1998) Feature selection via concave minimization and support vector machines. In: International conference on machine learning, pp 82–90
Cai D, He X, Han J et al (2007) Spectral regression: a unified approach for sparse subspace learning. In: International conference on data mining, pp 73–82
Cai D, He X, Han J et al (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33 (8):1548–1560
Chang X, Nie F, Yang Y et al (2014) A convex formulation for semi-supervised multi-label feature selection. In: Twenty-eighth AAAI conference on artificial intelligence. AAAI Press, pp 1171–1177
Chang X, Nie F, Yang Y et al (2016) Convex sparse PCA for unsupervised feature learning. ACM Trans Knowl Discov Data (TKDD) 11(1):3:1–3:16
Chang X, Yang Y (2016) Semisupervised feature analysis by mining correlations among multiple tasks. IEEE Transactions on Neural Networks and Learning Systems. doi:10.1109/TNNLS.2016.2582746
Chao Y, Yeh Y, Chen Y et al (2011) Locality-constrained group sparse representation for robust face recognition. In: International conference on image processing, pp 761–764
Chen Y, Zhang J, Cai D et al (2013) Nonnegative local coordinate factorization for image representation. IEEE Trans Image Process 22(3):969–979
Geng B, Tao D, Xu C et al (2012) Ensemble manifold regularization. IEEE Trans Pattern Anal Mach Intell 34(6):1227–1233
Gu Q, Li Z, Han J et al (2011) Joint feature selection and subspace learning. In: International joint conference on artificial intelligence, pp 1294–1299
Hou C, Nie F, Yi D et al (2011) Feature selection via joint embedding learning and sparse regression. In: International joint conference on artificial intelligence, pp 1324–1329
Hoyer PO (2002) Non-negative sparse coding. In: Proceedings of IEEE workshop on neural networks for signal processing, pp 557–565
Jiang W, Li M, Zhang Y (2014) Neighborhood preserving convex nonnegative matrix factorization. Math Probl Eng 2014(2):1–8
Jiang W, Liu J, Qi H et al (2016) Robust subspace segmentation via nonconvex low rank representation. Inf Sci 340:144–158
Kotsiantis SB (2014) RETRACTED ARTICLE: feature selection for machine learning classification problems: a recent overview[J]. Artif Intell Rev 42(1):157–157
Lee D, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–791
Liu H, Wu Z, Li X et al (2012) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299–1311
Liu H, Yang Z, Wu Z et al (2011) Locality-constrained concept factorization. In: International joint conference on artificial intelligence, pp 1378–1383
Liu H, Yang Z, Wu Z et al (2012) A-optimal non-negative projection for image representation. Comput Vision Pattern Recogn, 1592–1599
Luo M, Nie F, Chang X et al (2016) Avoiding optimal mean robust PCA/2DPCA with non-greedy l1-norm maximization. In: International joint conference on artificial intelligence
Luo M, Nie F, Chang X et al (2017) Probabilistic non-negative matrix factorization and its robust extensions for topic modeling. In: Thirty-first AAAI conference on artificial intelligence
Nie F, Huang H, Cai X et al (2010) Efficient and robust feature selection via joint ℓ 2,1-norms minimization. Neural Inform Process Syst, 1813–1821
Nie L, Song X, Chua TS (2016) Learning from multiple social networks. Synthesis Lect Inform Concepts Retriev Serv 8(2):118–129
Nie L, Zhang L, Wang M et al (2017) Learning user attributes via mobile social multimedia analytics. ACM Trans Intell Syst Technol (TIST) 8(3):36–47
Qi H, Li K, Shen Y et al (2012) Object-based image retrieval with kernel on adjacency matrix and local combined features. ACM Trans Multimed Comput Commun Appl 8(4):1–18
Roweis S, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326
Song X, Nie L, Zhang L et al (2015) Interest inference via structure-constrained multi-source multi-task learning. In: International conference on artificial intelligence. AAAI Press, pp 2371–2377
Wang J, Yang J, Yu K et al (2010) Locality-constrained linear coding for image classification. Comput Vision Pattern Recogn, 3360–3367
Wang R, Nie F, Yang X et al (2015) Robust 2DPCA with non-greedy, ℓ 1-norm maximization for image analysis[J]. IEEE Trans Cybern 45(5):1108–1112
Wei C, Chao Y, Yeh Y et al (2013) Locality-sensitive dictionary learning for sparse representation based classification. Pattern Recogn 46(5):1277–1287
Xu W, Gong Y (2004) Document clustering by concept factorization. In: Proceedings of the 27th annual international ACM SIGIR conference on research and development in information retrieval. ACM, pp 202–209
Xu W, Liu X, Gong Y et al (2003) Document clustering based on non-negative matrix factorization. In: International ACM SIGIR conference on research and development in information retrieval, pp 267–273
Yang Y, Shen HT, Ma Z et al (2011) ℓ 2,1-norm regularized discriminative feature selection for unsupervised learning[c]. In: International joint conference on artificial intelligence, pp 1589–1594
Yu K, Zhang T, Gong Y et al (2009) Nonlinear learning using local coordinate coding. Neural information processing systems, 2223–2231
Zheng M, Bu J, Chen C et al (2011) Graph regularized sparse coding for image representation. IEEE Trans Image Process 20(5):1327–1336
Acknowledgments
We would like to thank all anonymous reviewers for their helpful comments. This work is supported by the Natural Science Foundation of Liaoning No. 2015020070, and the Natural Science Foundation of China No.61171109 and 61175048.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xing, L., Dong, H., Jiang, W. et al. Nonnegative matrix factorization by joint locality-constrained and ℓ 2,1-norm regularization. Multimed Tools Appl 77, 3029–3048 (2018). https://doi.org/10.1007/s11042-017-4970-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-017-4970-9