Hyper-graph regularized discriminative concept factorization for data representation
For the tasks of pattern analysis and recognition, nonnegative matrix factorization and concept factorization (CF) have attracted much attention due to its effective application to find the meaningful low-dimensional representation of data. However, they neglect the geometry information embedded in the local neighborhoods of the data and fail to exploit the prior knowledge. In this paper, a novel semi-supervised learning algorithm named hyper-graph regularized discriminative concept factorization (HDCF) is proposed. For the sake of exploring intrinsic geometrical structure of the data and making use of label information, HDCF incorporates hyper-graph regularizer into CF framework and uses the label information to train a classifier for the classification task. HDCF can learn a new concept factorization with respect to the intrinsic manifold structure of the data and also simultaneously adapted to the classification task and a classifier built on the low-dimensional representations. Moreover, an iterative updating optimization scheme is developed to solve the objective function of the proposed HDCF and the convergence proof of our optimization scheme is also provided. Experimental results on ORL, Yale and USPS image databases demonstrate the effectiveness of our proposed algorithm.
KeywordsNMF Concept factorization Hyper-graph regularized Semi-supervised learning
This work is partially supported by the National Natural Science Foundation of China under Grant Nos. 61373063, 61233011, 61125305, 61375007, 61220301 and by National Basic Research Program of China under Grant No. 2014CB349303. Also this work is supported in part by the Natural Science Foundation of Jiangsu Province (BK20150867), the Natural Science Research Foundation for Jiangsu Universities (13KJB510022) and the Natural Science Foundation of Nanjing University of Posts and Telecommunications (NY215125).
Compliance with ethical standards
Conflict of interest
Jun Ye and Zhong Jin declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors. All the data used in the experiments were obtained from public datasets.
- Agarwal S, Branson K, Belongie S (2006) Higher order learning with graphs. In: Proceedings of the 23th international conference on machine learning. Pittsburgh, PA pp 17–24Google Scholar
- Agarwal S, Lim J, Zelnik Manor L, Perona P, Kriegman D, Belongie S (2005) Beyond pairwise clustering. Proceedings of the international conference on computer vision and pattern recognition. San Diego, CA, pp 838–845Google Scholar
- Belkin M, Niyogi P (2001) Laplacian eigenmaps and spectral techniques for embedding and clustering. In: 15th Annual Neural Information Processing Systems Conference, NIPS 2001, vol 14. MIT Press, Cambridge, pp 585–591Google Scholar
- Grira N, Crucianu M, Boujemaa N (2005) Semi-supervised fuzzy clustering with pairwise-constrained competitive agglomeration. In: The 14th IEEE international conference on fuzzy systems, FUZZ’05. IEEE, pp 867–872Google Scholar
- He R, Zheng W, Hu B, Kong X (2006) Nonnegative sparse coding for discriminative semi-supervised learning. In: 2011 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, pp 2849–2856Google Scholar
- Huang Y, Liu Q, Metaxas D (2009) Video object segmentation by hypergraph cut. In: Proceedings of the international conference on computer vision and pattern recognition. Miami, FL, pp 1738–1745Google Scholar
- Li X, Zhao CX, Shu ZQ, Guo JH (2015) Hyper-graph regularized concept factorization algorithm and its application to data representation. China Acad Control Decis 30(8):1399–1404Google Scholar
- Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Supervised dictionary learning. In: Koller D, Schuurmans D, Bengio Y, Bottou L (eds) Advances in neural information processing systems, vol 21. Hyatt Regency, Vancouver, pp 1033–1040Google Scholar
- Shashua A, Hazan T (2005) Nonnegative tensor factorization with applications to statistics and computer vision. In: Proceedings of the 22nd international conference on machine learning, pp 792–799Google Scholar
- Sun L, Ji S, Ye J (2008) Hypergraph spectral learning for multi-label classification. Proceedings of the international conference on knowledge discovery and data mining. Las Vegas, NV, pp 668–676Google Scholar
- Xu W, Gong Y (2004) Document clustering by concept factorization. In: Proceedings of 2004 international conference on research and development in information retrieval (SIGIR’04), Sheffield, UK, July 2004, pp 202–209Google Scholar
- Zass R, Shashua A (2008) Probabilistic graph and hyper graph matching. In: Proceedings of the international conference on computer vision and pattern recognition in Anchorage, AK, pp 1–8Google Scholar
- Zhang Y, Yeung D (2008) Semi-supervised discriminant analysis using robust path-based similarity. In: IEEE conference on computer vision and pattern recognition, p 18Google Scholar
- Zhou D, Huang J, Scholkopf B (2006) Learning with hypergraphs: clustering, classification, and embedding. In: 20th Annual Conference on Neural Information Processing Systems, NIPS 2006. MIT Press, Cambridge, pp 1601–1608Google Scholar