一种基于非负低秩稀疏图的半监督学习改进算法

张涛; 唐振民

doi:10.11999/JEIT160559

一种基于非负低秩稀疏图的半监督学习改进算法

doi: 10.11999/JEIT160559

张涛¹,
唐振民¹

基金项目:

国家自然科学基金(61473154)

计量
- 文章访问数: 1539
- HTML全文浏览量: 123
- PDF下载量: 458
- 被引次数: 0
出版历程
- 收稿日期: 2016-05-28
- 修回日期: 2016-09-23
- 刊出日期: 2017-04-19

Improved Algorithm Based on Non-negative Low Rank and Sparse Graph for Semi-supervised Learning

ZHANG Tao¹,
TANG Zhenmin¹

Funds:

The National Natural Science Foundation of China (61473154)

摘要

摘要: 该文针对基于非负低秩稀疏图的半监督学习算法不能准确地描述数据结构的问题，提出一种融合平滑低秩表示和加权稀疏约束的改进算法。该算法分别对经典算法的低秩项和稀疏项进行改进，准确地捕获了数据的全局子空间结构和局部线性结构。在构建目标函数时，使用对数行列式函数代替核范数平滑地估计秩函数，同时利用形状交互信息和有标签样本的类别信息构造加权稀疏约束正则项。然后通过带有自适应惩罚的线性交替方向方法求解目标函数并采用有效的后处理方法重构数据的图结构，最后利用基于局部和全局一致性的半监督分类框架完成学习任务。在ORL库，Extended Yale B库和USPS库上的实验结果表明，该改进算法提高了半监督学习的准确率。
- 半监督学习 /
- 图模型 /
- 低秩表示 /
- 稀疏约束
Abstract: Semi-supervised learning algorithm based on non-negative low rank and sparse graph can not describe the structures of the data exactly. Therefore, an improved algorithm which integrates smoothed low rank representation and weighted sparsity constraint is proposed. The low rank term and sparse term of the classical algorithm are improved by this algorithm respectively, and the global subspace structure and the locally linear structure can be captured exactly. When building the objective function, the logarithm determinant function instead of the nuclear norm is used to approximate the rank function smoothly. Meanwhile, the shape interaction information and the label information of labeled samples is used to build the weighted sparsity constraint regularization term. Then, the objective function is solved by a linearized alternating direction method with adaptive penalty and the graph construction is restructured by an available post-processing method. Finally, a semi-supervised classification framework based on local and global consistency is used to finish the learning task. The experimental results on ORL, Extended Yale B and USPS database show that the improved algorithm improves the accuracy of semi-supervised learning.
- Semi-supervised learning /
- Graph model /
- Low rank representation /
- Sparsity constraint

HTML全文

参考文献(20)

刘建伟, 刘媛, 罗雄麟. 半监督学习方法[J]. 计算机学报, 2015, 38(8): 1592-1617. doi: 10.11897/SP.J.1016.2015.01592.

LIU Jianwei, LIU Yuan, and LUO Xionglin. Semi-supervised learning methods[J]. Chinese Journal of Computers, 2015, 38(8): 1592-1617. doi: 10.11897/SP.J.1016.2015.01592.

ZHU X. Semi-supervised learning literature survey[R]. Madison: University of Wisconsin, 2006.

LIU G C, LIN Z C, YAN S C, et al. Robust recovery of subspace structures by low-rank representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(1): 171-184. doi: 10.1109/TPAMI.2012.88.

ZHUANG L S, GAO H Y, LIN Z C, et al. Non-negative low rank and sparse graph for semi-supervised learning[C]. Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, Providence, USA, 2012: 2328-2335. doi: 10.1109/CVPR.2012.6247944.

ZHENG Y G, ZHANG X G, YANG S Y, et al. Low-rank representation with local constraint for graph construction[J]. Neurocomputing, 2013, 122: 398-405. doi: 10.1016/j.neucom. 2013.06.013.

TANG K W, LIU R S, SU Z X, et al. Structure-constrained low-rank representation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(12): 2167-2179. doi: 10.1109/TNNLS.2014.2306063.

PENG Y, LU B L, and WANG S H. Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning[J]. Neural Networks, 2015, 65: 1-17. doi: 10.1016/j.neunet.2015.01.001.

MOHAN K and FAZEL M. Iterative reweighted algorithms for matrix rank minimization[J]. The Journal of Machine Learning Research, 2012, 13(1): 3441-3473.

王斯琪, 冯象初, 张瑞, 等. 基于最大范数的低秩稀疏分解模型[J]. 电子与信息学报, 2015, 37(11): 2601-2607. doi: 10. 11999/JEIT150468.

WANG Siqi, FENG Xiangchu, ZHANG Rui, et al. Low-rank sparse decomposition model based on max-norm[J]. Journal of Electronics Information Technology, 2015, 37(11): 2601-2607. doi: 10.11999/JEIT150468.

FAZEL M, HINDI H, and BOYD S. Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices[C]. Proceedings of the American Control Conference, Denver, USA, 2003, 3: 2156-2162. doi: 10.1109/ACC.2003.1243393.

KANG Z, PENG C, and CHENG Q. Robust subspace clustering via smoothed rank approximation[J]. IEEE Signal Processing Letters, 2015, 22(11): 2088-2092. doi: 10.1109/ LSP.2015.2460737.

LIN Z C, LIU R S, and SU Z X. Linearized alternating direction method with adaptive penalty for low-rank representation[C]. Proceedings of the Advances in Neural Information Processing Systems, Granada, Spain, 2011: 612-620.

ZHOU D Y, BOUSQUET O, LAL T N, et al. Learning with local and global consistency[C]. Proceedings of the Advances in Neural Information Processing Systems, Cambridge, UK, 2004: 321-328.

LIU B, JING L P, YU J, et al. Robust graph learning via constrained elastic-net regularization[J]. Neurocomputing, 2016, 171: 299-312. doi: 10.1016/j.neucom.2015.06.059.

KANG Z, PENG C, CHENG J, et al. Logdet rank minimization with application to subspace clustering[J]. Computational Intelligence and Neuroscience, 2015, 824289, doi: 10.1155/2015/824289.

LIN Z C, CHEN M M, and MA Y. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices [R]. UIUC Technical Report UILU-ENG-09-2215, 2009.

LIU G C, LIN Z C, and YU Y. Robust subspace segmentation by low-rank representation[C]. Proceedings of the International Conference on Machine Learning, Haifa, Israel, 2010: 663-670.

ELHAMIFAR E and VIDAL R. Sparse subspace clustering: algorithm,theory, and applications[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 34(11): 2765-2781. doi: 10.1109/TPAMI.2013.57.

施引文献

资源附件(0)

访问统计