基于约束低秩表示模型的联合半监督分类算法
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摘要
针对基于图的半监督学习算法由于先构造关联矩阵再在对应的图上进行标记传播而导致只能得到原问题次优解的问题,提出基于约束低秩表示模型的联合半监督分类算法。首先,使用约束矩阵,基于低秩表示模型,实现部分已标记样本对应的低秩表示系数一致;其次,解决基于图的半监督学习算法中两阶段模式所带来的次优解问题,实现了联合进行低秩图的学习与图上的半监督标记传播;最后,通过实验检验了算法的可行性。改进算法获得的结果比现有的主流算法均有较大优势,在标准数据集上的性能得到较高的提升。
Aiming at the problem that the graph-based semi-supervised learning algorithm can only get the sub-optimal solution of the original problem, which is also a result of constructing the correlation matrix first and then labeling and propagating on the corresponding graph, a joint semi-supervised classification algorithm based on constraint low rank representation model is proposed. Firstly, based on the low-rank representation model, the constraints matrix is used to achieve the consistency of the low-rank representation coefficients of some labeled samples; secondly, the sub-optimal solution problem caused by two-stage patterns in graph-based semi-supervised learning algorithm is solved, and the joint learning of low-rank graphs and semi-supervised label propagation on graphs are realized; finally, the feasibility of the algorithm is verified by experiments. The results obtained by the improved algorithm are superior to those of prevailing mainstream algorithms, and the performance of the improved algorithm on standard data sets is improved.
Aiming at the problem that the graph-based semi-supervised learning algorithm can only get the sub-optimal solution of the original problem, which is also a result of constructing the correlation matrix first and then labeling and propagating on the corresponding graph, a joint semi-supervised classification algorithm based on constraint low rank representation model is proposed. Firstly, based on the low-rank representation model, the constraints matrix is used to achieve the consistency of the low-rank representation coefficients of some labeled samples; secondly, the sub-optimal solution problem caused by two-stage patterns in graph-based semi-supervised learning algorithm is solved, and the joint learning of low-rank graphs and semi-supervised label propagation on graphs are realized; finally, the feasibility of the algorithm is verified by experiments. The results obtained by the improved algorithm are superior to those of prevailing mainstream algorithms, and the performance of the improved algorithm on standard data sets is improved.
引文
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[3] LI C G,LIN Z C,ZHANG H G,et al.Learning semi-supervised representation towards a unified optimization framework for semi-supervised learning[C]//International Conference on Computer Vision.IEEE,2015:2767-2775.
[4] YI Y,QIAO S,WEI Z,et al.Adaptive multiple graph regularized semi-supervised extreme learning machine[J].Soft Computing,2018,22(6):1-18.
[5] REN W,LI G.Graph based semi-supervised learning via label fitting[J].International Journal of Machine Learning and Cybernetics,2017,8(3):877-889.
[6] 张恒敏,杨健,郑玮.低秩矩阵近似与优化问题研究进展[J].模式识别与人工智能,2018,31(1):23-36.
[7] ELHAMIFAR E,VIDAL R.Sparse subspace clustering:algorithm,theory,and applications[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(11):2765-2781.
[8] LIU G C,LIN Z C,YU Y.Robust subspace segmentation by low-rank representation[C]//Proceedings of International Conference on Machine Learning,2010:663-670.
[9] WANG J,WANG X,TIAN F,et al.Constrained low-rank representation for robust subspace clustering[J].IEEE Transactions on Cybernetics,2017,47(12):4534-4546.
[10] SHANG F,LIU Y,CHENG J,et al.Recovering low-rank and sparse matrices via robust bilateral factorization[C]//International Conference on Data Mining,2014:965-970.
[11] ZHU X,GHAHRAMANI Z,LAFFERTY J D.Semi-supervised learning using gaussian fields and harmonic functions[C]// International Conference on Machine learning,2003:912-919.
[12] ZHENG Y G,ZHANG X R,YANG S Y,et al.Low-rank representation with local constraint for graph construction[J].Neurocomputing,2013,122:398-405.
[13] LU X Q,WANG Y L,YUAN Y.Graph-regularized low-rank representation for destriping of hyperspectral images[J].IEEE Transactions on Geoscience and Remote Sensing.2013,51(7):4009-4018.
[14] 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 IEEE Conference on Computer Vision and Pattern Recognition,2012:2328-2335.
[15] LI C G,LIN Z C,ZHANG H G,et al.Learning semi-supervised representation towards a unified optimization framework for semi-supervised learning[C]//Proceedings of International Conference on Computer Vision,2015:2767-2775.
[16] XIANG S M,NIE F P,ZHANG C S.Semi-supervised classification via local spline regression[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2010,32(11):2039-2053.
[17] YANG Y,NIE F P,XU D,et al.A multimedia retrieval framework based on semi-supervised ranking and relevance feedback[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,34(4):723-742.
[18] WANG F,ZHANG C.Label propagation through linear neighborhoods[J].IEEE Transactions on Knowledge and Data Engineering,2008,20(1):55-67.
[19] YAN S C,WANG H.Semi-supervised learning by sparse representation[C]//Proceedings of SIAM International Conference on Data Mining,2009:792-801.
[20] HE R,ZHENG W S,HU B G,et al.Nonnegative sparse coding for discriminative semi-supervised learning[C]//Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,2011:2849-2856.
[21] PENG Y,LU B L,WANG S H.Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning[J].Neural Networks,2015,65:1-17.