摘要
提出一种基于潜在低秩图判别分析(LatLGDA)算法,利用数据的自表示对数据的列表示系数矩阵和行表示系数矩阵同时施加低秩约束,得到保留数据结构的亲和矩阵,再与图嵌入模型相结合实现高光谱图像的流形降维并进行分类。与其他基于稀疏图或稀疏低秩图的高光谱特征提取算法相比,LatLGDA可利用数据的行信息弥补列信息的不足或缺失,对噪音的抗干扰能力更强;在真实数据集上的实验结果表明,LatLGDA算法具有较高的分类精度和运算效率,应用前景广阔。
In this paper, latent low-rank graph discrimination analysis(LatLGDA) is proposed. Our algorithm uses self-representation of the data to apply low-rank constraints to the column and row representation coefficient matrix in order to obtain the affinity matrix of the retained data structure. Combined with a graph embedding model, both manifold dimension reduction and classification of hyperspectral images can be realized. Compared with other hyperspectral feature extraction algorithms based on principles such as sparse graphs or sparse and low-rank graph discrimination analysis, LatLGDA can use the row information data to compensate for the lack of column information and has better resistance to interference from noise. Experiments on a real hyperspectral data set from the University of Pavia demonstrate that LatLGDA has the advantages of high classification accuracy, fast operation efficiency and broad application prospects.
引文
[1] 赵春晖,王立国,齐滨.高光谱遥感图像处理方法及应用[M].北京:电子工业出版社,2016:369- 381.ZHAO C H,WANG L G,QI B.Hyperspectral remote sensing image processing methods and applications[M].Beijing:Electronics Industry Press,2016:369- 381.(in Chinese)
[2] CHIVASA W,MUTANGA O,BIRADAR C.Application of remote sensing in estimating maize grain yield in heterogeneous African agricultural landscapes:a review[J].International Journal of Remote Sensing,2017,38(23):6816- 6845.
[3] YANG H,DU Q,CHEN G S.Particle swarm optimization-based hyperspectral dimensionality reduction for urban land cover classification[J].IEEE Journal of Selected Topics in Applied Earth Observations & Remote Sensing,2012,5(2):544- 554.
[4] LY N H,DU Q,FOWLER J E.Sparse graph-based discriminant analysis for hyperspectral imagery[J].IEEE Transactions on Geoscience & Remote Sensing,2014,52(7):3872- 3884.
[5] LI W,LIU J B,DU Q.Sparse and low-rank graph for discriminant analysis of hyperspectral imagery[J].IEEE Transactions on Geoscience & Remote Sensing,2016,54(7):4094- 4105.
[6] LIU G C,YAN S C.Latent low-rank representation for subspace segmentation and feature extraction[C]//Proceedings of the 2011 IEEE International Conference on Computer Vision.Barcelona,2011:1615- 1622.
[7] LIN Z C,CHEN M M,MA Y.The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[J/OL].(2013- 10- 18)[2018- 11- 02].https://arXiv.org/abs/1009.5055 .
[8] YAN S C,XU D,ZHANG B Y,et al.Graph embedding and extensions:a general framework for dimensionality reduction[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(1):40- 51.
[9] CAI J F,CANDES E J,SHEN Z.A singular value thresholding algorithm for matrix completion[J].SIAM Journal on Optimization,2010,20(4):1956- 1982.
[10] YANG J F,YIN W T,ZHANG Y,et al.A fast algorithm for edge-preserving variational multichannel image restoration[J].SIAM Journal on Imaging Sciences,2009,2(2):569- 592.
[11] GUATTERY S,MILLER G L.Graph embeddings and laplacian eigenvalues[J].SIAM Journal on Matrix Analysis and Applications,2000,21(3):703- 723.
[12] PENG B,LI W,XIE X M,et al.Weighted-fusion-based representation classifiers for hyperspectral imagery[J].Remote Sensing,2015,7(11):14806- 14826.