Separable Nonnegative Matrix Factorization Based Band Selection for Hyperspectral Imagery
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摘要: 高光谱影像波段众多且相关性强，导致分类存在信息冗余且计算量较大。提出了可分离非负矩阵分解方法来选取高光谱影像的代表性波段子集，在保证分类精度的同时降低计算量。该方法假设高光谱影像的波段集合具有可分离特性，改进传统非负矩阵分解模型，将波段选择转换为可分离非负矩阵分解问题，采用迭代投影方法来依次选取能够非负线性表达其他波段的代表性波段。在此基础上，利用两个公开高光谱数据集对比几种主流方法，采用定量评价和分类精度指标来综合评价所提的波段选择方法的效果。实验结果表明，可分离非负矩阵分解方法的分类精度高于其他几种方法，而且计算效率排名第2，能够选取合适的波段子集以满足高光谱遥感的应用需求。Abstract: Strong intra-band correlations along with numerous bands seriously hinder the processing and applications of hyperspectral remote sensing images in realistic applications. A separable non-negative matrix factorization (SepNMF) method is presented to explore the band selection problem on hyperspectral imagery (HSI). The method investigates the separability structure in the band set of the HSI data to improve the regular non-negative matrix factorization model, and it formulates the band selection problem into the problem of finding representative columns that represent other bands with non-negative and linear combinations in the SepNMF model. The method adopts the recursive projection method to iteratively select the representative bands to constitute the proper band subset. Three groups of experiments on two open HSI data sets are designed to carefully testify the performance of the SepNMF in band selection. Several popular methods are utilized to compare against the proposed SepNMF method. Experimental results show that the SepNMF obtains the best overall classification accuracies of all while taking shorter computational times ranking second among all the comparison methods. Therefore, the SepNMF method can be an alternative choice for selecting proper bands in hyperspectral image classification.
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图 4 不同方法的OCA曲线
Figure 4. OCA Curves of Different Band Selection Methods on Two Datasets
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图 5 不同波段选择方法的派恩斯市数据的SVM分类结果
Figure 5. SVM Classification Maps of Different Band Selection Methods on Indian Pines Dataset
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图 6 不同波段选择方法的某城市数据的SVM分类结果
Figure 6. SVM Classification Maps of Different BandSelection Methods on Urban Dataset
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图 7 不同训练样本大小下的各种波段选择方法的OCA曲线
Figure 7. OCA Curves of Different Band Selection Methods with Different Sizes of Training Samples per Class
表 1 印第安纳派恩斯市数据的地面地物样本信息
Table 1 Ground Truth of All Classes of Ground Objects on Indian Pines Dataset
类号 类名 样本数 1 苜蓿 46 2 非耕犁玉米 1 428 3 玉米幼苗 830 4 玉米 237 5 草地/牧场 483 6 草地/树木 730 7 收割的草地/牧场 28 8 打包的干草 478 9 燕麦 20 10 非耕犁大豆 972 11 大豆幼苗 2 455 12 清洁的大豆 593 13 小麦 205 14 树林 1 265 15 建筑物-草地-树木驱动器 386 16 石铁塔 93 样本总数 10 249 
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表 2 某城市数据的地面地物样本信息
Table 2 Samples of Ground Objects in Each Class for Urban Dataset
类号 类名 样本数 1 深色沥青 85 2 浅色沥青 58 3 混凝土01 124 4 牧草 236 5 草地 127 6 树木01 263 7 土壤01 113 8 土壤02 53 9 深色土壤03 59 10 墙面屋顶01 118 11 屋顶02A 91 12 屋顶02B 39 13 浅灰屋顶03 35 14 深色琉璃屋顶04 84 15 教堂屋顶05A 85 16 学校屋顶06 64 17 明亮屋顶07 72 18 蓝绿屋顶08 45 19 网球场 96 20 阴影植被 40 21 阴影地面 64 22 树木02 261 样本总数 2 212
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表 3 不同波段选择方法的定量评价结果
Table 3 Results of Quantitative Evaluations from Different Methods on Two Datasets
数据 评价因子 MVPCA SpaBS SNMF FDPC SepNMF 印第安纳派恩斯市 AIE 10.635 10.434 10.584 10.993 11.478 ACC 0.606 0.576 0.226 0.320 0.201 ARE 14.828 18.161 19.552 32.184 30.810 某城市 AIE 7.702 7.521 7.438 7.296 7.997 ACC 0.841 0.904 0.664 0.738 0.562 ARE 1.007 1.422 16.356 16.217 17.606
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表 4 不同波段选择方法的计算时间对比
Table 4 Contrast in Computational Time of Different Methods on Two Hyperspectral Datasets
影像 k 计算时间/s MVPCA SpaBS SNMF FDPC SepNMF 印第安纳派恩斯市 10 0.062 90.72 2.28 3.45 0.07 20 0.062 97.24 3.09 3.56 0.12 30 0.063 101.13 5.78 3.64 0.19 40 0.063 106.89 6.56 3.76 0.28 50 0.063 112.19 15.24 3.84 0.41 某城市 10 0.161 742.32 12.579 3.37 0.16 20 0.171 1013.57 21.35 3.37 0.28 30 0.182 1377.42 51.77 3.41 0.43 40 0.187 1423.55 135.06 3.51 0.61 50 0.194 1513.20 291.75 3.75 0.84
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