A Hyperspectral Image Classification Method Based on Collaborative Representation in Tangent Space
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摘要: 协同表示分类（collaborative representation classification，CRC）算法近年来成为高光谱遥感分类的研究热点。地物类别间区分性不高会严重影响现有CRC算法的性能。流形结构可有效地解决非线性问题，并解决高光谱遥感影像因数据冗余导致的类别间区分性低的问题。提出了一种基于切空间的高光谱遥感影像协同表示分类算法（tangent space collaborative representation classification，TCRC）和一种基于欧氏距离的自适应加权的切空间协同表示分类算法（weighted tangent space collaborative representation classification，WTCRC）。TCRC算法利用测试样本的切平面来估计区域流形，在测试样本的切空间中使用协同表示算法，寻找测试样本在各类训练样本中的最优线性表示估计，并用其最小误差来对测试样本进行分类。在此基础上，利用测试样本邻域像元、训练样本与测试样本的欧氏距离作为权矩阵来自适应调整各样本对测试样本的影响。实验采用ROSIS（reflective optics system image spectro-meter）和AVIRIS（airbone visible infrared imaging spectrometer）高光谱遥感影像对所提出算法的性能进行了评价，结果表明TCRC和WTCRC在分类效果上比CRC有明显的提升，WTCRC相较于TCRC具有更好的分类效果，具有更强鲁棒性。Abstract: Recently collaborative representation classification (CRC) for hyperspectral image analysis attract increasing attentions. The existing related algorithms can't distinguish classes efficiently because of information redundancy of the hyperspectral data. The local manifold structure can significantly enhance distinguishing between the classes and handle the nonlinear problems efficiently. To apply local manifold structure to CRC, a new CRC in tangent space and an adaptive weighted CRC method in tangent space based on the Euclidean distance are proposed. In order to approximate the local manifold of testing samples, the proposed method uses CRC in tangent space to find the best linearly representational approximation between testing sample and training sample. Furthermore, adaptive weighted diagonal matrices are adopted in the proposed method, which constituted by the Euclidean distances between testing samples and training samples, testing samples and neighbor samples respectively. In the experiments, two real hyperspectral images collected by different sensors were adopted for performance evaluations, and experimental results show that TCRC and WTCRC have significantly improved classification performance compared with the state-of-art SVM and other CR-based classifiers.
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图 1 PU数据集不同样本情况下的8种算法总体精度变化
Figure 1. Eight Algorithms' Overall Accuracy of PU Dataset's Using Different Training Samples
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图 2 IP数据集不同样本情况下的8种算法总体精度变化
Figure 2. Eight Algorithms' Overall Accuracy of IP Dataset's Using Different Training Samples
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图 3 PU数据集不同样本情况下的两种算法总体精度变化
Figure 3. Two Algorithms' Overall Accuracy of PU Dataset's Using Different Training Samples
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图 4 IP数据集不同样本情况下的两种算法总体精度变化
Figure 4. IP Dataset's Two Algorithms' Overall Accuracy Using Different Training Samples
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图 5 PU数据集地面真实地物分布和算法分类效果
Figure 5. Image of Ground Truth and Algorithms' Classification of PU Dataset
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图 6 IP数据集地面真实地物分布和算法分类效果
Figure 6. IP Dataset's Image of Ground Truth and Algorithms' Classification
表 1 PU数据集60个训练样本分类精度
Table 1 PU Dataset's Overall Accuracy of Different Algorithms Using 60 Training Samples
类 样本 分类算法/(%) 训练 测试 SVM CRC NRS LRNN JWCR JCRC NJCRC TCRC WTCRC C1 60 6 631 80.29 79.94 84.53 84.32 85.24 59.43 13.81 85.10 87.29 C2 60 18 649 84.32 74.58 78.66 78.70 89.50 91.57 85.72 93.42 92.23 C3 60 2 099 82.84 73.27 74.37 76.94 84.56 88.66 74.85 81.23 86.18 C4 60 3 064 92.26 96.54 94.55 97.06 96.67 97.78 96.77 98.24 97.55 C5 60 1 345 99.11 100 99.63 99.78 100 100 100 100 99.85 C6 60 5 029 89.12 79.70 89.18 88.59 94.47 61.66 84.47 79.42 91.31 C7 60 1 330 92.01 66.02 92.23 93.01 94.36 97.97 87.74 94.14 98.05 C8 60 3 682 79.71 70.97 85.71 83.65 91.12 68.17 78.30 87.51 94.62 C9 60 947 99.79 71.38 99.47 99.47 98.63 49.21 0 94.51 100 总体精度 84.06 77.67 83.89 83.96 90.52 80.88 72.66 89.98 92.24 Kappa 80.02 71.50 79.40 79.51 87.67 74.78 64.84 86.77 89.84 
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表 2 IP数据集60个训练样本分类精度
Table 2 IP Dataset's Overall Accuracy of Different Algorithms Using 60 Training Samples
类 样本 分类算法/(%) 训练 测试 SVM CRC NRS LRNN JWCR JCRC NJCRC TCRC WTCRC C1 60 1 428 65.13 58.40 57.35 59.03 69.92 78.15 75.56 83.26 78.57 C2 60 830 78.83 58.43 62.77 60.00 70.36 45.78 34.22 88.19 88.92 C3 60 483 95.98 87.37 88.41 91.10 93.37 92.75 86.75 95.86 95.45 C4 60 730 95.82 98.08 98.49 99.04 99.04 99.45 87.53 99.59 99.45 C5 60 478 99.28 99.16 99.16 99.16 98.54 100 100 100 100 C6 60 972 73.14 64.92 72.74 75.21 71.81 79.56 62.55 83.64 83.02 C7 60 2 455 58.71 57.47 60.81 57.64 69.57 61.30 61.96 81.51 82.16 C8 60 593 71.86 65.43 68.47 75.51 82.63 94.94 65.94 95.11 94.94 C9 60 1 265 95.93 98.26 98.42 97.47 99.37 99.76 99.45 99.92 99.92 总体精度 75.60 71.52 73.76 73.50 79.82 77.90 72.31 89.41 88.54 Kappa 71.73 63.66 63.66 69.32 76.54 74.48 67.75 87.32 86.03
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表 3 不同算法在高光谱遥感数据上的运行时间/s
Table 3 Computing Time of Different Algorithms for Hyperspectral Data
方法 PU数据集 IP数据集 SVM 1.91 1.94 CRC 1.08 0.33 NRS 86.61 24.24 LRNN 41.50 15.59 JWCR 54.59 19.90 JCRC 376.43 137.62 NJCRC 1 541.50 121.46 TCRC 161.21 34.36 WTCRC 168.69 55.26
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