Generalized Manifold Learning for High Resolution Remote Sensing Image Object Classification
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摘要: 针对传统的流形学习算法不能对位于黎曼流形上的协方差描述子进行有效降维这一问题，本文提出一种推广的流形学习算法，即基于Log-Euclidean黎曼核的自适应半监督正交局部保持投影（Log-Euclidean Riemannian kernel-based adaptive semi-supervised orthogonal locality preserving projection，LRK-ASOLPP），并将其成功用于高分辨率遥感影像目标分类问题.首先，提取图像每个像素点处的几何结构特征，计算图像特征的协方差描述子；其次，通过采用Log-Euclidean黎曼核将协方差描述子投影到再生核Hilbert空间；然后，基于流形学习理论，建立黎曼流形上半监督正交局部保持投影算法模型，利用交替迭代更新算法对目标函数进行优化求解，同时获得相似性权矩阵和低维投影矩阵；最后，利用求得的低维投影矩阵计算测试样本的低维投影，并用K—近邻、支持向量机（Support victor machine，SVM）等分类器对其进行分类.三个高分辨率遥感影像数据集上的实验结果说明了该算法的有效性与可行性.
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关键词:
- 协方差矩阵 /
- Log-Euclidean黎曼核 /
- 流形学习 /
- 目标分类
Abstract: It is not adequate to use classical manifold learning techniques to reduce the dimension of covariance descriptors lied on Riemannian manifold. A generalized manifold learning method named Log-Euclidean Riemannian kernel-based adaptive semi-supervised orthogonal locality preserving projection (LRK-ASOLPP) is proposed, and successfully applied to the high resolution remote sensing image classification issue. Firstly, geometric features of each pixel in the image are extracted, and covariance descriptor of each image is calculated. Secondly, the covariance descriptors are mapped into the reproducing kernel Hilbert space by using the Log-Euclidean Riemann kernel. Thirdly, the model of semi-supervised orthogonal locality preserving projection algorithm on Riemannian manifold is constructed based on manifold learning theory. Fourthly, by using the alternating iteration optimization algorithm to solve the objective function, the similarity weight matrix and low dimensional projection matrix are obtained simultaneously. Finally, low dimensional projections of test samples are computed by using the low dimensional projection matrix, and then classifiers such as K-NN, support victor machine (SVM), etc. are used to classify them. Experiment results on three high-resolution satellite images datasets demonstrate the feasibility and effectiveness of the proposed algorithm.1) 本文责任编委 胡清华 -
图 3 最佳分类精度随特征维数变化曲线图
Fig. 3 The varying curves of the optimal classiflcation accuracy with feature dimension
图 4 三个数据集上不同训练样本数算法最佳平均分类精度
Fig. 4 The average classification accuracy of different training sample number on three datasets
表 1 最佳分类精度(Ac)及对应特征维数($r$)
Table 1 The classification accuracy (Ac) and the corresponding feature dimension ($r$)
数据集 UCMerced WHU-RS Quick bird 算法 Ac (%) $r$ Ac (%) $r$ Ac (%) $r$ LRK-SOLPP 92.32 45 92.68 25 91.87 45 KLPP 93.15 20 93.64 50 92.84 25 LRK-ASOLPP 94.89 35 96.43 25 95.69 20 
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表 2 UCMerced LandUse dataset上的最佳分类精度(Ac)及对应特征维数(r)
Table 2 The classiflcation accuracy (Ac) and the feature dimension (r) on UCMerced LandUse dataset
算法 LRK-SOLPP KLPP LRK-ASOLPP 分类器 Ac(%) $r$ Ac(%) $r$ Ac(%) $r$ K-NN 84.45 20 84.38 20 90.18 35 K-means 85.65 20 89.06 25 91.16 25 SVM 87.25 15 90.76 15 94.27 20 BP-ANN 89.82 20 91.64 20 95.34 25
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表 3 WHU-RS dataset上的最佳分类精度(Ac)及对应特征维数(r)
Table 3 The classiflcation accuracy (Ac) and the feature dimension (r) on WHU-RS dataset
算法 LRK-SOLPP KLPP LRK-ASOLPP 分类器 Ac(%) $r$ Ac(%) $r$ Ac(%) $r$ K-NN 85.32 30 88.04 20 90.25 20 K-means 88.58 20 89.64 50 90.87 25 SVM 87.68 35 91.76 15 95.79 20 BP-ANN 90.47 20 90.43 20 96.18 25
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表 4 Quick bird dataset上的最佳分类精度(Ac)及对应特征维数(r)
Table 4 The classiflcation accuracy (Ac) and the feature dimension (r) on Quick bird dataset
算法 LRK-SOLPP KLPP LRK-ASOLPP 分类器 Ac(%) $r$ Ac(%) $r$ Ac(%) $r$ K-NN 84.98 25 93.65 20 94.18 35 K-means 86.62 20 92.06 50 96.28 25 SVM 88.76 25 90.38 25 93.69 20 BP-ANN 89.45 20 92.56 30 95.89 25
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