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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (6): 1159-1167    DOI: 10.3785/j.issn.1008-973X.2022.06.013
智能机器人     
层次型非线性子空间字典学习
周国华1,2,3(),卢剑伟1,2,倪彤光2,胡学龙3
1. 常州工业职业技术学院 信息工程学院，江苏 常州 213164
2. 常州大学 计算机与人工智能学院，江苏 常州 213164
3. 扬州大学 信息工程学院，江苏 扬州 225127
Hierarchical nonlinear subspace dictionary learning
Guo-hua ZHOU1,2,3(),Jian-wei LU1,2,Tong-guang NI2,Xue-long HU3
1. Department of Information Engineering, Changzhou Vocational Institute of Industry Technology, Changzhou 213164, China
2. School of Computer Science and Artifical Intelligence, Changzhou University, Changzhou 213164, China
3. College of Information Engineering, Yangzhou University, Yangzhou 225127, China
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摘要：

为了提高遥感图像场景分类的准确率，提出层次型非线性子空间字典学习(HNSDL)方法. 用所提方法训练多层网络模型学习多层非线性变换. 将遥感图像投影到子空间中，构建稀疏编码和投影编码的局部信息保持项，在保持局部结构信息的同时最小化样本的类内差异，增强模型的分类识别能力. 在模型目标式求解中，使用交替学习算法求解子空间和字典的联合学习任务，使所有参数同时达到最优解. 在Ucmerced、Google和WHU-RS数据集上进行实验设计和测试，结果表明所提方法在遥感图像的多种场景分类上均表现出较高的分类准确率.
关键词： 遥感图像分类;  稀疏表示;  子空间学习;  字典学习    
Abstract:

A hierarchical nonlinear subspace dictionary learning (HNSDL) method was proposed to improve the accuracy of remote sensing image scene classification. HNSDL trained a multi-layer network model to learn a series of hierarchical nonlinear transformations. The remote sensing images were projected into a series of subspaces, and the local information preserved terms of sparse coding and projection coding were constructed in the subspaces. By preserving the local structure information, the intra-class difference of samples was minimized, and the classification and recognition ability was enhanced. To solve the joint learning task of subspace and dictionary, the alternating optimization algorithm was adopted the objective solution of HNSDL, so that the optimal solution of all parameters were obtained at the same time. Extensive experiments results which were designed and tested on the Ucmerced, Google and WHU-RS data sets showed that the proposed method had high classification accuracy in a variety of scene classifications of remote sensing images.
Key words: remote sensing image classification    sparse representation    subspace learning    dictionary learning
收稿日期: 2021-07-27 出版日期: 2022-06-30
CLC:  TP 391  
基金资助: 国家自然科学基金资助项目（61806026）; 江苏省教育厅未来网络科研基金资助项目（FNSRFP-2021-YB-36）; 常州市科技支撑社会发展资助项目 （CE20215032）; 江苏省高职院校教师专业带头人高端研修资助项目（2020GRGDYX059）
作者简介: 周国华（1977—），男，副教授，从事智能学习、模式识别研究. orcid.org/0000-0001-8512-4499. E-mail： tiddyddd@sina.com.cn
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引用本文:

周国华,卢剑伟,倪彤光,胡学龙. 层次型非线性子空间字典学习[J]. 浙江大学学报(工学版), 2022, 56(6): 1159-1167.

Guo-hua ZHOU,Jian-wei LU,Tong-guang NI,Xue-long HU. Hierarchical nonlinear subspace dictionary learning. Journal of ZheJiang University (Engineering Science), 2022, 56(6): 1159-1167.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.06.013    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I6/1159

图 1  HNSDL求解过程示意图
　　 算法：HNSDL算法
　　输入：带类别标签的图像集X；
　　输出：字典矩阵 ${{\boldsymbol{D}}^{(m)}}$、权重矩阵 ${{\boldsymbol{W}}^{(m)}}$、偏移向量 ${{\boldsymbol{b}}^{(m)}}$， $1 \leqslant m \leqslant M$;
　　//训练阶段
　　1. 使用KSVD[25]算法初始化 $ {{\boldsymbol{D}}^{(m)}} $、 ${{\boldsymbol{W}}^{(m)}}$、 ${{\boldsymbol{b}}^{(m)}}$为单位矩阵;
　　开始循环
　　for m = 1 to M do
　　2. 分别使用式(7)、(10)构建最近邻图 $ {{\boldsymbol{G}}^{(m)}} $、类内紧致图 $ {{\boldsymbol{V}}^{(m)}} $;
　　3. 固定 $ {{\boldsymbol{D}}^{(m)}} $、 ${{\boldsymbol{b}}^{(m)}}$、 ${\boldsymbol{A}}_{}^{{\text{(}}m{\text{)}}}$，使用式(15)、 (17)更新 ${{\boldsymbol{W}}^{(m)}}$；
　　4. 固定 $ {{\boldsymbol{D}}^{(m)}} $、 ${{\boldsymbol{W}}^{(m)}}$、 ${\boldsymbol{A}}_{}^{{\text{(}}m{\text{)}}}$，使用式(16)更新 ${{\boldsymbol{b}}^{(m)}}$;
　　5. 固定 $ {{\boldsymbol{D}}^{(m)}} $、 ${{\boldsymbol{W}}^{(m)}}$、 ${{\boldsymbol{b}}^{(m)}}$，使用式(22)更新 ${\boldsymbol{A}}_{}^{{\text{(}}m{\text{)}}}$;
　　6. 固定 ${\boldsymbol{A}}_{}^{{\text{(}}m{\text{)}}}$、 ${{\boldsymbol{W}}^{(m)}}$、 ${{\boldsymbol{b}}^{(m)}}$，使用式(25)更新 $ {{\boldsymbol{D}}^{(m)}} $;
　　循环结束直到目标式(13)收敛或者达到最大迭代次数;
　　7. 返回 ${{\boldsymbol{D}}^{(m)}}$、 ${{\boldsymbol{W}}^{(m)}}$、 ${{\boldsymbol{b}}^{(m)}}$的最优解， $1 \leqslant m \leqslant M$；
　　//测试阶段
　　for m = 1 to M do
　　8. 使用式(26)计算测试样本的稀疏编码向量 $ {\boldsymbol{a}}_{{\text{test}}}^{(m)} $；
　　9. 使用KNN分类器对 $ {\boldsymbol{a}}_{{\text{test}}}^{(M)} $进行分类.
  
图 2  3个遥感图像数据集的图像示例
数据集 Acc
NPE K-SVD DTT-HD HNSDL-1L AlexNet UDFF TSDFF VGG-VD-16 HNSDL
Ucmerced 87.83 89.02 90.55 90.04 92.38 91.93 93.00 94.31 95.96
Google 86.30 87.46 88.04 87.87 89.53 89.12 90.73 91.01 92.34
WHU-RS 88.71 90.03 92.22 92.43 94.40 93.87 95.02 96.00 96.23
表 1  3个数据集上平均分类准确率比较
图 3  HNSDL方法在Ucmerced数据集上的混淆矩阵
图 4  HNSDL方法在Google数据集上的混淆矩阵
图 5  HNSDL方法在WHU-RS数据集上的混淆矩阵
取值范围 Acc1 Acc2 Acc3
%
10?4 92.32 93.22 94.72
10?3 94.96 93.66 95.06
10?2 95.63 95.06 95.96
10?1 95.96 95.80 95.56
1 95.85 95.96 95.26
表 2  不同正则化参数在Ucmerced数据集上的准确率
图 6  不同投影空间维数和子类字典原子数在Ucmerced数据集上的准确率
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