面向高光谱图像的局部多流形结构保持稀疏子空间聚类算法研究

Hyperspectral image clustering is one of the hot issues in the field of theoretic research of remote sensing. Unsupervised sparse subspace clustering algorithm(SSC), one of the most effective algorithm in high-dimensional data clustering, sometimes fail to get the ideal clustering effect for hyperspectral data due to its high complexity and lacking of utilizing local data characteristics. This project intends to research how to keep the local manifold structure in SSC algorithm, then improves the effect of hyperspectral image clustering. The main contents are as follows: (1) In order to increase the local characteristics constraints, enhance the ability of gathering in intra-class，the improvement of the regular factor is thus studied based on the analysis of hyperspectral data local manifold structure; (2) Combined with integration of the spectral similarity criterion of hyperspectral data, a new similarity measure criteria will be designed based on the complete sparse representation vector; (3) Based on the above researches, the corresponding sparse coefficient matrix of sampling points(landmark) is calculated at first, then by keeping the multi-manifold structure unchanged, the samples are inserted into the low-dimensional subspace represented by the eigenvectors of landmark, at last the global clustering will be realized. This study can effectively improve the clustering accuracy of hyperspectral remote sensing image and is very applicable in precision agriculture, environmental monitoring and mineral exploration.。

高光谱图像聚类是遥感基础研究领域的热点之一。而当前高维数据聚类中最有效的、无监督的稀疏子空间聚类算法（SSC），存在复杂度过高和对局部数据特征利用不足等问题，导致面向高光谱数据时难以得到理想聚类效果。本项目拟针对高光谱图像，研究加强局部流形结构保持的SSC算法。主要内容如下：(1)以高光谱数据局部多流形结构分析为基础，研究如何改进正则因子，以增加数据局部特征的约束，提高类内聚集能力；(2)结合高光谱数据的光谱相似性判别，基于完整的稀疏表示向量，设计新的相似性度量准则；(3)基于以上研究，对部分采样（landmark）点求取对应的稀疏系数矩阵，在保持样本和landmark点的局部多流形结构不变的前提下，将样本点插入到landmark点的特征向量所表示的低维子空间，为实现全局聚类服务。本项研究能有效提高高光谱遥感图像聚类精度，对精细农业、环境监测、矿物勘探具有重要应用价值。

高光谱图像高效的综合了地物的光谱信息、空间信息以及辐射能量，对地物识别具有重要的意义。但是因为高光谱图像自身数据的高维性和复杂性，常规聚类算法效果欠佳。将稀疏子空间聚类的算法思想引入该问题，能够有效提高聚类精度。本项目中，目前完成了以下工作：.1）基于高光谱图像样本的整体稀疏表示向量，提出了两种新型相似度矩阵构造方法：在余弦相似度的基础上引入高光谱空间信息算子，从而在聚类中反映空间信息；在基于稀疏表示向量的基础上引入动态加权的余弦欧式相似矩阵从而克服大气传输等条件的影响。.2）考虑到聚类中样本的局部特征的影响，在相似矩阵的构造中引入了流形正则项。.3）将基于稀疏子空间聚类的类概率模型引入聚类算法中，构造了半监督聚类算法。通过构造类概率模型学习由少量样本提供的监督信息改善聚类效果。