高光谱图像分类的流形学习和非负矩阵分解特征降维研究

Hyperspectral image classification was greatly affected by the nonlinear structure of hyperspectral image data, small number of training samples, high dimensionality of feature space, and strong inter-band relativity. In order to eliminate these influences on hyperspectral image classification, this project aims at studying feature dimensionality reduction by manifold learning and manifold regularized nonnegative matrix factorization to reveal the manifold distribution of hyperspectral image data, enhance the efficiency of feature extraction, and improve the classification accuracy. The novelties of this project are the following: Firstly, we will develop the nonlinear manifold learning method which not only integrate the spatial information into feature extraction step but also can handle large scale hyperspectral image data. Secondly, based on linear graph embedding, we will study the linear manifold learning feature extraction method which suit small-sample-size problem without the PCA preprocessing step. Thirdly, we will develop manifold learning theory and method based on sparse representation which avoid adjusting the model parameters and is more conducive to the practical application. Finally, based on manifold criterion and nonnegative factorization criterion, we will study manifold regularized sparse nonnegative matrix factorization and manifold regularized projective nonnegative matrix factorization theories and methods which consider both the geometrical structure and discriminant information of the data and have the faster optimization rules. The proposed methods manifold regularized nonnegative matrix factorization methods improve the convergence speed, reduce the calculation complexity, and is more suitable for hyperspectral image data. This project is expected to not only provide a new thought and method for feature dimensionality reduction of hyperspectral image, but also enrich and expand the theory of feature dimensionality reduction of hyperspectral image.

为消除非线性、训练样本不足、特征空间维数过高、波段间强相关性这些因素对高光谱图像分类的不利影响，本项目研究适合高光谱图像分类的流形学习和流形正则NMF特征降维算法，以揭示高光谱数据的流形分布，增强特征提取有效性，提高分类精度。 项目的创新之处：发展融入空间信息的非线性流形学习特征降维理论与方法，可处理大尺度高光谱数据；发展基于线性图嵌入模型的、不需要PCA预处理的线性流形学习特征降维理论与方法，实现了小样本情况下的高光谱图像特征降维；发展基于稀疏模型的流形学习特征降维理论与方法，避免了模型参数的调节，更利于实际应用；基于流形标准和数据非负分解标准发展同时考虑数据几何结构及其判别信息的快速优化流形正则稀疏NMF及流形正则PNMF理论与方法，提高了收敛速度，降低了计算复杂度低，更适合高光谱这样的高维数据。 本项目为高光谱图像特征降维引入了新的研究思路和方法，丰富发展了高光谱图像特征降维的理论。

为消除非线性、训练样本不足、特征空间维数过高、波段间强相关性这些因素对高光谱图像分类的不利影响，本项目致力于研究适合高光谱图像分类的流形学习和流形正则非负矩阵分解特征降维理论，以揭示高光谱数据的流形分布，增强特征提取有效性，提高分类精度。.按原定研究计划，通过3年的研究，已达到原定目标，取得了如下主要研究成果：对现有的线性流形学习算法—近邻保持嵌入(NPE)方法进行推广，提出了一可处理多流形数据的监督线性流形学习特征降维算法；基于流形学习标准、Fisher标准和最大边缘标准，提出了一种适用于高光谱图像小样本问题的监督线性流形学习特征降维算法；基于流形学习标准和非负矩阵分解标准，提出一种在非负分解的基础上保持数据局部几何结构和判别信息的流形正则非负矩阵分解特征降维算法；提出了一种组合高光谱图像多特征(如谱、纹理、形态学等特征)的正交非负矩阵分解谱-空间特征降维方法，高光谱图像的分类结果表明了所提算法的有效性。另外，在本项目的支持下，我们还研究了与本项目相关的仿射不变特征提取方法、图像去噪、图像分割、图像匹配、图像目标识别等内容，形成若干篇论文。.本项目的完成为高光谱图像特征降维提供了新的研究思路和方法，丰富发展了高光谱图像特征降维的理论。