稀疏低秩表示优化理论与新方法研究

Sparse representation (SR) and low rank representation (LRR) are hot topics of feature extraction in recent years. Aiming at the problems of existing algorithms of SR and LRR, this project mainly focuses on optimization theory and its associated algorithms of SR and LRR. The main research contents of the project are listed as follows:.(1) New nonconvex nonsmooth sparsity inducing functions will be studied to tackle the problems that exist in current research, such as the optimization process of existing nonconvex sparsity inducing functions is slow. The optimization algorithm for the new sparsity inducing functions will also be developed. A series of new algorithms of SR will be obtained by updating the existing main algorithms of SR..(2) Discriminative information is incorporated into LRR from different points of view, which leads to new algorithms of Discriminative LRR. The proposed new algorithms are effective for handling the situation that both training and test samples are corrupted due to occlusion and random noises..(3) New Riemannian metrics will be developed by extending conventional SR and LRR to the Riemannian space, which will lead to new algorithms of SR and LRR in Riemannian space..(4) The essence of SR and LRR will be investigated. A study on the possible problems of local optimum and over learning that happen in the existing algorithms of SR and LRR will be presented. In order to overcome this problems, a global optimization algorithm will be proposed to obtain regularization parameters in SR and LRR..The new ideas and algorithms proposed in this project will enrich the research of pattern recognition significantly. Furthermore, the research results of this project will benefit for the development of feature extraction.

稀疏表示和低秩表示是近年来特征抽取的热点研究话题。本项目针对现有稀疏表示和低秩表示存在的问题，研究其优化理论和相应的特征抽取新算法。主要包括4个方面的研究内容：（1）针对现有非凸稀疏诱导函数优化复杂度高的问题，研究新的非凸非平滑稀疏诱导函数，并设计相应的目标函数优化算法；在此基础上更新主流的稀疏表示学习算法，得到一系列的稀疏表示新方法；（2）针对训练样本和测试样本中均存在遮挡和噪声破坏的情形，我们将从不同的角度将鉴别信息引入低秩表示中，提出新的鉴别性低秩表示方法；（3）将现有的稀疏表示和低秩表示扩展到黎曼空间中，提出新的黎曼度量方法及目标函数优化算法；（4）研究稀疏和低秩表示的本质，并对现有算法可能出现的局部最优、过学习等问题进行研究，进而研究面向稀疏表示和低秩表示模型中的正则化参数全局优化算法。.本项目的研究将丰富模式识别的研究内容，同时项目研究取得的成果将对特征抽取的发展有一定的作用。

项目针对现有稀疏表示和低秩表示算法存在的问题，基于非凸目标函数优化、黎曼流形学习和深度学习设计新方法，取得了一些研究成果，提升了稀疏和低秩表示的鉴别性和鲁棒性。.项目提出统一的框架用于不同的实际聚类问题并将稀疏子空间聚类规划为一个平滑的Lp（0<p<1）最小化问题，给出了一个求解多约束非平滑的Lp最小化问题的有效算法。提出松弛的块对角结构用于约束表示系数矩阵，同时考虑样本数据中存在的混合噪声。提出图嵌入引导的多核度量学习框架对格拉斯曼流形特征进行鉴别学习，用于缓解视觉数据具有较大的类间相似性和类内离散性的问题。提出基于字典学习和低秩表示的图像融合算法，并将潜在低秩表示进行深度扩展。提出基于稀疏和低秩表示的目标跟踪新模型。在公开数据集上的实验结果证实了提出方法的有效性。.已在国际/国内权威期刊和会议上发表论文80余篇，其中IEEE Trans 10篇，ICCV/CVPR/ICPR等国际会议论文11篇。培养博士和硕士研究生27名。