鉴别性稀疏编码与模糊多核学习理论及其应用研究

This project mainly focuses on theories and methods of sparse representation and multiple kernel learning,which is further development of existing feature extraction technology. The main possible contributions of the project include following aspects: (1) Matrix measure theory in Riemannian space will be studied and feasible approaches to apply classical methods for high-dimensional pattern recognition problem will be developed,then a new measure will be suggested. (2) Several improved methods of sparse representation will be studied from different points of view and a new discriminatorily sparse coding method will be proposed. (3) An efficient algorithm of multiple kernel learning dimensionality reduction method will be proposed. (4) Theory of generalized multiple kernel learning will be proposed by incorporating discriminant analysis, sparse representation and fuzzy technology. (5) Experiments will be conducted on several image/video databases for feature extraction and pattern recognition on the basis of the above research. This project has an important research significance for image feature extraction and classification problems. In addition, the new ideas and methods proposed by this project will greatly improve the research of pattern recognition and computer vision.

本项目主要研究特征抽取中稀疏表示与多核学习的新理论与新方法，是对现有的特征抽取理论和方法的进一步丰富与拓展。本项目主要包括5个方面的研究内容：（1）研究黎曼空间矩阵度量理论并对经典方法在高维模式识别中的应用给出解决方案，进而提出一种新的度量方法；（2）对稀疏表示理论与方法在多个方面进行改进，并研究鉴别性的稀疏编码方法；（3）提出高效的多核学习降维理论与方法；（4）在经典多核学习理论与方法的基础上与鉴别性、稀疏性、模糊性相结合，提出广义多核学习理论与方法；（5）在上述理论和方法研究的基础上，在多个图像／视频库上进行进行图像特征抽取及识别实验研究。 本项目对图像特征抽取与分类问题具有重要的研究意义，此外项目中所提出的新思想与新方法将会丰富模式识别与计算机视觉的研究内容。

本项目针对模式识别中稀疏表示与多核学习的新理论与新方法进行研究，在黎曼流形学习、稀疏表示分类、鉴别低秩表示和多核学习等方面取得了丰硕的成果。一些代表性成果简述如下：针对黎曼流形学习不能有效消除图像中冗余信息的缺点，提出了基于Log-Gabor滤波与黎曼流形学习的图像识别算法；探索加快稀疏表示分类的方法，提出了一种新的局部稀疏表示分类方法，该方法依据测试样本和训练样本稀疏系数之间的相似性来构造字典矩阵；针对人脸识别中训练样本和测试样本均存在噪声等情况，提出了基于鉴别性低秩表示及字典学习的算法用于鲁棒人脸识别；针对 L1 范数多核学习方法产生核权重的稀疏解时可能会导致有用信息的丢失和泛化性能退化、Lp 范数多核学习方法产生核权重的非稀疏解时会产生很多冗余信息并对噪声敏感，提出了一种通用稀疏多核学习方法。.研究成果推动了图像特征抽取与分类领域的发展，具有较好的科学理论价值和工程应用价值。