鲁棒几何结构描述及图像识别

流形学习技术可以较好地描述数据的内在几何结构，已成为机器学习和模式识别领域的研究热点。然而，它所描述的几何结构主要刻画了数据的相似性，忽略了模式的多样性，导致内在几何结构描述不够稳定以及算法鲁棒性比较差；此外，流形学习技术不能够较好地保持数据的局部拓扑结构，导致几何结构描述不准确；最后，几何结构描述过于依赖邻接图的定义，导致算法自适应性不好。因此，如何自适应地且鲁棒地描述数据的内在几何结构已成为急需要解决的问题之一。基于此，本项目主要研究自适应的鲁棒性几何结构描述（包括多样性几何结构描述和相似性几何结构描述）；融合相似性、多样性和像素空间信息的流形学习技术；基于该技术的半监督学习和非负矩阵分解。项目研究内容是模式识别、机器学习等领域非常活跃的研究方向之一，具有非常重要的理论价值和应用价值.

Many previous works have demonstrated that manifold learning is straightforward to well represent the intrinsic geometrical structure of images and has become an active research topic in machine learning, pattern recognition, statistical learning and image retrieval. However, it only characterizes the similarity among nearby data and neglects the variation of the values among nearby data, which will impair the recognition accuracy and generalization ability of the algorithm. Moreover, it does not well preserve the local topology as we expected. Finally, the adjacency graph is manually defined in experiments, which will impair the flexibility of the algorithm. Therefore, how to self-adaptively represent the robust intrinsic geometrical structure of data becomes one of the very important problems that urgently need to be solved. In this project, we mainly study self- adaptively intrinsic geometrical structure representation, which well characterizes both the similarity and variability of data, and robust manifold learning thecnique via integrating the similarity, variability, and relationship among pixels in images into the objective function. Furthermore, we extend it to the semi-supervised and non-negative cases, i.e. semi-supervised discriminant learning, and sparse non- negative matrix factorization. These contents of this project are very important in pattern recognition and machine learning, and will help to promote the development of the related areas.