鲁棒几何结构描述及图像识别

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.

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.

流形学习的核心是寻找一个子空间，使得低维子空间能较好地刻画利用邻接图在高维刻画的数据内在几何结构。流形学习技术已成为数据聚类，图像识别，特征提取，可视化分析等领域的研究热点之一。本项目针对流形学习技术不能较好地刻画数据的多样性几何结构，且依赖人工选择参数，导致流形学习技术在实际应用中的性能稳定性不好等问题，主要研究了几何结构的稳定性描述（自适应局部相似性和多样性几何描述）。在此基础上，实现了基于该几何结构描述的流形学习技术，包括无监督、监督以及基于矩阵的流形学习相关算法；实现了自适应稀疏几何结构描述的流形学习特征提取算法；将上述研究内容推广，研究了半监督流形学习技术；为了进一步提高流形学习算法的鲁棒实现了，研究了鲁棒度量学习的线性判别分析和主成分分析。并将上述算法研究应用于图像识别。相关研究成果主要发表在国际国内核心期刊如IEEE Trans. Neural Networks and Learning Systems; IEEE Trans. Image Processing；IEEE Transactions on Information Forensics & Security；Pattern Recognition，Neural Networks， 自动化学报以及国际顶级会议CVPR, AAAI等处共篇25，申请专利3篇（评审中）。该项目较好地实现了基于图的相似性、多样性以及像素空间的几何结构描述，有力提高了流形学习技术的鲁棒性，可以进一步提高流形学习技术在实际应用如聚类，可视化分析，分类，图像分析的鲁棒性，具有重要的理论意义和实际价值.