面向高维复杂数据的流形学习算法与应用研究

Manifold learning has become one of the most active research areas in machine learning, data mining and pattern recognition. This project has made research systematically and thoroughly on performance improving techniques of classical manifold learning algorithms for high-dimensional complex data. The main work can be summarized as follows: (1) To improve the robustness of existing manifold learning algorithms in presence of noisy data, this project tries to study noisy manifold learning problem from the whole and puts forward some general ideas and methods. Neighborhood selection and outlier detection, which are two key techniques for noisy manifold learning ,will be the focus of this study. (2) To overcome the shortcomings of the original algorithm in dealing with sparse or non-uniformly distributed data, this project will design more accurate calculation method for part optimization and whole alignment. (3) The existing manifold learning-based feature extraction and feature selection algorithms are often sensitive to parameters and not suitable to deal with complex distributed multi-manifold data. To perfect the imperfection mentioned above, this project will study manifold learning-based feature extraction and feature selection algorithm based on subclass structure information. Firstly, the graph model is exploied for within-subclass structure and between-subclass structure description. Then, we will extract and select features by simultaneously using the between-subclass information and the within-subclass information. Since the local geometric structure and class information are involved in the subclass structure information, these feature extraction and feature selection methods will perform well in pattern classification applications.The successful implementation of the project will enable manifold learning algorithm better deal with complex data sets, so that the theoretical study of manifold learning has better practical significance.

流形学习是是当前机器学习、数据挖掘和模式识别领域的研究热点。本课题以提高流形学习处理实际问题的能力为目标，重点研究面向复杂数据的流形学习算法，并在视觉数据分析进行应用。拟开展的研究工作如下：（1）从整体上研究面向噪声数据的流形学习算法，提出噪声条件下提升流形学习性能的一般性思路和方法；（2）基于块对齐框架来研究面向稀疏采样和非均匀分布的流形学习算法，通过设计更为精确的局部优化和坐标排列计算方法来提高现有算法的鲁棒性；（3）研究面向复杂多流形数据的流形学习算法并在视觉数据分析进行应用，引入子类结构信息来研究复杂多流形数据的特征选择算法，并提出基于流形学习的显著度计算方法。该项目的实施将使非线性流形学习算法提高应对复杂数据的能力，从而使流形学习的理论研究具有更好的实际意义。

本项目在基金支持下，围绕现有流形学习算法在面向实际应用，特别是在处理分析复杂分布高维数据时所面临的技术挑战展开研究。首先，在流形学习的理论研究方面，针对噪声数据、稀疏采样和非均匀分布数据、多流形分布等数据条件下的稳健流形学习方法进行研究和探索。针对大规模高维数据和序列高维数据，项目分别提出2种噪声点检测算法。在噪声点检测性能评估方面，提出一种融合结构贡献度的改进信噪比方法。针对稀疏采样和非均匀分布数据，项目提出稳健的流形学习方法。其次，在流形学习的应用研究方面，将所研究的多流形学习成果和流形正则化策略应用于高维遥感数据处理分析当中，并尝试从数据驱动的角度来研究卫星任务规划方法。项目结合流形学习和深度学习，提出一系列遥感数据分析方法和卫星任务规划方法，获得了相比较传统方法更好的性能，进一步扩展了流形学习理论的应用价值。