二维多样性保持投影及人脸识别

流形学习有效地保持了数据的局部几何结构，已成为模式识别、机器学习等领域的研究热点．但是它忽略甚至破坏了对模式分析很重要的局部多样性信息，导致局部几何结构描述不够稳定，且性能不是很好．针对此问题，提出了基于图论的多样性保持投影．该方法利用邻接图刻画局部数据之间的变化关系，并给出度量数据多样性大小的差异离散度，然后通过最大化差异离散度提取投影方向．此外，该方法直接从图像矩阵估计差异离散度矩阵，有效地避免了小样本问题．在Yale，UMIST和AR数据库上的实验结果证实了该算法的有效性．

Face recognition using two-dimensional diversity preserving projection

Previous work has demonstrated that manifold learning can effectively preserve the local geometry among nearby data, and has become an active topic in pattern recognition and machine learning. However, it ignores or even impairs the local diversity of data, which will impair the recognition accuracy and lead to unstable local geometrical structure representation. In this paper, a novel approach, namely two-dimensional diversity preserving projection (2DDPP), is proposed for dimensionality reduction. 2DDPP constructs an adjacency graph to model the variation of data and measures the variation among nearby data by the diversity scatter, on the basis of which a concise criterion is raised by maximizing the diversity scatter. Moreover, 2DDPP directly calculates the diversity scatter matrix from the image matrix, which effectively avoids the small sample size problem. Experiments on Yale, UMIST, and AR databases show the effecitveness of the proposed method.