局部投影保留算法及其应用

Locality preserving projection (LPP) is a manifold learning method widely used in pattern recognition and computer vision. When LPP transforms different samples into new representations using the same linear transform, it tries to preserve the local structure of the samples, i.e., the neighbor relationship between samples so that samples that were originally in close proximity in the original space remain so in the new space. If LPP is implemented by solving the minimum eigenvalue problem, the minimum eigenvalue solution is not always optimal for preserving the local structure. When Kernel LPP (KLPP) algorithm is applied to a classi?cation problem that has a large number of training samples, the implementation of the corresponding classi?cation procedure may be time-consuming and even unfeasible. The automatically setting of the kernel parameter of KLPP has not been investigated. In this project, we will propose several improved LPP methods including pre-transform of LPP, decrease scheme of LPP, KLPP with high computational efficiency, automatically setting for the parameter of KLPP and image application oriented LPP. These improvements will make the LPP feasible in the application with high dimensional images.

作为一种基于变换的特征抽取技术，局部投影保留算法（LPP）有别于普通的特征抽取或降维技术的一个突出特点是：在降低数据维数的特征抽取过程中，其能很好地保持样本数据的局部结构，使得经过变换后，样本在新空间中仍能保持原有"邻居"关系。在已有的数据聚类、检索、文本分析以及识别等等问题的应用中，LPP方法表现出了良好的性能与应用前景。尽管如此，LPP方法也存在如下尚未解决的理论与应用缺陷：高维数据情况下，相应特征方程不可直接求解或已有的数值求解方案会使变换结果不符合LPP的本质要求；核LPP方法变换效率低下不能满足实际应用要求；核LPP方法参数选择功能的缺失也极大地影响了其实用性。本项目将针对如上问题，构造若干基于局地保持投影的新方案。这些方案包括：LPP预变换方案；LPP减方案；KLPP效率提升方案；KLPP参数选择方案；低计算复杂度的面向图像应用的新LPP方案等。这些研究将对高维数据情况下L

经过几年的研究，设计了几个局部特征抽取算法，算法的性能在人脸识别等问题中得到了验证。具体工作如下：（一）设计了基于韦伯图像描述子和多尺度图像块的局部特征抽取算法。在人脸图像等图像的特征抽取上，算法可以减少与分类无关的冗余信息，可在一定程度上消除人脸姿态变化对算法的影响。（二）设计了同时保持样本全局近邻关系与局部近邻关系的特征抽取算法。（三）设计的协同表示算法能利用一个误差矢量“模拟”训练样本的线性组合与测试样本间的差异，从而取得较优的分类结果。