基于主成分分析的自适应特征选择算法研究

提出了一种自适应性的特征提取方法。首先通过主成分分析求出样本全局投影空 间，然后基于最大化投影构建优化目标函数，最后通过该函数求出自适应于个体样本的投影空 间。该方法很好地考虑了样本集合中每个样本的分布特点。为了使得算法可应用于识别分类问 题中，给出了计算存在于不同投影空间的个体样本间相似性的方法，相比于欧式度量，该方法 被证明得到的相似性能够更好地表征样本间的测地距离关系，使其能够有效地对流型结构数据 进行学习。通过在不同数据库上进行分类及重构的对比实验，实验结果表明，该方法能够更好 地提取数据特征，且对离群点具有鲁棒性。

An Adaptive Feature Extraction Method Based on PCA

An adaptive features extraction method is proposed. It defines an adaptive objective function based on the projective space derived by using PCA method. Then the projection space of the individual sample is computed. The distribution characteristics of each sample are well considered. In order to make the algorithm applicable to the classification problem, a similarity measurement is proposed to calculate the similarity between individual samples in different projection spaces. Compared with the Euclidean metric, the proposed measurement is proved that can represent the geodesic distance relationship between the samples better, so that the proposed method can learn the manifold data effectually. The classification and reconstruction experiments on the different databases indicate that the new method can obtain features more effectively and robustly.