计算机科学 ›› 2021, Vol. 48 ›› Issue (6): 79-85.doi: 10.11896/jsjkx.200900014
贺文琪1,2,3, 刘保龙1,3, 孙兆川3, 王磊1,2,3, 李丹萍4
HE Wen-qi1,2,3, LIU Bao-long1,3, SUN Zhao-chuan3, WANG Lei1,2,3, LI Dan-ping4
摘要: 子空间学习是特征提取领域中的一个重要研究方向,其通过一种线性或非线性的变换将原始数据映射到低维子空间中,并在该子空间中尽可能地保留原始数据的几何结构和有用信息。子空间学习的性能提升主要取决于相似性关系的衡量方式和特征嵌入的图构建手段。文中针对子空间学习中的相似性度量与图构建两大问题进行研究,提出了一种基于核保持嵌入的子空间学习算法(Kernel-preserving Embedding based Subspace Learning,KESL),该算法通过自表示技术自适应地学习数据间的相似性信息和基于核保持的构图。首先针对传统降维方法无法挖掘高维非线性数据的内部结构问题,引入核函数并最小化样本的重构误差来约束最优的表示系数,以期挖掘出有利于分类的数据结构关系。然后,针对现有基于图的子空间学习方法大都只考虑类内样本相似性信息的问题,利用学习到的相似性矩阵分别构建类内和类间图,使得在投影子空间中同类样本的核保持关系得到加强,不同类样本间的核保持关系被进一步抑制。最后,通过核保持矩阵与图嵌入的联合优化,动态地求解出最优表示下的子空间投影。在多个数据集上的实验结果表明,所提算法在分类任务中的性能优于主流的子空间学习算法。
中图分类号:
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