基于迹比率的多数据集判别分析维数压缩

Trace ratio-based dimensionality reduction for discriminative analytics of multiple datasets

摘要:

主成分分析法常被用于维数压缩和特征提取，其在处理单一高维数据集时有很大优势.在很多实际场景中需要联合处理多个数据集，此时传统的主成分分析方法面临很大挑战.本文提出了迹比率主成分分析，该方法可以提取出目标数据相对其他数据特有的低维表示，进而通过迭代算法高效求解.数值算例验证了该方法的优越性.

Abstract:

Principal component analysis is widely applied in dimensionality reduction and feature extraction，especially in tackling single high-dimensional dataset. However，traditional principal component analysis faces challenge when it comes to analyzing multiple datasets jointly. This paper introduces a novel approach named trace ratio principal component analysis，which can discover low-dimensional structure unique to the target data relative to others. Furthermore，trace ratio principal component analysis and its variants can be solved by efficient iterative algorithm. Numerical experiments show the efficiency of the method.