基于逆幂法的组合稀疏约束主成分分析

Sparse Principal Component Analysis with Sparsity Constraints Based on the Inverse Power Method

讨论了在标准主成分分析的基础上增加L0罚,L1罚和L2罚约束条件,使主成分变得更加稀疏,以便于解释实际问题,运用逆幂法给出了求解目标函数的迭代算法.数据模拟实验展示了此算法在主成分的稀疏程度和累积贡献率上都取得了很好的效果.

In the report, based on the standard principal components analysis, in order to explain the practical problems, L0 penalty, L1 penalty, and L2 penalty constraint conditions were added, which made the principal components more sparse. The inverse power method was used to obtain the iterative algorithm for solving the objective function. The data simulation experiment results suggested that our algorithm has achieved good effects on the sparse degree and the cumulative contribution rate of the principal component.