Lp范数约束下的最大化L1范数主成分分析

Principal Component Analysis Based on L1-Norm Maximization with Lp-Norm Constraints

针对主成分分析在处理污染数据时的敏感性且其投影向量非稀疏的特性,提出一种鲁棒主成分分析的优化模型.该模型的目标函数采用L1范数且投影向量受Lp范数约束.范数约束下的主成分分析算法被用来求解该模型且其理论分析表明该算法可取得局部最优解.另外把核函数嵌入到线性模型并给出核方案.通过在UCI数据集和人脸库上的实验表明该算法的可行性和有效性.

Aiming at the sensitivity of principal component analysis in dealing with the contaminated data and the property that its projection vectors are not sparse, a robust principal component analysis optimization model is proposed. The objective function of the proposed model adopts L 1 norm and projective vectors are constrained by Lp norm. An iterative algorithm is used to solve the proposed model and the theoretical analysis shows that the algorithm can obtain the locally optimal solution. In addition, the kernel version is made by embedding kernel functions into the model. The experiments on UCI datasets and face datasets to demonstrate the feasibility and effectiveness of the proposed method.