【摘要】：主成分分析(Principle component analysis,PCA)是一種被廣泛應用的降維方法.然而經(jīng)典PCA的構造基于L2-模導致了其對離群點和噪聲點敏感,同時經(jīng)典PCA也不具備稀疏性的特點.針對此問題,本文提出基于Lp-模的稀疏主成分分析降維方法 (Lp SPCA).Lp SPCA通過極大化帶有稀疏正則項的Lp-模樣本方差,使得其在降維的同時保證了稀疏性和魯棒性.Lp SPCA可用簡單的迭代算法求解,并且當p≥1時該算法的收斂性可在理論上保證.此外通過選擇不同的p值,Lp SPCA可應用于更廣泛的數(shù)據(jù)類型.人工數(shù)據(jù)及人臉數(shù)據(jù)上的實驗結果表明,本文所提出的Lp SPCA不僅具有較好的降維效果,并且具有較強的抗噪能力.
[Abstract]:Principal component Analysis (Principle component analysis,PCA) is a widely used dimensionality reduction method. However, the construction of classical PCA based on L2-norm leads to its sensitivity to outliers and noise points, and the classical PCA does not have the characteristics of sparsity. In order to solve this problem, a sparse principal component analysis (Lp SPCA). LP SPCA) method based on Lp- norm is proposed to minimize the intrinsic variance of Lp- pattern with sparse canonical terms. It can be solved by a simple iterative algorithm, and the convergence of the algorithm can be guaranteed theoretically when p 鈮，

本文編號：2220289