基于L1-范数和弹性网约束的鲁棒稀疏块PCA

Robust and Sparse BPCA with the Constraints of L1-norm and the Elastic Net

块主成份分析(block principal component analysis,BPCA)是一种重要的子空间学习方法,能充分利用图像矩阵的部分关联.基于L1-范数的BPCA是近年来发展起来的鲁棒降维的有效方法.本研究提出了一种新的鲁棒稀疏BPCA方法,称之为BPCAL1-S.该方法相对于传统的基于L2-范数的PCA对噪声更加鲁棒.为了建立稀疏模型,优化过程中引入弹性网,联合使用Lasso与Ridge惩罚因子进行约束.提出了一种贪心算法逐个提取特征向量,对迭代过程的收敛性做了理论证明.将BPCAL1-S应用于图像分类与图像重构,实验结果验证了该方法的有效性.

Block principal component analysis(BPCA),which can utilize part correlation of image matrix sufficiently,is an important subspace learning approach.L1-norm based BPCA is an effective technique for robust learning in dimensionality reduction developed recently.We propose a novel robust and sparse BPCA method referred to as BPCAL1-S.The approach is more robust to outliers than the traditional L2-norm based PCA.To develop a model with sparsity,the elastic net constraint which combining ridge and lasso penalty,is integrated into the optimization procedure.We present a greedy algorithm to extract basic feature vectors one by one,and proposed theoretical analysis to guarantee the convergence of the iterative process.The proposed BPCAL1-S is applied to the analysis of image classification and image reconstruction,and the experimental results verify its effectiveness.