Non-Greedy L21-Norm Maximization for Principal Component Analysis

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due high computational complexity its eigen-decomposition solution, it hard apply PCA large-scale data with dimensionality, e.g., millions points variables. Meanwhile, squared L2-norm based objective makes sensitive outliers. In recent research, L1-norm maximization method was proposed for efficient computation and being robust this work used a greedy strategy solve eigenvectors. Moreover, may not be correct formulation, because loses theoretical connection minimization reconstruction error, which intuitions goals PCA. paper, we propose maximize L21-norm objective, theoretically connected error. More importantly, non-greedy optimization algorithms our more general problem guaranteed convergence. Experimental results on real world sets show effectiveness principal component analysis.