Robust Principal Component Analysis with Non-Greedy l1-Norm Maximization

Principal Component Analysis (PCA) is one of the most important methods to handle highdimensional data. However, the high computational complexitymakes it hard to apply to the large scale data with high dimensionality, and the used 2-norm makes it sensitive to outliers. A recent work proposed principal component analysis based on 1-normmaximization, which is efficient and robust to outliers. In that work, a greedy strategy was applied due to the difficulty of directly solving the 1-norm maximization problem, which is easy to get stuck in local solution. In this paper, we first propose an efficient optimization algorithm to solve a general 1-norm maximization problem, and then propose a robust principal component analysis with non-greedy 1-norm maximization. Experimental results on real world datasets show that the nongreedy method always obtains much better solution than that of the greedy method.