---
title: "Robust Principal Component Analysis with Non-Greedy l1-Norm Maximization"
authors:
  - "Feiping Nie"
  - "Heng Huang"
  - "Chris H. Q. Ding"
  - "Dijun Luo"
  - "Hua Wang"
doi: "10.5591/978-1-57735-516-8/IJCAI11-242"
url: "https://ijcai.org/proceedings/2011/242"
pdf: "https://ijcai.org/proceedings/2011/0242.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "1433-1437"
track: ""
keywords:
---

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

Feiping Nie, Heng Huang, Chris H. Q. Ding, Dijun Luo, Hua Wang

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 1433-1437. DOI: [10.5591/978-1-57735-516-8/IJCAI11-242](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-242)

## Abstract

Principal Component Analysis (PCA) is one of the most important methods to handle high-dimensional data. However, the high computa-tional complexity makes 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-norm maximization, 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 non-greedy method always obtains much better solution than that of the greedy method.