Robustness Can Be Cheap: A Highly Efficient Approach to Discover Outliers under High Outlier Ratios

  • Siqi Wang National University of Defense Technology
  • En Zhu National University of Defense Technology
  • Xiping Hu Chinese Academy of Science
  • Xinwang Liu National University of Defense Technology
  • Qiang Liu National University of Defense Technology
  • Jianping Yin National University of Defense Technology
  • Fei Wang Cornell University


Efficient detection of outliers from massive data with a high outlier ratio is challenging but not explicitly discussed yet. In such a case, existing methods either suffer from poor robustness or require expensive computations. This paper proposes a Low-rank based Efficient Outlier Detection (LEOD) framework to achieve favorable robustness against high outlier ratios with much cheaper computations. Specifically, it is worth highlighting the following aspects of LEOD: (1) Our framework exploits the low-rank structure embedded in the similarity matrix and considers inliers/outliers equally based on this low-rank structure, which facilitates us to encourage satisfying robustness with low computational cost later; (2) A novel re-weighting algorithm is derived as a new general solution to the constrained eigenvalue problem, which is a major bottleneck for the optimization process. Instead of the high space and time complexity (O((2n)2)/O((2n)3)) required by the classic solution, our algorithm enjoys O(n) space complexity and a faster optimization speed in the experiments; (3) A new alternative formulation is proposed for further acceleration of the solution process, where a cheap closed-form solution can be obtained. Experiments show that LEOD achieves strong robustness under an outlier ratio from 20% to 60%, while it is at most 100 times more memory efficient and 1000 times faster than its previous counterpart that attains comparable performance. The codes of LEOD are publicly available at