Performance evaluation for outlier detection from numerical perspective

Outlier detection is an important topic in data mining and statistics. Various outlier-detection methods consist of intermediate steps that require solving linear equations. In many occasions, the efficiency and effectiveness of the outlier-detection results hinge on the runtime, precision, and stability of the solution to the related linear equations. This paper presents the performance evaluation of several numerical solvers employed for solving linear equations in the process of identifying outliers, including LU factorization, Cholesky decomposition, Gaussian elimination, Gaussian decomposition with partial pivoting, and the conjugate gradient method, from the numerical perspective. Both the theoretical analysis and the experiment results are provided for the detailed evaluation.