(untitled) (CSIAM Transactions on Applied Mathematics, 2021)
In addition to measurement noises, real world data are often corrupted by unexpected internal or external errors. Corruption errors can be much larger than the standard noises and negatively affect data processing results. In this paper, we propose a method of identifying corrupted data in the context of function approximation. The method is a two-step procedure consisting of approximation stage and identification stage. In the approximation stage, we conduct straightforward function approximation to the entire data set for preliminary processing. In the identification stage, a clustering algorithm is applied to the processed data to identify the potentially corrupted data entries. In particular, we found k-means clustering algorithm to be highly effective. Our theoretical analysis reveals that under sufficient conditions the proposed method can exactly identify all corrupted data entries. Numerous examples are provided to verify our theoretical findings and demonstrate the effectiveness of the method.