Identification of Corrupted Data via $k$-Means Clustering for Function Approximation (CSIAM Transactions on Applied Mathematics, 2021)
In addition to measurement noises, real world data are often corrupted byunexpected internal or external errors. Corruption errors can be much larger thanthe standard noises and negatively affect data processing results. In this paper, wepropose a method of identifying corrupted data in the context of function approximation. The method is a two-step procedure consisting of approximation stage andidentification stage. In the approximation stage, we conduct straightforward functionapproximation to the entire data set for preliminary processing. In the identificationstage, a clustering algorithm is applied to the processed data to identify the potentially corrupted data entries. In particular, we found $k$-means clustering algorithm tobe highly effective. Our theoretical analysis reveals that under sufficient conditions theproposed method can exactly identify all corrupted data entries. Numerous examplesare provided to verify our theoretical findings and demonstrate the effectiveness of themethod.
Keywords: Data corruption; function approximation; sparse approximation; $k$-means clustering.