Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance

The Singular Value Decomposition (SVD) is a fundamental algorithm used to understand the structure of data by providing insight into the relationship between the row and column factors. SVD aims to approximate a rectangular data matrix, given some rank restriction, especially lower rank approximation. In practical data analysis, however, outliers and missing values maybe exist that restrict the performance of SVD, because SVD is a least squares method that is sensitive to errors in the data matrix. This paper proposes a robust SVD algorithm by applying an adjustable robust estimator. Through adjusting the tuning parameter in the algorithm, the method can be both robust and efficient. Moreover, a sequential robust SVD algorithm is proposed in order to decrease the computation volume in sequential and streaming data. The advantages of the proposed algorithms are proved with a financial application.