Robust Singular Value Decomposition

The singular value decomposition of a rectangular data matrix can be used to understand the structure of the data and give insight into the relationships of the row and column factors. For example, the rows linked to the rows might be experimental conditions of temperature and the experimental conditions linked to the columns might pressure. In a biological setting the rows might be linked to tissues and the columns linked to genes. In experimentation, there might be aberrant values, outliers, or missing values that arise from flaws in the execution of the experiment so there is a need for singular value decomposition of data tables with missing values and outliers. Our idea is to use a sequential estimation of the eigenvalues and left and right eigenvectors that ignores missing values and is resistant to outliers. The benefit of our robust SVD is that data tables with experimental flaws, outliers and missing data, can be examined more easily.