Robust Principal Component Analysis for Outlier Handling

This technical report discusses the handling of data containing outliers, particularly in the context of principal component analysis (PCA). It outlines the limitations of standard singular value decomposition (SVD) methods, which are highly susceptible to outliers that can skew results. The report introduces robustSvd, a singular value decomposition method designed to be resistant to outliers, and robustPca, which implements this robustSvd approach. The authors explain that outliers are often artifacts of experiments and can mislead analyses. They recommend preliminary removal of obvious outliers before applying PCA to ensure accurate results. The report includes a practical example demonstrating the effect of outliers on PCA results, comparing standard SVD and robust SVD outcomes. Additionally, it provides code snippets for implementing these methods in R, emphasizing the importance of robust techniques in data analysis involving microarray or metabolite data.