Visualization of robust L1PCA. Issue 1 (24th May 2016) - Zhou, Yi‐Hui; Marron, J. S.
Abstract : Robust principal components are particularly challenging to find for high‐dimensional data sets, including genomic data. Conventional principal component analysis is often unduly influenced by a few closely related family members. This phenomenon is explained using the ideas of a high‐dimensional low sample size geometric representation. These ideas further show why the earlier robust method of spherical principal components fails to solve this problem. A solution is provided, which is called the visual L1 principal component analysis (VL1PCA). This approach is based on a backwards L1‐norm best‐fit idea. VL1PCA improves upon the best previous version of L1PCA by providing interpretable scores and a scatterplot visualization of the data. Another contribution is a new notion of robust centre, the backwards L1 median. The utility of VL1PCA is illustrated on examples and a real high‐dimensional data set. Our VL1PCA is not only robust to outliers but also gives a meaningful population stratification for data even in the presence of special family structure, when other methods fail. © 2016 The Authors. Stat Published by John Wiley & Sons Ltd