Principal component analysis (PCA; Jolliffe (2002)) is one of the most popular methods used to find a low-dimensional subspace in which a given dataset lies. Classical PCA (cPCA) can be formulated as a problem to find a subspace that minimizes the sum of squared residuals, but squared residuals make PCA vulnerable to outliers. A lot of PCA algorithms have been proposed to robustify cPCA. The R1-PCA proposed by Ding et al. (2006) replaced the sum of squared residuals in cPCA with the sum of unsquared ones. The optimal solution of R1-PCA has similar properties to those of cPCA, that is, it is given as the eigenvectors of the weighted covariance matrix and it is rotationally invariant. The absolute residuals can reduce negative impact of outliers, but an arbitrary large outlier can still break down the estimate. More recently, Zhang and Lerman (2014) and Lerman et al. (2015) relaxed the optimization problem so that the set of projection matrices is extended to a set of convex set of matrices, and 1