## Robust Principal Component Analysis using Facial Reduction

We study algorithms for robust principal component analysis (RPCA) for a partially observed data matrix. The aim is to recover the data matrix as a sum of a low-rank matrix and a sparse matrix so as to eliminate erratic noise (outliers). This problem is known to be NP-hard in general. A classical way to solve … Read more

## An LMI description for the cone of Lorentz-positive maps II

Let L_n be the n-dimensional second order cone. A linear map from R^m to R^n is called positive if the image of L_m under this map is contained in L_n. For any pair (n,m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n-1)(m-1) that … Read more

## An LMI description for the cone of Lorentz-positive maps

Let \$L_n\$ be the \$n\$-dimensional second order cone. A linear map from \$\mathbb R^m\$ to \$\mathbb R^n\$ is called positive if the image of \$L_m\$ under this map is contained in \$L_n\$. For any pair \$(n,m)\$ of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality (LMI) that … Read more