  This paper proposes a framework for simultaneous dimensionality reduction and
regression in the presence of outliers in data by applying low-rank and sparse
matrix decomposition. For multivariate data corrupted with outliers, it is
generally hard to estimate the true low dimensional manifold from corrupted
data. The objective of the proposed framework is to find a robust estimate of
the low dimensional space of data to reliably perform regression. The
effectiveness of the proposed algorithm is demonstrated experimentally for
simultaneous regression and dimensionality reduction in the presence of
outliers in data.
