Operations Research, Systems Engineering and Industrial Engineering Commons^™

The L1-Norm Regularized L1-Norm Best-Fit Line Problem And Applications, Xiao Ling

Theses and Dissertations

The best-fit subspace or low-rank approximation of a data matrix revolves
around the norm approximation technique. l²-norm criterion is probably the most
widely used norm for fitting subspaces. As the computational power increases, the
l¹-norm analogue has recently gained attention from the academic community. It is
widely agreed that the l¹ norm is insensitive to outliers, compared to its l² variant.
Because of the polyhedral structure interrelated with linear programming (LP),
the l⁰ norm is commonly relaxed into the l¹-norm problem to induce sparsity in
models. In this work, we examine …