Optimal Algorithms for <formula formulatype="inline"> <tex Notation="TeX">$L_{1}$</tex></formula>-subspace Signal Processing

We describe ways to define and calculate L_1norm signal subspaces which are less sensitive to outlying data than L_2calculated subspaces. We start with the computation of the L_1maximum-projection principal component of a data matrix containing Nsignal samples of dimension D We show that while the general problem is formally NP-hard in asymptotically large N D the case of engineering interest of fixed dimension Dand...