JH Dulá Sufficient conditions are provided for a deterministic algorithm for estimating an L1-norm best-fit one-dimensional subspace. To prove the conditions are sufficient, fundamental properties of the L1-norm projection of a point onto a one-dimensional subspace are derived. Also, an equivalence is established between the algorithm, which involves the calculation of several weighted medians, and independently-derived algorithms … Read more
The general formulation for finding the L1-norm best-fit subspace for a point set in $m$-dimensions is a nonlinear, nonconvex, nonsmooth optimization problem. In this paper we present a procedure to estimate the L1-norm best-fit one-dimensional subspace (a line through the origin) to data in $\Re^m$ based on an optimization criterion involving linear programming but which … Read more
The L1 norm has been applied in numerous variations of principal component analysis (PCA). L1-norm PCA is an attractive alternative to traditional L2-based PCA because it can impart robustness in the presence of outliers and is indicated for models where standard Gaussian assumptions about the noise may not apply. Of all the previously-proposed PCA schemes … Read more
We formalize an algorithm for solving the L1-norm best-fit hyperplane problem derived using first principles and geometric insights about L1 projection and L1 regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This … Read more