l1 regression

A Pure L1-norm Principal Component Analysis

  • E.L. Boone
  • J. Paul Brooks
  • JH Dulá
    • Categories Data-Mining, Linear Programming Tags , ,

    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

    The L1-Norm Best-Fit Hyperplane Problem

  • J. Paul Brooks
  • JH Dulá
    • Categories Data-Mining, Linear Programming, Statistics Tags , , ,

    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