$$\ell _1$$ ℓ 1 -Norm Based Central Point Analysis for Asymmetric Radial Data

Multivariate asymmetric radial data clouds with irregularly positioned “spokes” and “clutters” are commonly seen in real life applications. In identifying the spoke directions of such data, a key initial step is to locate a central point from which each spoke extends and diverges. In this technical note, we propose a novel method that features a preselection procedure to screen out candidate points that have sufficiently many data points in the vicinity and identifies the central point by solving an $$\ell _1$$ ℓ 1 -norm constrained discrete optimization program. Extensive numerical experiments show that the proposed method is capable of providing central points with superior accuracy and robustness compared with other known methods and is computationally efficient for implementation.