Optimization for L1-Norm Error Fitting via Data Aggregation
This provides a more efficient solution for researchers and practitioners working with L1-norm error fitting problems, though it appears to be an incremental extension of existing methods.
The authors tackled the problem of solving generalized L1-norm error fitting models by proposing a data aggregation-based algorithm with monotonic convergence to a global optimum. Their algorithm was faster than state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere, with relative performance improving as data size increased.
We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multi-dimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Further, the relative performance of the proposed algorithm improves as data size increases.