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We propose a data aggregation-based algorithm with monotonic convergence to aglobal optimum for a generalized version of the L1-norm error fitting modelwith an assumption of the fitting function. The proposed algorithm generalizesthe 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 solvedoptimally if it follows the form of the L1-norm error fitting problem and ifthe fitting function satisfies the assumption. The proposed algorithm can alsosolve multi-dimensional fitting problems with arbitrary constraints on thefitting coefficients matrix. The generalized problem includes popular modelssuch as regression and the orthogonal Procrustes problem. The results of thecomputational experiment show that the proposed algorithms are faster than thestate-of-the-art benchmarks for L1-norm regression subset selection and L1-normregression over a sphere. Further, the relative performance of the proposedalgorithm improves as data size increases.

Optimization for L1-Norm Error Fitting via Data Aggregation