Sparsifying spherical radial basis functions based regional gravity models

Abstract

ABSTRACT Regularization is often necessary in parameter estimation of spherical radial basis function (SRBF) based regional gravity modelling. In this work, a new regularization method, namely the L1-norm regularization, also called the least absolute shrinkage selection operator (Lasso), is employed. This is different from the commonly used L2-norm regularization, also called the Tikhonov regularization. The solution produced by Lasso is sparse, namely with part of the parameters being exactly zero. A sparse model would be beneficial in terms of better interpretability and improved variable assigning efficiency. The optimization problem involving the L1-norm regularization is solved by employing a highly efficient numerical algorithm called fast iterative shrinkage threshold algorithm (FISTA). The hyperparameter, namely the regularization coefficient, is selected through 10-fold cross validation. Simple closed-loop simulation is conducted using EGM2008. Without loss of generality, the point-mass method, a special kind of SRBF kernels, is employed. The accuracy and the sparsity of the Lasso-based SRBF model is demonstrated in this simulation. In this work, the Tikhonov regularization method outperforms the L1-norm regularizations method about 20% in regions with rough gravity field features, in regions with smooth gravity field features two regularization methods perform almost equivalently in terms of modelling accuracy. Sparsity of Lasso is obvious, to be more specific, sparsity ratio, namely the ratios of the number of zero parameters to that of the original full parameters, are greater than 0.5.