Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics

The classification of vertical displacements and the estimation of a local geometric geoid model and coordinate transformation were recently solved by the L² support vector machine and support vector regression. The L^p quasi-norm SVM and SVR (0<p<1) is a non-convex and non-Lipschitz optimization problem that has been successfully formulated as an optimization model with a linear objective function and smooth constraints (LOSC) that can be solved by any black-box computing software, e.g., MATLAB, R and Python. The aim of this talk is to show that interior-point based algorithms, when applied correctly, can be effective for handling different LOSC-SVM and LOSC-SVR based models with different p values, in order to obtain better sparsity regularization and feature selection. As a comparative study, some artificial and real-life geoscience datasets are used to test the effectiveness of our proposed methods. Most importantly, the methods presented here can be used in geodetic classroom teaching to benefit our undergraduate students and further bridge the gap between the applications of geomatics and machine learning.