Jacqueline J. Meulman

Solomiia Kurchaba, Jasper van Vliet, Fons J. Verbeek et al.

The shipping industry is one of the strongest anthropogenic emitters of $\text{NO}_\text{x}$ -- substance harmful both to human health and the environment. The rapid growth of the industry causes societal pressure on controlling the emission levels produced by ships. All the methods currently used for ship emission monitoring are costly and require proximity to a ship, which makes global and continuous emission monitoring impossible. A promising approach is the application of remote sensing. Studies showed that some of the $\text{NO}_\text{2}$ plumes from individual ships can visually be distinguished using the TROPOspheric Monitoring Instrument on board the Copernicus Sentinel 5 Precursor (TROPOMI/S5P). To deploy a remote sensing-based global emission monitoring system, an automated procedure for the estimation of $\text{NO}_\text{2}$ emissions from individual ships is needed. The extremely low signal-to-noise ratio of the available data as well as the absence of ground truth makes the task very challenging. Here, we present a methodology for the automated segmentation of $\text{NO}_\text{2}$ plumes produced by seagoing ships using supervised machine learning on TROPOMI/S5P data. We show that the proposed approach leads to a more than a 20\% increase in the average precision score in comparison to the methods used in previous studies and results in a high correlation of 0.834 with the theoretically derived ship emission proxy. This work is a crucial step toward the development of an automated procedure for global ship emission monitoring using remote sensing data.

Jacqueline J. Meulman, Anita J. van der Kooij

In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the process finds quantifications for the categories that are optimal for the regression model in the sense that they maximize the multiple correlation. Although the optimal scaling method was developed initially for variables with a limited number of categories, optimal transformations of continuous variables are a special case. We will consider a variety of transformation types; typically we use step functions for categorical variables, and smooth (spline) functions for continuous variables. Both types of functions can be restricted to be monotonic, preserving the ordinal information in the data. In addition to optimal scaling, three regularization methods will be considered: Ridge regression, the Lasso, and the Elastic Net. The resulting method will be called ROS Regression (Regularized Optimal Scaling Regression. We will show that the basic OS algorithm provides straightforward and efficient estimation of the regularized regression coefficients, automatically gives the Group Lasso and Blockwise Sparse Regression, and extends them with monotonicity properties. We will show that Optimal Scaling linearizes nonlinear relationships between predictors and outcome, and improves upon the condition of the predictor correlation matrix, increasing (on average) the conditional independence of the predictors. Alternative options for regularization of either regression coefficients or category quantifications are mentioned. Extended examples are provided. Keywords: Categorical Data, Optimal Scaling, Conditional Independence, Step Functions, Splines, Monotonic Transformations, Regularization, Lasso, Elastic Net, Group Lasso, Blockwise Sparse Regression.