# Icing Detection over East Asia from Geostationary Satellite Data Using Machine Learning Approaches
## 3 Methodology
### Machine Learning  
Random forest (RF) has proven very effective for several meteorological satellite-based applications such as the detection of convective initiation and overshooting tops, and rainfall rate estimation [29; 30; 31; 41]. The multinomial log-linear model (MLL) is an improved version of logistic regression that incorporates an artificial neural network approach for parameter optimization [42]. Logistic regression has often been used in meteorological satellite applications [30; 31] and operational systems, such as to monitor rapid development thunderstorms (RDT) using Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite data [43]. Thus, in this study, the two machine learning classification approaches--RF and MLL via neural networks--were used to develop icing detection models. RF, which is based on classification and regression trees (CART; [44]), produces numerous CARTs and adopts an ensemble approach to obtain the final output from the resultant trees. It incorporates two randomizations to overcome the major limitation of CART, which is the sensitivity to training data configuration, which often results in overfitting. By developing many independent trees from different sets of training samples and input variables, RF tries to provide relatively unbiased results [45; 46; 47]. RF has proven useful in various remote sensing tasks for both classification and regression [48; 49; 50; 51]. RF also provides information on how input variables contribute to a given task. It calculates the decrease in accuracy using out-of-bag samples when an input variable is perturbed [52; 53; 54]. The larger the decrease in accuracy, the more significant the variable. RF can provide results in probability form from the ensemble approach.  
Figure 2: An example of icing and non-icing sample extraction from COMS data. Preprocessed images are masked using the threshold at the infrared-1 (IR1) channel and a spatial buffer. In this example, icing was reported on 5 July 2011 23:50 UTC at N37.42\({}^{\circ}\) and E129.2\({}^{\circ}\) and non-icing was reported on 5 July 2011 23:48 UTC at N36.58\({}^{\circ}\) and E130.25\({}^{\circ}\).  
MLL is a type of linear classification model for predicting the logarithmic form of a dependent variable [55; 56]. MLL can be calculated by Equation (1):  
\[\log(y)=c+\sum_{i}\omega_{i}f_{i}(X)\qquad\left\{\begin{array}{ll}\text{ \"0\" }label,&if\;\;y<0\\ \text{ \"1\" }label,&if\;\;y\geq 0\end{array}\right. \tag{1}\]  
where \(y\) is the instant target variable, \(i\) is each input variable, \(\omega\) is the weight of each variable, and the \(f(X)\) is the value of each variable [55; 56; 57]. MLL works well when a dependent variable has complex relations with the input variables. The coefficients associated with input variables are determined through an advanced coefficient fitting approach, named neural networks. Since the coefficients of the normalized regression model imply the relative contribution of the input variables, they can be used to analyze the relative importance of the variables. In this study, MLL is implemented using an 'nnet' package in R, which builds a feed-forward single-hidden-layer neural network to fit MLL [57].