## 2 Materials and Methods
### Machine Learning-Aided Sea Ice Monitoring Methods
#### 2.4.1 Decision Tree Algorithm  
Decision tree (DT) is one of the simplest and most useful algorithms for classification [49; 50]. It has been used to various remote sensing applications [51; 52; 53]. The structure of a decision tree is constructed upside down with three parts: internal node, branches and leaf. The first internal node is called the root, where classification starts. The internal node stands for a condition that is expressed by the feature parameters. Based on the node, the decision tree splits into branches according to a discriminant function. The tree ends at the leaf, which represents a final classification decision. Distinguishing between sea ice and water can be regarded as a binary classification problem. Thus, the algorithm C4.5 [54] is used, which recursively splits training data into subdivisions using a set of attributes described by input variables. C4.5 builds decision trees from a set of training data using the concept of information entropy. The training data are a set \(S=s_{1},s_{2},\ldots s_{i}\) of already classified samples. Each sample \(s_{i}\) consists of a p-dimensional vector \(\left(x_{1,i},x_{2,i},\ldots,x_{p,i}\right)\), where the \(x_{i}\) values represent attribute values or features of the sample, as well as the class in which \(s_{i}\) falls. C4.5 uses the information gain ratio to construct a decision tree. The information gain ratio is defined as:  
\[G_{ratio}=\frac{\left[\sum_{k=1}^{m}p(k)log_{2}p(k)+\sum_{j=1}^{p}\left(\left| D_{j}\right|/\left|D\right|\right)Ent\left(D_{j}\right)\right]}{\sum_{j=1}^{p} \left(\left|D_{j}\right|/\left|D\right|\right)log_{2}\left(\left|D_{j}\right|/ \left|D\right|\right)} \tag{4}\]  
Figure 4: Flow diagram of the sea ice monitoring using machine learning (ML). In the first stage (marked by rectangle with black dashed line), the TDS-1 data are processed to extract effective features. In the second stage (marked by a rectangle with a blue line), a classifier is developed using the training data, selected feature sequences (i.e., RESC, RESI, RESD, REWC, REWI and REWD) and ML algorithms, e.g., decision tree (DT) and random forest (RF). In the third stage (marked by a rectangle with a magenta dotted line), the classifier is applied to the test data to generate the sea ice monitoring results and evaluate the performance through comparing with the OSISAF and ASI sea ice data.  
where \(m\) is the number of categories; \(v\) is the number of selected features; \(D\) is the number of samples; \(D_{j}\) is the jth sample. In this paper, only two categories, i.e., sea ice and sea water, are included, so \(m=2\). As six features are selected, \(v\) is equal to 6. The information gain ratio can be simplified as:  
\[G_{ratio}=\frac{\left[\sum_{k=1}^{2}p(k)log_{2}p(k)+\sum_{j=1}^{6}\left(\left|D _{j}\right|/|D|\right)Ent\left(D_{j}\right)\right]}{\sum_{j=1}^{6}\left(\left|D _{j}\right|/|D|\right)log_{2}\left(\left|D_{j}\right|/|D|\right)} \tag{5}\]  
C4.5 has several advantages. It can mitigate overfitting through single pass pruning process, handle both discrete and continuous data and address the problem of incomplete data, which is common in practical applications.