## 2 Materials and Methods
### Sampling of Training Patch  
#### 2.2.1 Sampling Design Using Class Purity  
To extract the representative training patches, the class purity and the patch size of a training patch were considered in this study. The former was considered to quantify the class representativeness of a training patch because a training patch contains pixels whose classes may differ from the representative class of a center pixel. The latter was considered owing to its significant effect on classification performance. The extraction of a training patch depends on the degree of difference between the representative class of a center pixel and the classes to which the surrounding pixels belong. The degree of class difference means the compositional homogeneity of classes within a training patch. In this study, this compositional homogeneity within a training patch is referred to as class purity. More specifically, the class purity is defined as the proportion of pixels present in a patch that belong to the same class as the center pixel. Figure 3 illustrates the selection of a training patch for a specific class and the calculation of class purity values. For example, if the class of a center pixel in a 5 by 5 patch is A, and the classes of 15 pixels within the patch correspond to class A, this patch is regarded as a training patch for class A with a class purity value of 60% (Figure 3a). This selection procedure assumes that the class of the center pixel is the representative class of the patch, which is typical in patch-based classification [30; 31]. In contrast, the two patches in Figure 3b are not considered as a training patch for class A because the class of the center pixel is not class A. Instead, the two patches in Figure 3b can be training patch candidates for classes B and D, separately. However, because these patch candidates have low class purity values (24% and 28%, respectively), they cannot be used as training patches. Furthermore, if the class of the center pixel is not one of the crop types in the study area, the patch candidate is not selected as a training patch for crop classification. In the case where non-crop pixels are contained in a training \begin{table}
\begin{tabular}{c c} \hline
**Category** & **Specification** \\ \hline Satellite/Sensor & Landsat-8 OLI \\ Image size & 633 by 673 \\ Area of crop parcels & 198,476 ha \\ Spectral bands & Red, NIR, SWIR \\ Spatial resolution & 30 m \\  & 7 March 2017 \\  & 8 April 2017 \\ Acquisition date & 27 May 2017 \\  & 15 September 2017 \\  & 17 October 2017 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of Landsat-8 OLI images used for crop classification in Illinois. patch, they are still considered to calculate the class purity value for a specific crop type but are masked out in the final classification result. Figure 4 presents a procedure to extract training patch candidates using class purity values for a comparative study. After determining both the patch size and a reference or threshold value of class purity, a patch configuration with a predefined size is overlaid on all crop pixels in an image of interest such that each pixel in the image is the center of the patch. Any patch that has the reference class purity value is then selected. The representative class of each patch is determined by counting the number of the most frequent class in the patch from the ground truth data in the study area. As a result, the proportion of the representative class in the patch is the same number as the predefined class purity value. The training patch candidates can then be selected by applying the following two criteria: (1) the class of the center pixel in a patch should be the same as the representative class; (2) the representative class of the center pixel should be one of the crop types. The final training patches are extracted by applying specific selection criteria. Figure 4: Flow chart of selection of training patch candidates with respect to class purity and patch size.