## 3 Proposed Methodology
### Dataset and Pre-Processing  
The WM-811k dataset includes the largest quantity of publicly available WBM data. The WM-811k consists of approximately 811,000 WBMs produced by the semiconductor industry. In the WM-811k dataset, labeled wafers account for 21.3% of the total data, or 172,950 wafers, and among the labeled wafers, those labeled with defect patterns account for 3.1% of the total, or 25,519 wafers. When labeling, the WM-811k dataset assumed that one wafer map had one defect pattern. Here, the label consisted of a total of nine defect patterns, including the 'none' pattern (i.e., no defect on the wafer). To reliably train defect pattern classifiers and generative models, dependable and clearly labeled data are required. As mentioned above, the WM-811k dataset has a significant amount of unlabeled data, and the wafers that make up this dataset are of 632 different sizes. Therefore, it is not suitable to use the WM-811k dataset directly for experiments, and appropriate preprocessing steps must be performed. We preprocessed the WM-811k dataset in the following order. First, we selected all (26, 26)-sized WBMs. Since the WBMs of wafer size (26, 26) had all been labeled by domain experts, this was an effective way to obtain WBMs that were well refined and uniform without performing unnecessary work for data preprocessing. Table 1 shows the number of WBMs of (26, 26) size in the WM-811k dataset. As shown in Table 1, most defects were classified as 'none', and the frequency of the occurrence of each defect pattern was significantly less than that of the 'none' pattern. In addition, the frequency of occurrence for each defect pattern was extremely different. We used two different data augmentation methods to address these data imbalance problems and compared the performances of  
Figure 2: Schematic of the proposed methodology. each method. Figure 3 shows the proportion of each defect pattern, excluding the 'none' pattern, among the (26, 26)-sized WBMs selected for experiment in the WM-811k dataset. Next, the selected (26, 26) WBMs were resized to (64, 64). This preprocessing procedure helps the WBMs generated through the generative model to include more diverse types of defect bits compared to the case wherein the 26 \(\times\) 26-sized WBM is used for generative model learning. After resizing, we mapped the 'good' die, 'failed' die, and 'non-wafer areas' to different channels. In the WM-811k dataset, a WBM is composed of a combination of numbers 0, 1, and 2. We reconstructed the original dataset of (26, 26) shape into a (64, 64, 3) shape, specifying that only one of the same coordinates of each reconstructed channel had a value of 1, while the rest had a value of 0. In other words, the (n, m) coordinates of the reconstructed WBM had one of the values of [1, 0, 0], [0, 1, 0], or [0, 0, 1], where 0 \(\leq\) n \(\leq\) 63, 0 \(\leq\) m \(\leq\) 63. As shown in Figure 3, there were extreme differences between the frequencies of the occurrence of defect patterns. This data imbalance is common in industry data. To prove the effectiveness of the proposed generative model on extremely imbalanced data, we selected only a part of the original data and used it for augmentation model learning; the remaining original WBBs were not used for learning. At this time, the data were selected so that the imbalanced nature of the original data was maintained. In Figure 4, the ratio of the number of the WBMs selected for augmented model learning to the number of original WBMs with the (26, 26) shape in the WM-811K dataset is shown for each defect pattern. As can be observed in Figure 4, we selected WBMs at various ratios from a minimum of 2.7% to a maximum of 18.75% for each defect pattern, except for the 'donut' pattern. As shown in Table 1, there was only one 'donut' WBM in the WM-811K dataset with a 26 \(\times\) 26 shape.