# GAN Training Acceleration Using Frechet Descriptor-Based Coreset
## 4 Experiments and Results
### Experiment I: Validation Experiments Using 3D Synthetic Image Data  
To validate the performance of the FDD-Coreset on the BlobGAN, we synthesized an independent dataset of 1000 3D blob images (64 \(\times\) 64 \(\times\) 32 voxels) with Gaussian distributed noise as the test data. The version of these images without noise and their blob masks were recorded as ground truth to compare the performance with other approaches. The goal of this experiment is to show that the FDD-Coreset is capable of accelerating the training of the BlobGAN, while maintaining the BlobGAN's performance on blob identification. First, we selected \(k\) Coreset from these 1000 3D blob images to train the BlobGAN. To train the BlobGAN, \(\lambda_{cycle}\) and \(\lambda_{convex}\) were set to 10, and \(\lambda_{identity}\) was set to 0.5. The BlobGAN was trained from scratch using a learning rate of 0.0002 with the Adam optimizer (batch size = 1). The training typically took about 20 epochs to converge, so we did not set up the decay policy for the learning rate. We compared the computation time of the IED-Coreset [16] with the proposed FDD-Coreset under varying sample size \(k\) (see Table 1). As shown in Table 1, the FDD-Coreset is significantly faster (266-42,784 times) than the IED-Coreset for size \(k\) from 1 to 10. We compared the total computation time from Coreset selection to training Coreset on the BlobGAN. We randomly sampled 1000 3D blob images to train the BlobGAN as baseline. We generated a Coreset using the IED-Coreset (size \(k=10\)) and the FDD-Coreset (size \(k=10\), 20, 30), respectively, and trained these groups of Coreset on the BlobGAN by 20 epochs. Note that we did not evaluate the Coreset via the IED-Coreset with \(k=20\), 30. This is because with \(k=10\), the IED-Coreset took 42,784 times compared to the FDD-Coreset with \(k=10\). Once these Coresets were generated, we compared the total computational time from the Coreset generation to the BlobGAN training (see Table 2). It is apparent that the BlobGAN trained on the IED-Coreset with \(k=10\) takes the longest time. The reason is that the Coreset selection in the IED-Coreset takes almost 99% of the whole process. The BlobGAN trained on the FDD-Coreset with \(k=10\), 20 and 30 all performs significantly faster (31-87 times) than training on the entire dataset. This is because the FDD-Coreset reduces the entire 1000 3D images to \(k\) core images which significantly reduces the BlobGAN training time. The BlobGAN trained on the FDD-Coreset with \(k=10\), 20 and 30 performs significantly faster (189-530 times) than training on the IED-Coreset with \(k=10\). The reason is that the IED-Coreset calculated the distance between images based on Inception embedding from images, and there exists duplicated computation in the batch selection. We conclude that the total computation time for training BlobGAN on the FDD-Coreset with \(k=10\), 20 and 30 is significantly less than the entire dataset and the IED-Coreset, even with \(k=10\). We evaluated the model performance (blob identification) using eight metrics: Peak Signal-to-Noise Ratio (\(PSNR\)), Detection Error Rate (\(DER\)), Precision, Recall, F-score, Dice coefficient, Intersection over Union (\(loU\)), and Blobness (\(PB\)), as follows:  
1. Peak Signal-to-Noise Ratio (\(PSNR\)) metric is to measure the performance of image denoising. Let the final 3D denoised blobs image be \(x:\ R^{3}\to R\) and the 3D blobs image without noises be \(y:\ R^{3}\to R\), then \(PSNR\) is defined as follows: \[PSNR=20 log_{10}\frac{MAX_{x}}{||x-y||_{2}},\] (9) where \(MAX_{x}\) is the possible maximum voxel values of \(x\). 2. Detection Error Rate (\(DER\)) is to measure the difference ratio between the number of detected blobs and the ground truth. \(DER\) can be calculated by Equation (10). \[DER=\frac{\mid N_{GT}-N_{Det}\mid}{N_{GT}}\] (10) where \(N_{GT}\) represents the # of ground truth blobs and \(N_{Det}\) represents the # of detected blobs.