# A Comparison of Pooling Methods for Convolutional Neural Networks
## 5 Dataset Description  
The datasets chosen to evaluate this study were named as MNIST [72], CIFAR-10 [73] and CIFAR-100 [74]. One of the most prominent datasets with handwritten digits 0 to 9 is MNIST. In a 28 \(\times\) 28 pixel grayscale image, there have been 60,000 training samples and 10,000 test samples. The CIFAR-10 dataset is an object classification benchmark that represents 10 classes using 32 \(\times\) 32 color images; 10,000 samples were used for testing and 50,000 samples used for training. This is another dataset benchmark for object classification, extended from CIFAR-10. The dataset consists of 60,000 32 \(\times\) 32 color images divided into 100 categories (50,000 for training and 10,000 for testing). Performance evaluation of these datasets was compared on different pooling methods and is presented in Table 2.  
Fractional max pooling and S3 Pool (ResNet + data augmentation) performed very well on the CIFAR-10 and CIFAR-100 datasets. Almost all architectures aimed at eliminating the pooling layer, such as a network in the network (NIN) and ALL-CNN, were superior to both fractional max pooling and S3 Pool pooling schemes. RWP (LReLU activation) and spatial pyramid pooling had the lowest performance on CIFAR-10 and CIFAR-100, respectively. Average pooling, on the other hand, showed the worst performance on both datasets and was ranked second. In addition, implementing range-based pooling for various activation functions (with or without data expansion) within the NIN network achieved acceptable performance, individually monitored NINs, max out networks, and high density. It proved to perform better than networks. In addition, rank-based pooling significantly reduced the performance of networks consisting of 64 \(5\times 5\) filters and 64 convolution  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Pooling Methods**} & \multirow{2}{*}{**Architecture**} & \multirow{2}{*}{**Activation**} & \multicolumn{3}{c}{**Error Rate of Different Datasets**} & \multirow{2}{*}{**Accuracy**} & \multirow{2}{*}{**Reference**} \\ \cline{3-3} \cline{5-6}  & & & **MNIST** & & **CIFAR-10** & & **CIFAR-100** \\ \hline t & ResNet & RELU & & 7.08 & 29.38 & \\ S3 pooling & \multirow{2}{*}{ResNet} & \multirow{2}{*}{RELU} & \multirow{2}{*}{7.74} & \multirow{2}{*}{30.86} & \multirow{2}{*}{84.5\%} & \multirow{2}{*}{[66]} \\ (Flip + Crop) & & & & & & \\ \hline S3 pooling & CNN With Data & \multirow{2}{*}{RELU} & \multirow{2}{*}{7.35} & \multirow{2}{*}{———————————————————————————————————————  
filters, whereas wavelet pooling required location may even be improved by modifying the wavelet basis and investigating which basis performs the pooling the best. It is conceivable to somehow achieve better image feature reductions outside of the 2 \(\times\) 2 scale by adjusting the up sampling and downsampling variables in the decomposition and reconstructions. Preserving the sub-bands that are normally rejected for backpropagation should result in more reliability and reduced errors. Evidence from this study makes it very clear that average pooling is the weakest compared to alternative pooling strategies. The performance of the pooling approach is strongly influenced by the network and activation factors applied in the implementation. However, the strategy used for data augmentation has a tremendous influence on the network's overall performance. For the CIFAR-10 and CIFAR-100 datasets, rank-based stochastic pooling (RSPs) with extended data had a lower error rate than pooling without augmented data.