# Non-Iterative Cluster Routing: Analysis and Implementation Strategies
## 5 Results
### Comparison with the Baseline CNN  
In our study, our proposed cluster routing variations demonstrated superior performance when compared to the baseline CNN in two key aspects: the number of parameters and test error rates. Notably, when tested on the smallNORB data set, which is known for its variations in viewpoint, the proposed variations achieved higher accuracy while employing fewer parameters, as illustrated in Table 1. The CNN baseline, with 3.3 million parameters, achieved a test error rate of 3.76% on the smallNORB data set, while our strategy halved the test error rate to 1.95% while using approximately one-third of the parameters (1.11 M). The proposed variation achieved the best performance on this data set, with a test error rate of 1.46%. This proves the robustness of CapsNets in handling viewpoint variations in object recognition and pose estimation tasks. This accomplishment can be attributed to the capsule network's inherent capability to retain and utilize pose information within the features, enabling robust generalization even when confronted with images captured from viewpoints that have not been previously encountered [25]. While demonstrating superior performance and robustness on the smallINORB data set, our proposed variations also exhibited improved performance with a reduction in the number of parameters across image processing tasks, including the real-world digit recognition task in the SVHN data set, as well as image classification in the Fashion-MNIST and CIFAR-10 data sets, as illustrated in Table 1. This can be useful in real-world scenarios, where objects may be partially occluded or where the viewpoint of the object may vary.  
CNNs are adept at a wide array of tasks, but encounter difficulties in maintaining the spatial relationships between objects due to the incorporation of max-pooling layers [13; 15; 41]. These layers, which are designed for feature extraction and dimensionality reduction, inadvertently result in the loss of spatial information among objects. Consequently, CNNs may demonstrate decreased robustness in scenarios involving changes in viewpoint, scale, and rotation [14]. Capsule networks offer a solution to this issue by eliminating the need for pooling layers. Instead of relying on scalar values for feature representation--as is common in CNNs--CapsNets employ vectors or \"capsules\". Furthermore, they utilize a \"routing-by-agreement\" mechanism instead of pooling, which allows capsules to collaboratively decide on the existence of higher-level features [10]. This capability to preserve spatial relationships renders CapsNets particularly beneficial in the field of medical image analysis for tasks such as tumor detection, semantic segmentation, and disease classification, especially considering the variability in the body shapes and sizes of patients, as well as tumor locations.  
Despite their potential, CapsNets face inherent challenges; notably, they depend on a sophisticated routing algorithm that requires extensive agreement computations among capsules. In seminal CapsNet studies, such as those cited by [1; 4], routing iterations have been shown to be crucial for updating capsule agreements, considerably lengthening training and inference times [10]. This issue could limit the ability of CapsNets to match the depth and scalability of CNNs [12]. Nevertheless, our novel approaches leverage a non-iterative strategy to calculate capsule agreement, effectively reducing the training duration by an average of 15%, when compared to conventional iterative methods [1; 4].