# Non-Iterative Cluster Routing: Analysis and Implementation Strategies
## 6 Conclusions  
This research aimed to clarify the key definitions and concepts integral to cluster routing, with an emphasis on demystifying the terminologies and principles underlying the original cluster routing algorithm. Additionally, we provided a comprehensive guide for the implementation of different versions of the original cluster routing algorithm. Our goal was to streamline the deployment process, making it easier for users to adopt and effectively utilize the cluster routing approach. We conducted extensive experiments to assess the limitations associated with increasing the number of votes per cluster and explore alternative agreement indicators for cluster routing. Our findings indicated that the standard deviation of the votes within a cluster stands out as the optimal choice for the agreement indicator, due to its simplicity and efficiency. Additionally, we observed that increasing the number of votes per cluster, denoted as \(\mathbf{K}\), led to decreased performance in the original cluster routing for both single- and multiple-channel versions. Furthermore, we proposed two innovative cluster routing variations, which were designed to enhance its capabilities. Our first variation attempts to simplify the original cluster routing computation process through omitting the summation over weighted centroids, thereby reducing the training time. In some cases, it achieved superior performance while utilizing fewer parameters. This simplification is beneficial, as computational complexity and memory requirements pose challenges for constructing deeper and larger capsule networks. Our second variation addresses the impact of increasing the number of votes per cluster, denoted as \(\mathbf{K}\), in the original cluster routing. This variation enables us to manage capsule layers with substantial dimensions and mitigate the effects of increasing the number of votes per cluster, leading to improved performance when compared to the original cluster routing approach. Additionally, it offers the advantage of faster convergence throughout the network training phase. Our proposed novel methods improved the effectiveness of cluster routing and appear promising for numerous applications. Future research will aim to evaluate the applicability of our variations in various fields, including medical image analysis and deepfake detection. **Author Contributions:** Supervision, S.C.; Writing--original draft, H.P. ; Writing--review & editing, H.P. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Vice President for Research and Partnerships, the Data Institute for Societal Challenges, and the Stephenson Cancer Center at the University of Oklahoma through the 2021 DISC/SCC Seed Grant Award. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All research data used in this study were sourced from publicly available data on public websites. The source codes developed for this study are accessible at [[https://github.com/hngpham/cluster_routing_variations](https://github.com/hngpham/cluster_routing_variations)]([https://github.com/hngpham/cluster_routing_variations](https://github.com/hngpham/cluster_routing_variations)) starting from 16 March 2023. **Acknowledgments:** The authors extend their gratitude to [PERSON] for valuable discussions. Additionally, the authors would like to acknowledge the partial provision of computational resources for this project by the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma (OU). **Conflicts of Interest:** The authors declare no conflict of interest. * [26] [PERSON]; [PERSON]; [PERSON]; [PERSON] Capsules with Inverted Dot-Product Attention Routing. _arXiv_**2020**, arXiv:2002.04764. * [27] [PERSON]; [PERSON]; [PERSON] Capsule Routing via Variational Bayes. In Proceedings of the PAAAI Conference on Artificial Intelligence, New York, NY, USA, 7-12 February 2020; pp. 3749-3756.