Fig 1.
The architecture of DC-CapsNet consists of four main components: a convolutional layer, a primary capsule layer, a divide-and-conquer module, and inter-group routing.
The convolutional layer extracts low-level features from the input image, which are then processed by the primary capsule layer to capture spatial hierarchies and pose variations. The divide-and-conquer module partitions the fully connected dynamic routing process into multiple groups, each focusing on learning distinct local vector representations associated with different classes. By structuring the routing process into independent groups, computational cost is reduced while preserving model accuracy and expressiveness. Finally, inter-group routing aggregates the locally learned capsule representations for final training.
Fig 2.
Illustration of coupling coefficient initialization and capsule aggregation methods.
(a) CapsNet-DR: Standard dynamic routing with coupling coefficients initialized using softmax over upper capsules, leading to normalization across classes. (b) CapsNet-CRI: Reverse initialization with softmax over lower capsules, resulting in normalization across input capsules. (c) DC-CapsNet (Ours): Group-based reverse initialization and aggregation, aligning coefficient normalization with the hierarchical structure and avoiding the over-smoothing of coupling coefficients, which limits capsule activation in CapsNet-CRI.
Table 1.
Experimental results comparing the classification accuracy (Acc., %) and standard deviation (Std.) of the proposed method with the original dynamic routing algorithm. CNN refers to a convolutional neural network with a parameter count comparable to the original dynamic routing capsule network. CapsNet-DR refers to the capsule network using the standard dynamic routing algorithm, CapsNet-CRI denotes the dynamic routing algorithm with inverse initialization of the coupling coefficients, DC-CapsNet-DR applies the group strategy with standard dynamic routing, and DC-CapsNet (Ours) is our full method.
Fig 3.
Comparison of F1 score, Precision, Recall, AUC among CNN, CapsNet-DR and DC-CapsNet across different datasets.
Table 2.
Comparison of runtime (seconds per epoch), number of parameters (M), and memory consumption (MB) for CapsNet-DR and DC-CapsNet (Ours) on different datasets.
Table 3.
Experimental results comparing the classification accuracy (Acc., %) and standard deviation (Std.) of advanced capsule network routing algorithms with the proposed DC-CapsNet method. The values in parentheses represent the standard deviation of three independent runs.
Fig 4.
Comparison of F1 score, Precision, Recall, and AUC for different advanced capsule network routing algorithms (baseline) and their improvements with our method across various datasets.
Table 4.
Experimental results evaluating the impact of different group numbers in the proposed DC-CapsNet. The results demonstrate how varying the number of groups affects classification accuracy (Acc., %) and standard deviation (Std.) across different datasets.
Table 5.
Evaluation of the impact of different routing iterations on the classification accuracy (Acc., %) and standard deviation (Std.) of the proposed DC-CapsNet across various datasets. The results illustrate how variations in the number of routing iterations affect model performance.
Fig 5.
Comparison of the original images and visualizations from different capsule groups.
The first five rows display samples from the MNIST dataset, while the last five rows are from the KMNIST dataset. The Orig column shows the original input image, and the Group + number columns present reconstructed features derived from different capsule groups. These visualizations demonstrate how distinct capsule groups capture specific image features, offering clearer and more focused representations than the original input. This improved interpretability contributes to better discrimination and enhanced performance in downstream tasks.
Fig 6.
Comparison of input image reconstruction results between the dynamic routing algorithm and our method on the MNIST, F-MNIST, and K-MNIST datasets.
The MNIST+Orig, F-MNIST+Orig, and K-MNIST+Orig columns represent the original images from the respective datasets, while the MNIST+DR, F-MNIST+DR, and K-MNIST+DR columns show the reconstructed images using the dynamic routing algorithm. The MNIST+Ours, F-MNIST+Ours, and K-MNIST+Ours columns display the reconstructed images using our proposed method.