## 4 Discussion  
BC remains the leading cause of cancer-related deaths among women worldwide, underscoring the urgent need for effective screening and diagnostic tools. Three-dimensional ABUS has emerged as a promising method for improving the screening and diagnosis of women with dense breast tissue, offering numerous advantages over traditional imaging techniques. While a limited number of studies have begun to explore deep learning-based approaches for tumor classification in ABUS, the challenge of balancing time efficiency with predictive accuracy has yet to be adequately addressed. This study introduces a novel strategy, termed the SV strategy, which employs voxel weighting to enhance classification performance. This method can be seamlessly integrated into any 2D-input CNN models. To the best of our knowledge, this is the first application of voxel-level probabilities for distinguishing between benign and malignant tumors in the context of volumetric tumor classification, marking a significant advancement in the use of deep learning for BC diagnosis. The SV strategy significantly enhances tumor classification performance when applied to 2D-input CNN models. As shown in Table 1, this strategy leads to notable improvements in various metrics compared to the baseline models. For instance, MedMamba achieves reasonable results (ACC, 0.738; SEN, 0.726; SPE, 0.755; AUC, 0.799), while the SV-powered MedMamba demonstrates excellent performance (ACC, 0.954; SEN, 0.975; SPE, 0.943; AUC, 0.954). Several factors may contribute to this improvement. First and foremost, the SV strategy incorporates voxel probabilities into the computation of volumetric tumor classification (see Figure 2). This approach effectively balances both the number of voxels and slice-wise probabilities in the final prediction. Secondly, the baseline 2D-input CNN models are proficient at slice-wise tumor classification. When a slice contains sufficient voxels for deep learning-based hierarchical feature representation, these models excel in slice-level classification. This is supported by the \(t\)-SNE visualization (Figure 8), which illustrates a clear separation between benign and malignant image slices. However, tumors exhibit diverse shapes, sizes, and textures, and the baseline models may struggle with smaller slices, leading to inaccurate predictions. Furthermore, the SV strategy outperforms the HV strategy, indicating that voxel-level weighting is more effective than slice-level weighting. Both the number of voxels and predicted probabilities play crucial roles in the accurate classification of tumor volumes (Figure 7). It is important to note that this concept has parallels in the artificial intelligence community [42; 43]. Unlike approaches that weight multiple classifiers or networks [27], the proposed strategy re-weights voxel importance to enhance prediction performance. The 3D-input CNN models demonstrate poor performance in ABUS tumor classification, as indicated by their metrics (AUC \(<\) 0.65) and as shown in Table 2. Although these models have witnessed success in disease classification using multi-plane multi-slice Transformer (M3T3D [32]), fusing ResNeXt and Bi-LSTM (ResNeXt3D [33]), and densely connecting global and local features (DenseNet3D [34]), several factors contribute to their shortcomings in this context. Firstly, a limited number of 300 training epochs hinders the iterative optimization of representation learning. The training parameters, such as learning rate, patch size, and loss function, are critical for prediction performance [44]. However, grid searching of optimal parameters is bound to dramatically increase the time cost in model training. As shown in Table 2, when the number of iteration epochs increases, the time cost is correspondingly and linearly increased. Compared to 2D-input CNN models, 3D data input increases computational complexity, requiring high memory and longer training time. Secondly, the insufficient number of ABUS tumor cases restricts the effective training of 3D-input CNN models.