A Multi-modal Approach for the Molecular Subtype Classification of Breast Cancer by using Vision Transformer and Novel SVM Polyvariant Kernel

Accurate classification of breast cancer into distinct molecular subtypes is crucial for personalized treatment and improved patient outcomes. Despite advancements in machine learning, predicting these subtypes remains challenging due to tumor heterogeneity and complex data characteristics. This study introduces the Polyvariant kernel, a novel SVM kernel that leverages the Vision Transformer (ViT) for multimodal data integration from the TCGA dataset of 1,081 breast cancer patients. The ViT extracts features from Whole Slide Imaging (WSI), which are fused with gene expression profiles through an Optimization-Based Search mechanism. These fused features are then classified using the Polyvariant kernel. The proposed approach significantly enhances breast cancer subtype classification, outperforming classical RBF, Polynomial, and Utility kernels, achieving 87% accuracy and 87% recall. The Polyvariant kernel is designed with distinct hyperparameters, enabling effective integration of diverse data sources such as gene expression profiles and WSI. We theoretically validated the proposed Polyvariant kernel by proving the Mercer conditions and establishing it as both a universal approximator and a universal kernel. Furthermore, we empirically demonstrated its superiority by benchmarking it against deep learning models (ResNet-50, VGG16, GoogLeNet) and classical ML datasets. Statistical significance tests confirmed its robustness, reinforcing its effectiveness for complex biomedical data integration. The proposed research demonstrates the efficacy of multimodal data fusion in improving breast cancer subtype classification and establishes the Polyvariant kernel as a powerful tool for complex biomedical data analysis.