Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis

Multimodal brain network analysis faces a persistent trade-off between predictive accuracy and interpretability. Deep neural networks achieve high accuracy but behave as black boxes that reveal little about the brain modules driving their decisions, whereas matrix factorization methods provide parts-based interpretability yet remain largely shallow, unsupervised, and restricted to a single view, integrating modalities through predefined or heuristic fusion rules. To bridge this gap with a formulation that couples hierarchical modeling capacity with structured, interpretable representations and data-driven fusion, we present Supervised Deep Multimodal Matrix Factorization (SD3MF), an interpretable framework for integrative brain network analysis that generalizes Symmetric Nonnegative Matrix Tri-Factorization (SNMTF) from unsupervised single-graph clustering to supervised prediction over populations of multimodal graphs. SD3MF learns deep hierarchical factorizations for each modality together with a shared latent representation that aligns subjects across modalities. An encoder-decoder formulation jointly optimizes graph reconstruction and supervised prediction, while adaptive weights enable data-driven multimodal fusion. By representing each subject through community-level interaction matrices, the model yields interpretable and discriminative features. Experiments on multimodal connectome datasets show that SD3MF consistently outperforms strong deep learning baselines such as {Convolutional Neural Networks and Graph Neural Networks}, while enabling biologically interpretable insights. Code for reproducibility is available at https://github.com/amjadseyedi/SD3MF.