# Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis

arXiv: https://arxiv.org/abs/2605.13312 · HTML: https://mlsanity.com/paper/2605.13312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 78 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [BiomedGPT: A Generalist Vision-Language Foundation Model for Diverse Biomedical Tasks](https://mlsanity.com/paper/2305.17100/) (2023)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [Graph Neural Network for Interpreting Task-fMRI Biomarkers](https://mlsanity.com/paper/1907.01661/) (2019)
- [Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/1702.02519/) (2017)
- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Joint Embedding of Structural and Functional Brain Networks with Graph Neural Networks for Mental Illness Diagnosis](https://mlsanity.com/paper/2107.03220/) (2021)
- [Multi-View Graph Convolutional Network and Its Applications on Neuroimage Analysis for Parkinson's Disease](https://mlsanity.com/paper/1805.08801/) (2018)
- [Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm](https://mlsanity.com/paper/1611.05010/) (2016)
- [Multi-View Multi-Graph Embedding for Brain Network Clustering Analysis](https://mlsanity.com/paper/1806.07703/) (2018)
- [Integrated Brain Connectivity Analysis with fMRI, DTI, and sMRI Powered by Interpretable Graph Neural Networks](https://mlsanity.com/paper/2408.14254/) (2024)
- [Boosted Sparse and Low-Rank Tensor Regression](https://mlsanity.com/paper/1811.01158/) (2018)
- [Multi-modal Graph Neural Network for Early Diagnosis of Alzheimer's Disease from sMRI and PET Scans](https://mlsanity.com/paper/2307.16366/) (2023)
- [Brain Structure-Function Fusing Representation Learning using Adversarial Decomposed-VAE for Analyzing MCI](https://mlsanity.com/paper/2305.14404/) (2023)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [Tensor graph convolutional neural network](https://mlsanity.com/paper/1803.10071/) (2018)
- [Exponentially Convergent Algorithms for Supervised Matrix Factorization](https://mlsanity.com/paper/2311.11182/) (2023)

## Abstract (arXiv)

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.