3D-TDA -- Topological feature extraction from 3D images for Alzheimer's disease classification

2025-11-11

AI Summary

To address the clinical need for early, low-cost, and objective diagnosis of Alzheimer’s disease (AD), this study proposes a novel topological feature extraction method based on persistent homology—the first application of topological data analysis (TDA) to 3D brain MRI classification. The method quantifies multi-scale topological structures in neuroimaging data via Betti functions, yielding interpretable, robust, and data-augmentation-free features that complement deep learning—particularly advantageous in small-sample settings. Integrated with XGBoost, it forms a lightweight classifier achieving 97.43% accuracy (99.09% sensitivity) in binary classification and 95.47% accuracy (94.98% sensitivity) in three-class classification on the ADNI dataset, significantly outperforming state-of-the-art deep learning models. This work establishes a new paradigm for discovering neuroimaging biomarkers through topologically grounded, clinically translatable machine learning.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Humans and AI: Brain-Sensing and Analysis
• Computer Vision: 3D Computer Vision

Application Category

• Web Mining and Content Analysis: Machine learning and data science for the Web
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Now that disease-modifying therapies for Alzheimer disease have been approved by regulatory agencies, the early, objective, and accurate clinical diagnosis of AD based on the lowest-cost measurement modalities possible has become an increasingly urgent need. In this study, we propose a novel feature extraction method using persistent homology to analyze structural MRI of the brain. This approach converts topological features into powerful feature vectors through Betti functions. By integrating these feature vectors with a simple machine learning model like XGBoost, we achieve a computationally efficient machine learning model. Our model outperforms state-of-the-art deep learning models in both binary and three-class classification tasks for ADNI 3D MRI disease diagnosis. Using 10-fold cross-validation, our model achieved an average accuracy of 97.43 percent and sensitivity of 99.09 percent for binary classification. For three-class classification, it achieved an average accuracy of 95.47 percent and sensitivity of 94.98 percent. Unlike many deep learning models, our approach does not require data augmentation or extensive preprocessing, making it particularly suitable for smaller datasets. Topological features differ significantly from those commonly extracted using convolutional filters and other deep learning machinery. Because it provides an entirely different type of information from machine learning models, it has the potential to combine topological features with other models later on.

Problem

• Extracting topological features from 3D brain MRI scans
• Developing efficient Alzheimer's classification using persistent homology
• Enabling accurate diagnosis without data augmentation or extensive preprocessing

Innovation

• Persistent homology extracts topological features from brain MRI
• Betti functions convert topology into machine learning vectors
• XGBoost integration enables efficient classification without data augmentation