Four-Stage Alzheimer's Disease Classification from MRI Using Topological Feature Extraction, Feature Selection, and Ensemble Learning

TL;DR

Alzheimer's disease severity classification from MRI is challenged by limited data and interpretability when using deep learning. The paper introduces TDA-Alz, a topology-driven framework that extracts persistent-homology descriptors (Betti-0 and Betti-1) from cubical filtrations of 2D MRI slices, followed by feature selection with XGBoost and ensemble classification (XGBoost and Random Forest). On the OASIS-1 dataset, TDA-Alz achieves a high accuracy of $98.19 ext{ extperthousand}$ and an AUC of $99.75 ext{ extperthousand}$, outperforming or matching many CNN-based methods while remaining computationally efficient and interpretable. The work demonstrates that combining topological descriptors with selective feature aggregation and ensemble learning offers a practical, data-efficient alternative to deep models for clinical MRI-based AD staging, with strong potential for decision-support in real-world settings.

Abstract

Accurate and efficient classification of Alzheimer's disease (AD) severity from brain magnetic resonance imaging (MRI) remains a critical challenge, particularly when limited data and model interpretability are of concern. In this work, we propose TDA-Alz, a novel framework for four-stage Alzheimer's disease severity classification (non-demented, moderate dementia, mild, and very mild) using topological data analysis (TDA) and ensemble learning. Instead of relying on deep convolutional architectures or extensive data augmentation, our approach extracts topological descriptors that capture intrinsic structural patterns of brain MRI, followed by feature selection to retain the most discriminative topological features. These features are then classified using an ensemble learning strategy to achieve robust multiclass discrimination. Experiments conducted on the OASIS-1 MRI dataset demonstrate that the proposed method achieves an accuracy of 98.19% and an AUC of 99.75%, outperforming or matching state-of-the-art deep learning--based methods reported on OASIS and OASIS-derived datasets. Notably, the proposed framework does not require data augmentation, pretrained networks, or large-scale computational resources, making it computationally efficient and fast compared to deep neural network approaches. Furthermore, the use of topological descriptors provides greater interpretability, as the extracted features are directly linked to the underlying structural characteristics of brain MRI rather than opaque latent representations. These results indicate that TDA-Alz offers a powerful, lightweight, and interpretable alternative to deep learning models for MRI-based Alzheimer's disease severity classification, with strong potential for real-world clinical decision-support systems.

Figures (7)

• Figure 1: Visual analysis of topological features using the first three principal components. (a) Betti-0 features and (b) Betti-1 features demonstrate clear and distinct clustering corresponding to the four AD severity stages, highlighting the discriminative power of topological descriptors.
• Figure 2: Representative brain MRI samples from the OASIS-1 dataset illustrating the four Alzheimer’s disease categories used in this study.
• Figure 3: TDA-Alz preprocessing and classification pipeline. Schematic illustration of the complete workflow employed in this study. The pipeline begins with loading brain MRI scans from the OASIS-1 dataset, followed by cubical sublevel filtration and computation of persistence diagrams in dimensions $PD_0$ and $PD_1$. The resulting topological summaries are vectorized using Betti curves to form discriminative feature representations. Class labels corresponding to four Alzheimer’s disease severity stages are then assigned, after which the data are split into training and testing sets. Feature selection is performed using XGBoost to identify the most informative topological descriptors, and the selected features are finally used to train ensemble classifiers. The workflow concludes with testing and quantitative performance evaluation.
• Figure 4: Overview of the proposed TDA-Alz framework. The workflow illustrates the end-to-end pipeline for MRI-based four-class Alzheimer’s disease classification. A 2D brain MRI image is first processed using cubical sublevel filtration to compute persistence diagrams, which capture the birth and death of topological features. These diagrams are subsequently transformed into fixed-length Betti feature vectors that summarize the evolution of connected components and loops. The resulting topological feature representations are assembled into feature vectors, refined through feature selection, and finally fed into ensemble machine learning classifiers for disease severity classification.
• Figure 5: Sublevel filtration of an MRI image. Illustration of the cubical (sublevel) filtration process, where pixels are progressively activated based on their grayscale intensity values. The binary images $\mathcal{X}_{60}$, $\mathcal{X}_{80}$, and $\mathcal{X}_{120}$ correspond to threshold values of $60$, $80$, and $120$, respectively, revealing the gradual emergence and evolution of connected components and topological structures across increasing intensity levels.