Hybrid Topological and Deep Feature Fusion for Accurate MRI-Based Alzheimer's Disease Severity Classification

TL;DR

This study tackles MRI-based four-class Alzheimer's disease severity classification by coupling Topological Data Analysis (TDA) with DenseNet121 in a late-fusion architecture that merges global topological descriptors with local deep features. The method computes persistent-homology–based Betti features from 2D MRI slices and combines them with CNN embeddings, yielding a 192-dimensional fused representation that drives classification. On the OASIS-1 Kaggle dataset, the approach achieves $99.93\%$ accuracy and an AUC of $1.00$ (100%), outperforming recent CNN-, transfer learning-, ensemble-, and multi-scale-based methods. Ablation shows the hybrid model substantially benefits from the complementary information provided by TDA and CNN features. The framework offers robustness, data efficiency, and interpretability, with clear potential for clinical adoption in settings with limited data and resources.

Abstract

Early and accurate diagnosis of Alzheimer's disease (AD) remains a critical challenge in neuroimaging-based clinical decision support systems. In this work, we propose a novel hybrid deep learning framework that integrates Topological Data Analysis (TDA) with a DenseNet121 backbone for four-class Alzheimer's disease classification using structural MRI data from the OASIS dataset. TDA is employed to capture complementary topological characteristics of brain structures that are often overlooked by conventional neural networks, while DenseNet121 efficiently learns hierarchical spatial features from MRI slices. The extracted deep and topological features are fused to enhance class separability across the four AD stages. Extensive experiments conducted on the OASIS-1 Kaggle MRI dataset demonstrate that the proposed TDA+DenseNet121 model significantly outperforms existing state-of-the-art approaches. The model achieves an accuracy of 99.93% and an AUC of 100%, surpassing recently published CNN-based, transfer learning, ensemble, and multi-scale architectures. These results confirm the effectiveness of incorporating topological insights into deep learning pipelines and highlight the potential of the proposed framework as a robust and highly accurate tool for automated Alzheimer's disease diagnosis.

Figures (6)

• 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 examples from the OASIS-1 dataset corresponding to the four Alzheimer’s disease categories considered in this study.
• Figure 3: Overview of the proposed TDA+DenseNet121 framework for Alzheimer’s disease classification. The architecture consists of two complementary feature extraction branches. In the first branch, a 2D brain MRI slice is processed through a DenseNet121-based convolutional network to learn hierarchical deep features, followed by convolution, pooling, and flattening operations. In parallel, the second branch applies Topological Data Analysis (TDA) to the same MRI input, where cubical sublevel filtrations are used to compute persistence diagrams that capture the birth and death of topological features. These diagrams are transformed into fixed-length Betti feature vectors and further refined using a multilayer perceptron (MLP). The deep convolutional features and topological features are then concatenated to form a unified representation, which is finally fed into a feed-forward neural network for four-class Alzheimer’s disease severity classification.
• Figure 4: 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.
• Figure 5: Interpretable visualization of topological feature distributions derived from persistent homology. The violin plots illustrate the class-wise distributions of aggregated Betti-0 and Betti-1 features for all MRI samples. Distinct and non-overlapping patterns are observed across the four Alzheimer’s disease severity stages, indicating progressive and discriminative topological changes in brain structure. These clear separations highlight the strong interpretability and class-discriminative capability of the proposed TDA-based descriptors.