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

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

Problem Statement
Accurate and early diagnosis of Alzheimer's Disease (AD) and the classification of its severity stages remain critical challenges in neuroimaging. While Magnetic Resonance Imaging (MRI) is a cornerstone for assessing structural alterations like hippocampal atrophy, automated classification is hindered by subtle, non-linear structural changes, class imbalance, and the limitations of traditional machine learning approaches that rely on handcrafted features. Furthermore, existing deep learning solutions, particularly Convolutional Neural Networks (CNNs), often require aggressive data augmentation, large training sets, or complex ensemble strategies to achieve high accuracy. These methods can be computationally expensive, sensitive to data imbalance, and difficult to interpret, limiting their clinical applicability. Additionally, purely topology-driven models may struggle to capture fine-grained local textures in high-dimensional MRI data.

Methodology
The authors propose a novel hybrid deep learning framework that integrates Topological Data Analysis (TDA) with a DenseNet121 backbone to perform four-class AD severity classification (Non-Demented, Very Mild Dementia, Mild Dementia, Moderate Dementia) using structural MRI data from the OASIS-1 dataset. The architecture operates via two parallel feature extraction branches followed by a late-fusion strategy:

1. Topological Feature Extraction (TDA Branch):

   • The framework employs Persistent Homology (PH) to extract robust structural descriptors from 2D MRI slices.
   • A cubical sublevel filtration is constructed by progressively thresholding pixel intensities.
   • Homology groups are computed to capture connected components ($k=0$, Betti-0) and loops/cavities ($k=1$, Betti-1).
   • Persistence diagrams are transformed into fixed-length Betti curves (discretized into 100 bins for each dimension), resulting in a 200-dimensional topological feature vector ($T = [\beta_0, \beta_1]$).
   • These features are processed through a Multilayer Perceptron (MLP) to generate a 128-dimensional topological embedding. This branch captures global morphological characteristics invariant to geometric transformations.

2. Deep Feature Extraction (DenseNet121 Branch):

   • Grayscale MRI slices (resized to $248 \times 248$) are projected into a three-channel representation to utilize the DenseNet121 backbone.
   • The network, initialized with ImageNet pretrained weights and stripped of its classification head, learns hierarchical spatial features.
   • Global Average Pooling aggregates spatial information, which is then refined through a fully connected layer with ReLU activation to produce a 64-dimensional image feature embedding. This branch captures local texture patterns and spatial variations.

3. Feature Fusion and Classification:

   • The topological embedding (128-dim) and the CNN embedding (64-dim) are concatenated to form a unified 192-dimensional feature vector.
   • This fused vector passes through dense layers (256 and 128 neurons) with ReLU activation and a dropout rate of 0.2 to model higher-order interactions and prevent overfitting.
   • A final softmax layer predicts the probability distribution across the four AD severity classes.
   • The model is trained end-to-end using the Adam optimizer and categorical cross-entropy loss for 50 epochs with a batch size of 32. Notably, no data augmentation is employed.

Key Contributions

• Novel Hybrid Framework: The paper introduces a TDA+DenseNet121 architecture that synergizes global topological descriptors (via persistent homology) with local deep convolutional features.
• Data Efficiency and Robustness: The approach demonstrates that integrating topological information allows for high performance without relying on extensive data augmentation or complex ensemble strategies, addressing limitations in small or imbalanced datasets.
• Interpretability: By utilizing topological descriptors, the model offers a more interpretable representation of brain structural changes compared to "black-box" deep learning models.
• State-of-the-Art Performance: The framework achieves superior results on the OASIS-1 dataset compared to existing CNN-based, transfer learning, and ensemble methods.

Results
Evaluated on the OASIS-1 (Kaggle) MRI dataset with a 90:10 train-test split, the proposed model achieved:

• Accuracy: 99.93%
• AUC (Area Under the Curve): 100%
• Precision/Recall: 99.94% / 99.95%

These results significantly outperform previously published methods on similar datasets, including:

• Deep Multi-scale CNN (98.00% accuracy, 99.33% AUC).
• Four-way Siamese CNN (93.85% accuracy, 95.10% AUC).
• Transfer Learning using AlexNet (92.85% accuracy).
• Ensemble of deep neural networks (93.18% accuracy).

An ablation study confirmed that the hybrid model outperforms both the standalone TDA-only model (97.99% accuracy) and the standalone DenseNet121 model (97.78% accuracy), validating the complementary nature of the two feature types. Visualizations of Betti-0 and Betti-1 features via PCA and violin plots demonstrated clear separation and distinct clustering among the four disease stages.

Significance and Claims
The paper claims that the proposed framework offers a computationally efficient, data-efficient, and interpretable alternative to conventional deep learning-based MRI classification. By capturing global structural patterns that complement local intensity-based representations, the TDA+DenseNet121 model enhances class separability and robustness. The authors assert that this approach is particularly valuable for clinical scenarios where data availability is limited and where interpretability is crucial for clinician trust. The study highlights the potential of topology-aware deep learning as an effective paradigm for neuroimaging-based AD diagnosis, suggesting that integrating global structural descriptors with convolutional representations can advance the state of the art in severity classification without the need for excessive data augmentation.