Image Classification Based on Bayesian Tensor Modeling for Alzheimer’s Disease

Introduction

Neuroimaging research is a crucial component of contemporary neuroscience, significantly enhancing our understanding of brain structure and function. Through these non-invasive visualization techniques, researchers can more accurately predict the risk of certain neurological and psychiatric diseases, enabling early intervention and treatment to improve patients’ health and quality of life. Particularly in Alzheimer’s Disease (AD) research, neuroimaging provides valuable insights into the pathological mechanisms, tracks disease progression, identifies early symptoms, and distinguishes other causes of dementia.

However, processing neuroimaging data presents several major challenges, such as spatial dependencies of data, high dimensionality, and noise, making it difficult to identify suitable neurobiomarkers under heterogeneous conditions. To address these complex imaging data issues, researchers have proposed various statistical and machine learning methods, including image feature-based classification models.

Despite the different advantages and disadvantages of existing methods, they do not explicitly consider the spatial configuration of imaging voxels, potentially leading to bottlenecks when handling high-dimensional imaging data. In this context, this paper proposes a Bayesian classification method based on tensor representation with data augmentation, particularly suitable for imaging predictors.

Research Source

This research was jointly conducted by Rongke Lyu and Marina Vannucci from Rice University, Suprateek Kundu from MD Anderson Cancer Center, and researchers from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). The paper has been accepted by the journal “Neuroinformatics” and was officially published on May 20, 2024.

Research Process

Methods

The Bayesian classification method proposed in this paper primarily models data augmentation based on tensor representation, including two enhancement schemes: one generates a Support Vector Machine (SVM) type classifier, and the other generates a logistic regression classifier.

Key techniques adopted in the study include:

1. Tensor Decomposition: Tensors naturally inherit multi-dimensional structures, representing complex data structures well, such as spatial features of brain regions. Additionally, tensor techniques can achieve dimension reduction while maintaining data structure.
2. Parafac Decomposition: This tensor decomposition technique expresses high-dimensional tensors as combinations of low-dimensional factors, retaining spatial information while reducing the number of parameters.
3. Data Augmentation: The study uses the Markov Chain Monte Carlo (MCMC) algorithm to implement the model and introduces Polya-gamma latent variables for Bayesian inference in logistic regression models.

Simulation Study

We validated the method’s performance in multiple simulation scenarios, including:

1. Scenario 1: Tensor coefficients constructed through low-rank Parafac decomposition generating binary classification results.
2. Scenario 2: Manually setting tensor marginal values to generate binary classification results.
3. Scenario 3: Tensor coefficients set to 1 within a rectangular area and 0 in other areas.
4. Scenario 4: Tensor coefficients set to 1 within a circular area and 0 in other areas.
5. Scenario 5: Simulations based on actual cortical thickness images from the ADNI dataset.

The results showed that our method outperformed existing penalized logistic regression (Fallahati et al., 2014) and l1-norm SVM methods in terms of coefficient estimation, classification accuracy, and feature selection.

Application Study

We applied the method to the ADNI dataset for the following classification tasks:

1. Classification of normal controls (NC) and AD patients.
2. Classification of normal controls and patients with mild cognitive impairment (MCI).
3. Classification of MCI and AD patients.
4. Gender classification (male vs. female).
5. Cognitive performance classification based on MMSE scores (high vs. low).

The study found that our method exhibited higher classification accuracy across various tasks, particularly in distinguishing between AD and MCI. Slice 23 performed best in the AD vs. MCI classification task.

Main Results

1. Classification Accuracy: Whether using SVM or logistic regression enhancement schemes, our method demonstrated higher classification accuracy across various tasks. In contrast, traditional penalized logistic regression and l1-norm SVM methods performed poorly with high-dimensional imaging data.
2. Feature Selection: The Bayesian logistic regression method showed higher sensitivity and specificity in feature selection.
3. Parameter Estimation: The Bayesian SVM method provided more precise parameter estimation.

Conclusion

The Bayesian tensor modeling-based image classification method proposed in this paper effectively addresses high-dimensionality and spatial dependency issues in imaging data through efficient Parafac decomposition and data augmentation techniques. It significantly improves classification accuracy and enables clear feature selection and uncertainty quantification. In the future, we aim to develop more efficient and scalable versions for three-dimensional imaging classification tasks and explore more effective priors to enhance feature selection performance.

Research Value

This study provides important methodological support for the efficient analysis of neuroimaging data, especially for the early detection and risk prediction of neurodegenerative diseases. Compared to traditional methods, the proposed method ensures classification accuracy while precisely selecting key features, reducing model complexity, and avoiding overfitting. This advances the application of Bayesian tensor modeling in neuroscience and medical data analysis.