Bayesian Tensor Modeling for Image-based Classification of Alzheimer's Disease.

Area of Science:

• Statistical modeling
• Machine learning
• Medical imaging analysis

Background:

• Tensor representations offer dimension reduction and spatial information preservation for complex data like medical images.
• Bayesian scalar-on-tensor regression is established, but Bayesian classification methods for tensor-valued covariates are underdeveloped.
• Standard methods like vectorization lose spatial structure, and feature extraction methods risk information loss.

Purpose of the Study:

• To propose a novel data augmentation-based Bayesian classification approach for tensor-valued covariates, specifically for imaging predictors.
• To extend existing classification methodologies to effectively handle high-dimensional tensor predictors while preserving spatial information.
• To develop an efficient Markov chain Monte Carlo (MCMC) algorithm for implementing the proposed methods.

Main Methods:

• Developed two data augmentation schemes for Bayesian classification: one SVM-type and one logistic regression-type classifier.
• Extended existing classification techniques to incorporate high-dimensional tensor predictors with low-rank coefficient matrix decomposition.
• Preserved spatial information within imaging predictors throughout the classification process.
• Implemented the methods using an efficient Markov chain Monte Carlo (MCMC) algorithm.

Main Results:

• Simulation studies demonstrated significant improvements in classification accuracy compared to standard methods.
• Parameter estimation accuracy was also enhanced by the proposed Bayesian classification approach.
• The method showed superior classification accuracy in neuroimaging applications, including differentiating Alzheimer's Disease (AD) patients, normal controls, and MCI patients.

Conclusions:

• The proposed data augmentation-based Bayesian classification method effectively utilizes tensor-valued imaging data.
• The approach preserves crucial spatial information, leading to improved classification accuracy in complex datasets.
• The method shows promise for various neuroimaging classification tasks, outperforming existing techniques.