Learning Covariance-Based Multi-Scale Representation of Neuroimaging Measures for Alzheimer Classification

TL;DR

This work tackles data-scarce medical imaging by replacing deep, heavily parameterized networks with a covariance-based multi-scale transform (COVLET) that produces informative, high-dimensional representations from limited samples. By treating the transform’s scales as trainable parameters and operating in the covariance domain via eigenbasis filtering, the approach yields efficient end-to-end learning with a downstream classifier and interpretable Grad-CAM-like maps. Empirical results on ADNI MRI cortical thickness and tau PET show higher accuracy and faster convergence than baselines, particularly for cortical thickness in 2- and 4-way Alzheimer’s classification, and provide ROI insights consistent with established AD literature. The method offers practical impact by delivering strong predictive performance with smaller models and transparent, region-specific interpretations useful for clinical grounding.

Abstract

Stacking excessive layers in DNN results in highly underdetermined system when training samples are limited, which is very common in medical applications. In this regard, we present a framework capable of deriving an efficient high-dimensional space with reasonable increase in model size. This is done by utilizing a transform (i.e., convolution) that leverages scale-space theory with covariance structure. The overall model trains on this transform together with a downstream classifier (i.e., Fully Connected layer) to capture the optimal multi-scale representation of the original data which corresponds to task-specific components in a dual space. Experiments on neuroimaging measures from Alzheimer's Disease Neuroimaging Initiative (ADNI) study show that our model performs better and converges faster than conventional models even when the model size is significantly reduced. The trained model is made interpretable using gradient information over the multi-scale transform to delineate personalized AD-specific regions in the brain.

Figures (4)

• Figure 1: Overall scheme of our multi-scale learning network. Input $X$ is transformed to a high-dimensional space with kernels $g(s)$ and Principal Components $U$ (i.e., convolution) and fed to a downstream classifier (solid line). The $S$ and classifier are trained to obtain the optimal task-specific multi-scale representation (dashed line).
• Figure 2: Visualization of $M$ on a random AD-sample that identifies personalized AD-specific ROIs. Various AD-specific ROIs are identified as in AD_journalAD_journal2AD_journal3 including hippocampus, thalamus, amygdala and several temporal regions. Drawings were generated using BrainPainter brain_painter.
• Figure 3: Comparisons of mean test accuracy from our model and 2-MLP$_I$ on 4-way classification with cortical thickness. Our model reaches 0.6 significantly faster than 2-MLP$_I$. Measures are computed from 5-fold CV (shaded areas are range of the test accuracy).
• Figure 4: Mean test accuracy w.r.t. scale in our model on 4-way classification using cortical thickness (5-fold CV). Test accuracy improves with scale training (solid line) over without training (dashed line).