A Multicollinearity-Aware Signal-Processing Framework for Cross-$\beta$ Identification via X-ray Scattering of Alzheimer's Tissue

TL;DR

This paper presents a three-stage, multicollinearity-aware framework for detecting Alzheimer's-related cross-$eta$ structures in X-ray scattering data, improving classification accuracy and interpretability in complex, correlated datasets.

Contribution

It introduces a novel multicollinearity-aware feature pruning scheme with formal guarantees, combined with a neural network classifier for cross-$eta$ detection in neurodegenerative tissue.

Findings

Achieved 84.3% F1-score on test data.

Reduced feature set from 211 to 11 features.

Demonstrated interpretability and effectiveness in data-limited scenarios.

Abstract

X-ray scattering measurements of in situ human brain tissue encode structural signatures of pathological cross-$\beta$ inclusions, yet systematic exploitation of these data for automated detection remains challenging due to substrate contamination, strong inter-feature correlations, and limited sample sizes. This work develops a three-stage classification framework for identifying cross-$\beta$ structural inclusions-a hallmark of Alzheimer's disease-in X-ray scattering profiles of post-mortem human brain. Stage 1 employs a Bayes-optimal classifier to separate mica substrate from tissue regions on the basis of their distinct scattering signatures. Stage 2 introduces a multicollinearityaware, class-conditional correlation pruning scheme with formal guarantees on the induced Bayes risk and approximation error, thereby reducing redundancy while retaining class-discriminative information. Stage 3 trains a compact neural network on the pruned feature set to detect the presence or absence of cross-$\beta$ fibrillar ordering. The top-performing model, optimized with a composite loss combining Focal and Dice objectives, attains a test F1-score of 84.30% using 11 of 211 candidate features and 174 trainable parameters. The overall framework yields an interpretable, theory-grounded strategy for data-limited classification problems involving correlated, high-dimensional experimental measurements, exemplified here by X-ray scattering profiles of neurodegenerative tissue.