Explainable Graph-theoretical Machine Learning: with Application to Alzheimer's Disease Prediction

Alzheimer's disease (AD) affects 50 million people worldwide and is projected to overwhelm 152 million by 2050. AD is characterized by cognitive decline due partly to disruptions in metabolic brain connectivity. Thus, early and accurate detection of metabolic brain network impairments is crucial for AD management. Chief to identifying such impairments is FDG-PET data. Despite advancements, most graph-based studies using FDG-PET data rely on group-level analysis or thresholding. Yet, group-level analysis can veil individual differences and thresholding may overlook weaker but biologically critical brain connections. Additionally, machine learning-based AD prediction largely focuses on univariate outcomes, such as disease status. Here, we introduce explainable graph-theoretical machine learning (XGML), a framework employing kernel density estimation and dynamic time warping to construct individual metabolic brain graphs that capture the distance between pair-wise brain regions and identify subgraphs most predictive of multivariate AD-related outcomes. Using FDG-PET data from the Alzheimer's Disease Neuroimaging Initiative, XGML builds metabolic brain graphs and uncovers subgraphs predictive of eight AD-related cognitive scores in new subjects. XGML shows robust performance, particularly for predicting scores measuring learning, memory, language, praxis, and orientation, such as CDRSB ($r = 0.74$), ADAS11 ($r = 0.73$), and ADAS13 ($r = 0.71$). Moreover, XGML unveils key edges jointly but differentially predictive of several AD-related outcomes; they may serve as potential network biomarkers for assessing overall cognitive decline. Together, we show the promise of graph-theoretical machine learning in biomarker discovery and disease prediction and its potential to improve our understanding of network neural mechanisms underlying AD.