Cross fitted topology alignment entropy for brain graph analysis in Alzheimer research

Abstract

Entropy calculated after graph filtering depends on both signal dynamics and the graph estimated from those signals, complicating the interpretation of regional complexity in Alzheimer research. We introduce cross fitted topology alignment graph entropy (TAGE), which estimates a graph on one temporal segment and evaluates dispersion entropy on another. An alignment contrast compares the observed topology with node permutations that preserve its spectrum and edge-weight multiset. Three fixed filters sum to the identity, and a training-block bootstrap describes sensitivity to graph estimation. The reported synthetic audit includes five configurations, 80 recordings per configuration, and 99 graph permutations. For independent autoregressive signals, the mean low-band contrast decreased from 0.01057 with same-segment estimation to 0.00029 with cross fitting. Nevertheless, 11.25% of cross fitted ranks were at or below 0.05; this proportion increased to 26.25% under temporal heterogeneity. These findings support temporal separation as an audit of graph-dependent entropy while demonstrating that alignment ranks require further calibration. The study provides methodological and simulation evidence only; it does not establish an Alzheimer biomarker or patient-level diagnostic performance.