Nonlinear discriminant graph embeddings for detecting white matter lesions in FLAIR MRI

Brain abnormalities such as white matter lesions (WMLs) are not only linked to cerebrovascular disease, but also with normal aging, diabetes and other conditions increasing the risk for cerebrovascular pathologies. Discovering quantitative measures which assess the degree or probability of WML in patients is important for evaluating disease burden, progression and response to interventions. In this paper, we introduce a novel approach for detecting the presence of WMLs in periventricular areas of the brain with a discriminant graph-embedding framework, introducing within-class and between-class similarity graphs described in nonlinear manifold subspaces to characterize intra-regional compactness and inter-regional separability. The geometrical structure of the data is exploited to perform linearization and canonical kernalization based on fuzzy-matching principles of 876 normal tissue patches in 73 subjects, and tested on patches imaging both WML (263) and healthy areas (133) in 33 subjects with diabetes. Experiments highlight the advantage of introducing separability between submanifolds to learn the studied data and increase the discriminatory power, with detection rates over 91% in true-positives, and the importance of measuring similarity for specific pathological patterns using kernelized distance metrics.