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. Obtaining quantitative measures which assesses the degree or probability of WML in patients is important for evaluating disease burden, and for evaluating its 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 using manifold-constrained embeddings. The proposed method uses locally linear embedding (LLE) to create "normality" distributions in 12 locations of the brain where deviations from the manifolds are estimated by calculating geodesic distances along locally linear planes in the embedding. A smooth mapping function approximating the relationship between ambient and manifold spaces as a joint distribution maps unseen test images in the intrinsic space. We create a set of low-dimensional embeddings from 876 patches of healthy tissue in 73 subjects and test it on 396 patches imaging both WML and healthy areas in 33 subjects with diabetes. Experiments highlight the need of nonlinear techniques to learn the studied data with detection rates over 85% in true-positives, and the relevance of the computed distance for comparing individuals to a specific pathological pattern.