  Human brain connectome studies aim at extracting and analyzing relevant
features associated to pathologies of interest. Usually this consists in
modeling the brain connectome as a graph and in using graph metrics as
features. A fine brain description requires graph metrics computation at the
node level. Given the relatively reduced number of patients in standard
cohorts, such data analysis problems fall in the high-dimension low sample size
framework. In this context, our goal is to provide a machine learning technique
that exhibits flexibility, gives the investigator grip on the features and
covariates, allows visualization and exploration, and yields insight into the
data and the biological phenomena at stake. The retained approach is dimension
reduction in a manifold learning methodology, the originality lying in that one
(or several) reduced variables be chosen by the investigator. The proposed
method is illustrated on two studies, the first one addressing comatose
patients, the second one addressing young versus elderly population comparison.
The method sheds light on the graph metrics and underlying neurobiological
phenomena.
