Apparaît dans la collection : Meeting in mathematical statistics: new procedures for new data / Rencontre de statistiques mathématiques : nouvelles procédures pour de nouvelles données
Consider a sample of points drawn from some unknown density on $R^d$. Assume the only information we have about the sample are the $k$-nearest neighbor relationships: we know who is among the $k$-nearest neighors of whom, but we do not know any distances between points, nor the point coordinates themselves. We prove that as the sample size goes to infinty, it is possible to reconstruct the underlying density p and the distances of the points (up to a multiplicative constant).
$k$-nearest neighbor graph - random geometric graph - ordinal embedding
De Juan Luis Gastaldi
De Giulio Biroli
