Intrinsic dimension identification via graph-theoretic methods

Three graph theoretical statistics are considered for the problem of estimating the intrinsic dimension of a data set. The first is the “reach” statistic, r¯j,k, proposed in Brito et al. (2002)  [4] for the problem of identification of Euclidean dimension. The second, MnMn, is the sample average of squared degrees in the minimum spanning tree of the data, while the third statistic, Unk, is based on counting the number of common neighbors among the kk-nearest, for each pair of sample points {Xi,Xj}{Xi,Xj}, i