Multivariate statistical simulation
Multivariate statistical simulation
Graph-theoretic procedures for dimension identification
Journal of Multivariate Analysis
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
An Intrinsic Dimensionality Estimator from Near-Neighbor Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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, M"n, is the sample average of squared degrees in the minimum spanning tree of the data, while the third statistic, U"n^k, is based on counting the number of common neighbors among the k-nearest, for each pair of sample points {X"i,X"j}, i