Intrinsic dimension identification via graph-theoretic methods

M.R. Brito, A.J. Quiroz and J.E. Yukich

Journal of Multivariate Analysis, 2013, vol. 116, issue C, 263-277

Abstract: 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, Mn, 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 k-nearest, for each pair of sample points {Xi,Xj}, iKeywords: Intrinsic dimension; Graph theoretical methods; Stabilization methods; Dimensionality reduction (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.jmva.2012.12.007

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