Degree Frequencies in the Minimal Spanning Tree and Dimension Identification
M. R. Brito, Adolfo J. Quiróz · Communication in Statistics- Theory and Methods · 2004
We discuss the application of linear combinations of the degree frequencies in the minimal spanning tree to the problem of identifying the appropriate dimension for a data set from its interpoint distance matrix. This graph-theoretical methodology, of very low computational cost, can be of aid in the problem of Multidimensional Scaling and in dimensionality reduction. Results of Lee [Lee, S. (1999). The central limit theorem for euclidean minimal spanning trees II. Adv. Appl. Probability 31(4): 969–984] imply that the procedure proposed here is asymptotically consistent.