Degree Frequencies in the Minimal Spanning Tree and Dimension Identification

Abstract

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.