The Factorial Minimum Spanning Tree as a Reference for a Synthetic Index of Complex Phenomena

A method is herewith proposed which after analyzing the data matrix in principal components, searches the subspace representing the initial configuration of the inter-point distances by eliminating the “background noise” present in the data considered. In that subspace a factorial minimum spanning tree is built which becomes a reference structure for the design of a synthetic index of the phenomenon analyzed. The initial configuration is compared with the final one by means of adequate “quality indicators”. The validity of the method is confirmed by results achieved in various applications to real data.