A Further (Itakura-Saito/beta=0) Bi-stochaticization and Associated Clustering/Regionalization of the 3,107-County 1995-2000 U. S. Migration Network

TL;DR

This paper extends bi-stochaticization analysis of U.S. migration networks to the beta=0 (Itakura-Saito) divergence, revealing new regional clustering patterns and county cosmopolitanism differences compared to previous beta=1 and beta=2 cases.

Contribution

It introduces a heuristic algorithm for beta=0 bi-stochaticization and applies it to U.S. migration data, uncovering novel regional and county-level insights.

Findings

Greater uniformity of entries in beta=0 case.

Identification of more cosmopolitan counties in beta=0 analysis.

Fragmentation of Connecticut counties into smaller clusters.

Abstract

We extend to the beta-divergence (Itakura-Saito) case beta =0, the comparative bi-stochaticization analyses-previously conducted (arXiv:1208.3428) for the (Kullback-Leibler) beta=1 and (squared-Euclidean) beta = 2 cases -of the 3,107 - county 1995-2000 U. S. migration network. A heuristic, "greedy" algorithm is devised. While the largest 25,329 entries of the 735,531 non-zero entries of the bi-stochasticized table - in the beta=1 case - are required to complete the widely-applied two-stage (double-standardization and strong-component hierarchical clustering) procedure, 105,363 of the 735,531 are needed (reflective of greater uniformity of entries) in the beta=0 instance. The North Carolina counties of Mecklenburg (Charlotte) and Wake (Raleigh) are considerably relatively more cosmopolitan in the beta=0 study. The Colorado county of El Paso (Colorado Springs) replaces the Florida Atlantic county of Brevard (the "Space Coast") as the most cosmopolitan, with Brevard becoming the second-most. Honolulu County splinters away from the other four (still-grouped) Hawaiian counties, becoming the fifth most cosmopolitan county nation-wide. The five counties of Rhode Island remain intact as a regional entity, but the eight counties of Connecticut fragment, leaving only five counties clustered.