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

Abstract We extend to the β-divergence (Itakura-Saito) case β = 0, the comparative bi-stochaticization analyses–previously conducted (arXiv:1208.3428) for the (Kullback-Leibler) β = 1 and (squaredEuclidean) β = 2 cases–of the 3,107-county 1995-2000 U. S. migration network. A heuristic, ”greedy” algorithm–using the β = 1 results as an initial configuration–is devised. While the largest 25,329 entries of the 735,531 non-zero entries of the bi-stochasticized table–in the β = 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 β = 0 instance. The North Carolina counties of Mecklenburg (Charlotte) and Wake (Raleigh) are considerably relatively more cosmopolitan in the β = 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.