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- Title
COMBINATORIAL PROCEDURES FOR STRUCTURING INTERNAL MIGRATION AND OTHER TRANSACTION FLOWS.
- Authors
Slater, Paul B.
- Abstract
The article comments on combinatorial procedures for structuring internal migration and other transaction flows. The author has developed several procedures for clustering using asymmetric matrices. The most widely applied of them has been a two-stage algorithm, IPFPHC. In the first stage, an n X n table of recorded flows is adjusted by the iterative proportional fitting procedure (IPFP). The entries of the adjusted table are then maximum entropy estimates of the flows that would occur in an idealized situation in which no size differences between the n units with respect to the total amounts of movement into and out of each of them existed. In the second stage of the procedure, a hierarchical clustering (HC) method, the directed graph analogue of single linkage clustering, is implemented, employing the adjusted table as an asymmetric dissimilarity matrix. A series of directed graphs on n vertices is obtained through the sequential insertion of links that correspond to the entries of the table ordered by decreasing magnitude. The strong components, sets of mutually reachable vertices, of any one of these digraphs partition the n vertices into non-overlapping groups. Initially, the digraph contains no links and thus has n strong components. These n groups then merge hierarchically as more and more links are inserted, until all vertices can be reached from one another.
- Subjects
INTERNAL migration; MATRICES (Mathematics); ALGORITHMS; ITERATIVE methods (Mathematics); DIRECTED graphs; ENTROPY
- Publication
Quality & Quantity, 1981, Vol 15, Issue 2, p179
- ISSN
0033-5177
- Publication type
Article
- DOI
10.1007/BF00144259