Hierarchical Aggregation Procedures for Interaction Data

Masser, Ian; Brown, Peter J.

doi:10.1068/a070509

Cited by 113 publications

(108 citation statements)

References 10 publications

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“…While the use of the spatial contiguity constraint was included in the procedure already from the very beginning (Masser and Brown, 1975), this is the first time that the other two constraints have been considered in the hierarchical aggregation procedure.…”

Section: Resultsmentioning

confidence: 99%

“…However, the procedure seeks to maximise the intra-group shares of total interactions, which take place within the aggregations of BDUs that form the diagonal elements of the matrix (Masser and Brown, 1975). The procedure monotonically raises the internal flows of the consolidated areas by aggregating small BDUs/FRs with relatively high interconnections first.…”

Section: Intramaxmentioning

confidence: 99%

“…The original objective function in the Intramax procedure, as suggested by Masser and Brown (1975), improved by Hirst (1977) and Masser and Brown (1977), and simplified by Brown and Pitfield (1990) (2) It should be noted that: (a) the standardization of the entries of the interaction matrix is not necessary, (b) the procedure maximizes the intra-regional (inner) share of total flows at each stage of the grouping process, and (c) the intra-regional (inner) flows, i.e. the values on the main sub-diagonal matrices of the partitioned matrix, should be taken into account in the row and column totals at each step of the aggregation procedure.…”

Section: Intramaxmentioning

confidence: 99%

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Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Drobne

Lakner

2016

Business Systems Research Journal

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Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past. Objectives: In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint. Methods/Approach: The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically. Results: The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation. Conclusions: The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions.

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Section: Resultsmentioning

confidence: 99%

Section: Intramaxmentioning

confidence: 99%

Section: Intramaxmentioning

confidence: 99%

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Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Drobne

Lakner

2016

Business Systems Research Journal

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“…Masser in Brown, 1975, 1977Slater, 1981;Coombes in sod., 1986;Florez-Revuelta in sod., 2008;Farmer in Fotheringham, 2011). Nedavno je bil v Karlsson in Olsson (2006) opravljen pregled različnih pristopov k razmejitvi funkcionalnih regij.…”

Section: Uvodunclassified

A concept to define the number of functional regions: an application to NUTS 2 and NUTS 3 levels in Slovenia

Drobne¹,

Bogataj²

2012

Geod. vestn.

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UVODKoncept regij je globoko zasidran v zgodovini Evrope. Še preden je tehnologija prometa omogočila nastanek in povezovanje nacionalnih trgov, so večino Evrope sestavljale gospodarsko avtonomne regije, katerih velikost je bila omejena z enodnevno dostopnostjo do regionalnega središča -peš ali z vozom z vprego. Le najbolj razvita mesta in mestne regije, predvsem obmorske, so lahko premostili fizične razdalje in postali del višjerazrednih, vseevropskih, trgovskih in drugih struktur moči. Šele proti koncu predindustrijske dobe so centralizirana državna gospodarstva zaradi krepitve osrednje birokratske moči nadomestila srednjeveške regije. Kasneje pa je proces etatizacije po Evropi dobil različne oblike (Maier, 2005).Danes se pojem regij pogosto nanaša na povezovanje v okviru Evropske unije (EU). Toda sam koncept regije različni akterji razumejo zelo različno. Administrativne in statistične regije so opredeljene z nominalno določenimi mejami, homogeno naj bi pokrivale celoten pripadajoči Samo Drobne, Marija Bogataj -METODA OPREDELITVE ŠTEVILA FUNKCIONALNIH REGIJ: APLIKACIJA NA RAVNEH NUTS 2 IN NUTS 3 V SLOVENIJI

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“…Secondly, Voronoi polygon boundaries are merged based on cluster membership derived from a hierarchical clustering solution (Masser and Brown, 1975). Two emerging clusters, "world affairs" and "middle east", are highlighted in Figure 35.5c.…”

Section: Space Transformationsmentioning

confidence: 99%