Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Abstract

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.

GNSS-Condition Impacts on Land Boundary Coordinates and Land Area Determination

“…The aim was to show the importance of the establishment of relations between the points of the same closed polygon structure for optimal geometric structure estimation. In the future, we plan to incorporate also other applications, for example a multi-level specification problem with the association of the data set reduction, already presented by Drobne and Lakner (2016).…”

Intramax and other objective functions: The case of Slovenia

“…Variation of intra-regional flows, delimitated by other objective functions analysed herein, is always higher. The tendency to generate FRs with similar intra-regional flows is the reason why the original Intramax function divides metropolitan urban areas into smaller sub-regions (Drobne and Lakner, 2016).…”

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“…FR smo modelirali po hierarhičnem postopku Intramax (Masser in Brown 1975, 1977 z lastno programsko kodo v orodju za tehnično računanje Mathematica 12.0 (Drobne, 2016;Drobne in Lakner, 2016). Analiza Intramax je postopek hierarhičnega združevanja, ki se izvede korakoma.…”