Exploring Parallel Efficiency and Synergy for Max-P Region Problem Using Python

Given a set of n areas spatially covering a geographical zone such as a province, forming contiguous regions from homogeneous neighboring areas satisfying a minimum threshold criterion over each region is an interesting NP-hard problem that has applications in various domains such as political science and GIS. We focus on a specific case, called Max-p regions problem, in which the main objective is to maximize the number of regions while keeping heterogeneity in each region as small as possible. The solution is broken into two phases: Construction phase and Optimization phase. We present a parallel implementation of the Max-p problem using Python multiprocessing library. By exploiting an intuitive data structure based on multi-locks, we achieve up 12-fold and 19-fold speeds up over the best sequential algorithm for the construction and optimization phases respectively. We provide extensive experimental results to verify our algorithm

Spanish unemployment: normative versus analytical regionalisation procedures

In applied regional analysis, statistical information is usually published at different territorial levels with the aim of providing information of interest for different potential users. When using this information, there are two different choices: first, to use normative regions (towns, provinces, etc.), or, second, to design analytical regions directly related with the analysed phenomena. In this paper, provincial time series of unemployment rates in Spain are used in order to compare the results obtained by applying two analytical regionalisation models (a two stages procedure based on cluster analysis and a procedure based on mathematical programming) with the normative regions available at two different scales: NUTS II and NUTS I. The results have shown that more homogeneous regions were designed when applying both analytical regionalisation tools. Two other obtained interesting results are related with the fact that analytical regions were also more stable along time and with the effects of scale in the regionalisation process. Keywords: Unemployment, normative region, analytical region, regionalisation. JEL Codes: E24, R23, C61.

Spanish unemployment: Normative versus analytical regionalisation procedures

In applied regional analysis, statistical information is usually published at different territorial levels with the aim of providing information of interest for different potential users. When using this information, there are two different choices: first, to use normative regions (towns, provinces, etc.), or, second, to design analytical regions directly related with the analysed phenomena. In this paper, provincial time series of unemployment rates in Spain are used in order to compare the results obtained by applying two analytical regionalisation models (a two stages procedure based on cluster analysis and a procedure based on mathematical programming) with the normative regions available at two different scales: NUTS II and NUTS I. The results have shown that more homogeneous regions were designed when applying both analytical regionalisation tools. Two other obtained interesting results are related with the fact that analytical regions were also more stable along time and with the effects of scale in the regionalisation process.unemployment, regionalisation, analytical region, normative region

Supervised regionalization methods, a survey.

This paper reviews almost four decades of contributions on the subject of supervised regionalization methods. These methods aggregate a set of areas into a predefined number of spatially contiguous regions while optimizing certain aggregation criteria. The authors present a taxonomic scheme that classifies a wide range of regionalization methods into eight groups, based on the strategy applied for satisfying the spatial contiguity constraint. The paper concludes by providing a qualitative comparison of these groups in terms of a set of certain characteristics, and by suggesting future lines of research for extending and improving these methods.regionalization, constrained clustering, analytical regions.

Design of homogenous territorial units: a methodological proposal

One of the main questions to solve when analysing geographically added information consists of the design of territorial units adjusted to the objectives of the study. In fact, in those cases where territorial information is aggregated, ad-hoc criteria are usually applied as there are not regionalization methods flexible enough. Moreover, and without taking into account the aggregation method applied, there is an implicit risk that is known in the literature as Modifiable Areal Unit Problem (MAUP) (Openshaw, 1984). This problem is related with the high sensitivity of statistical and econometric results to different aggregations of geographical data, which can negatively affect the robustness of the analysis. In this paper, an optimization model is proposed with the aim of identifying homogenous territorial units related with the analyzed phenomena. This model seeks to reduce some disadvantages found in previous works about automated regionalisation tools. In particular, the model not only considers the characteristics of each element to group but also, the relationships among them, trying to avoid the MAUP. An algoritm, known as RASS (Regionalization Algorithm with Selective Search) it also proposed in order to obtain faster results from the model. The obtained results permit to affirm that the proposed methodology is able to identify a great variety of territorial configurations, taking into account the contiguity constraint among the different elements to be grouped.

Supervised regionalization methods: A survey

This paper reviews almost four decades of contributions on the subject of supervised regionalization methods. These methods aggregate a set of areas into a predefined number of spatially contiguous regions while optimizing certain aggregation criteria. The authors present a taxonomic scheme that classifies a wide range of regionalization methods into eight groups, based on the strategy applied for satisfying the spatial contiguity constraint. The paper concludes by providing a qualitative comparison of these groups in terms of a set of certain characteristics, and by suggesting future lines of research for extending and improving these methods

An exploration of methodologies to improve semi-supervised hierarchical clustering with knowledge-based constraints

Clustering algorithms with constraints (also known as semi-supervised clustering algorithms) have been introduced to the field of machine learning as a significant variant to the conventional unsupervised clustering learning algorithms. They have been demonstrated to achieve better performance due to integrating prior knowledge during the clustering process, that enables uncovering relevant useful information from the data being clustered. However, the research conducted within the context of developing semi-supervised hierarchical clustering techniques are still an open and active investigation area. Majority of current semi-supervised clustering algorithms are developed as partitional clustering (PC) methods and only few research efforts have been made on developing semi-supervised hierarchical clustering methods. The aim of this research is to enhance hierarchical clustering (HC) algorithms based on prior knowledge, by adopting novel methodologies. [Continues.