Bidimensional Regression Research Articles

Mapmaking Process Reading from Local Distortions in Historical Maps: A Geographically Weighted Bidimensional Regression Analysis of a Japanese Castle Map

Shoho Castle Maps are maps of castle towns throughout Japan drawn by Kano School painters on the order of the shogun in 1644. The Shoho Castle Map of Takada, Joetsu City, Niigata Prefecture was used to visualize local distortions in historical maps and to scrutinize the mapmaking process. A novel method, geographically weighted bidimensional regression, was developed and applied to visualize the local distortions of the map. Exaggerated expressions by mapmakers that have not been identified in previous studies were revealed. That is, in addition to the castle being drawn enlarged, the town where the merchants and artisans lived was drawn larger than the castle. Therefore, the Takada Shoho Castle Map reflects mapmakers’ intentions, besides enlarging military facilities, which appear to have emphasized the pictorial composition of the map by placing the main gate to the castle at the center and drawing the map area evenly from the center in a well-balanced layout.

Geometric Morphometrics Applied to Cartography

The morphological differences between two geographical maps can be highlighted by a polycentric distance cartogram resulting from a bidimensional regression. Beyond the communicational interest of the transformations thus produced, the method makes it possible to reveal the differences in structure and therefore constitutes a real research tool. However, bidimensional regression can only compare the shape of two maps. Since the 1990s, geometric morphometrics has revolutionized the morphological analysis of natural structures (and others). It has since been applied in many fields of research but not in cartography. This article describes the theoretical and methodological bases of a method combining bidimensional regression with a geometric morphometrics approach to compare the shape of several geographical maps. Geometric morphometrics and bidimensional regression indeed share common approaches of the statistical shape analysis like homologous landmarks and interpolation grids. However, there is no software in geometric morphometrics capable of directly reading geographical data, which would facilitate the work of cartographers accustomed to GIS software. That is why we present MapMorphy, a tool specifically developed for this task. An example on ancient maps illustrates the method.

An integrated approach of gravity modelling and spatial planning: the example of US megaregions

ABSTRACT Many theoretical works aim to describe the spatial structure of the US, where spatial relations have undergone continuous change. The authors describe the economic spatial structure of the US through bidimensional regression analysis based on a gravity model. The spatial image of megaregions can be examined by can be examined through comparison with the authors' practical results. To what extent does the structure of the economic space justify megaregional delimitations? The most important economic spatial structural changes between 2001 and 2020 have also been identified. Moreover, the forces behind changes, which are seen as potential for development, are examined. Our goal is not to create and present a new model that overwrites the existing ones, but rather to contribute to deeper understanding of the US economic spatial structure and its relation to megaregions through a new methodological approach.

Geographically weighted bidimensional regression on the 17th-century map of a castle town in Japan

Abstract. Previous studies on historical maps have frequently used the bidimensional regression method to analyze the distortion of the maps. In many cases, however, the residuals of bidimensional regression are spatially auto-correlated. Of course, we can understand map distortions by those spatially auto-correlated residuals. At the same time, however, there is a possibility for another approach, which is to expand the bidimensional regression method to one consisting of spatial auto-correlations. Geographically weighted regression is a famous example of such a regression method that consists of spatial auto-correlations. Thus, a new method, called geographically weighted bidimensional regression, is proposed in this study. This regression method was applied to the 17th-century map of a castle town in Japan. The results indicate that spatial auto-correlation of residuals no longer exists. In addition, local parameters of the new method can describe map distortions directly. Ordinary bidimensional regression divides map distortions into global distortions and local distortions, which means that the ordinary technique assumed global distortions. The new method, however, can explore map distortions without assuming global distortions.

Distance Matters: a more than euclidean approach to visualizing gerrymandering

Distance Matters: a more than euclidean approach to visualizing gerrymandering

Spatial Evolution of the Energy and Economic Centers of Gravity

Increasing energy demand and economic performance can be observed in emerging markets and, in parallel, their share in world energy use and in global GDP is growing as well. It causes significant spatial shifts and calls attention for a new geography of energy demand. The main purpose of this study is to reveal the spatial distribution of energy use and economic growth focusing on the link between them. Developing gravity models, we identify the economic and energy centres of gravity in the world and on different continents and reveal their movements between 1990 and 2015, in particular, the directions of the shifts. Bi-dimensional regression analysis and the method of standard distance are applied to compare these movements. The study utilizes cartograms to visualize how the space is changed and distorted by the field of force. It can be stated that the economic and energy centre of gravity can be found in the Mediterranean Basin, but a slow and gradual shift to the east can be observed. Currently it reflects the dominance of the north, but it marks the position loss of the northern hemisphere and the greater importance of developing economies (in the southern hemisphere).

On the Correspondence Between Procrustes Analysis and Bidimensional Regression

Procrustes analysis is defined as the problem of fitting a matrix of data to a target matrix as closely as possible (Gower and Dijksterhuis, 2004). The problem can take many forms, but the most common form, orthogonal Procrustes analysis, has as allowable transformations, a translation, a scaling, an orthogonal rotation, and a reflection. Procrustes analysis and other rotation methods have a long history in quantitative psychology, as well as in other fields, such as biology (Siegel and Benson, 1982) and shape analysis (Kendall, 1984). In the field of quantitative geography, the use of bidimensional regression (Tobler, 1965) has recently become popular. Tobler (1994) defines bidimensional regression as "an extension of ordinary regression to the case in which both the independent and dependent variables are two-dimensional." In this paper, it is established that orthogonal Procrustes analysis (without reflection) and Euclidean bidimensional regression are the same. As such, both areas of development can borrow from the other, allowing for a richer landscape of possibilities.

Mapping the position of cities in corporate research and development through a gravity model-based bidimensional regression analysis

In her seminal work entitled ‘The Global City’, Saskia Sassen (1991) specified New York, London, Tokyo, Frankfurt and Paris as leading examples of global cities. Furthermore, she defined the most important characteristics of global cities (Sassen 2001: 4), one of which is that global cities are major sites of production of innovation. Since Sassen’s global city notion was first introduced, significant changes have occurred in the world economy, which can be characterised by, for example, the massive economic growth of developing countries, especially that of China, and rapid technological changes due to fast-growing industries such as nanotechnology, biotechnology and information technology (Nicolini and Nozza 2008; Dernis et al. 2015; Csomos and Toth 2016a). As a result of these developments, global cities have been continuously losing their privileged position as major sites of production of innovation, and new competitors have emerged in developing countries, even in the home countries of the global cities.

Modelling the shifting command and control function of cities through a gravity model based bidimensional regression analysis

Modelling the shifting command and control function of cities through a gravity model based bidimensional regression analysis

Gardony Map Drawing Analyzer: Software for quantitative analysis of sketch maps.

Sketch maps are effective tools for assessing spatial memory. However, despite their widespread use in cognitive science research, sketch map analysis techniques remain unstandardized and carry limitations. In the present article, we present the Gardony Map Drawing Analyzer (GMDA), an open-source software package for sketch map analysis. GMDA combines novel and established analysis techniques into a graphical user interface that permits rapid computational sketch map analysis. GMDA calculates GMDA-unique measures based on pairwise comparisons between landmarks, as well as bidimensional regression parameters (Friedman & Kohler, 2003), which together reflect sketch map quality at two levels: configural and individual landmark. The configural measures assess the overall landmark configuration and provide a whole-map analysis. Individual landmark measures, introduced in GMDA, assess individual landmark placement and indicate how individual landmarks contribute to the configural scores. Together, these measures provide a more complete psychometric picture of sketch map analysis, allowing for comparisons between sketch maps and between landmarks. The calculated measures reflect specific and cognitively relevant aspects of interlandmark spatial relationships, including distance and angular representation. GMDA supports complex environments (up to 48 landmarks) and two software modes that capture aspects of maps not addressed by existing techniques, such as landmark size and shape variation and interlandmark containment relationships. We describe the software and its operation and present a formal specification of calculation procedures for its unique measures. We then validate the software by demonstrating the capabilities and reliability of its measures using simulation and experimental data. The most recent version of GMDA is available at www.aarongardony.com/tools/map-drawing-analyzer.

Direct current brain stimulation enhances navigation efficiency in individuals with low spatial sense of direction.

The aim of this study was to evaluate the influence of right versus left temporal transcranial direct current stimulation (tDCS) on navigation efficiency and spatial memory in individuals with low versus high spatial skills. A mixed design administered low (0.5 mA) versus high (2.0 mA) anodal tDCS (within-participants) over the right or the left temporal lobe (between-participants), centered at electrode site T8 (right) or T7 (left). During stimulation, participants navigated virtual environments in search of specified landmarks, and data were logged in terms of current position and heading over time. Following stimulation, participants completed pointing and map-drawing spatial memory tests. Individual differences in sense of direction reliably and inversely predicted navigation advantages in the 2.0 versus 0.5 mA right hemisphere stimulation condition (R=0.45, P<0.01); in other words, individuals with lower sense of direction showed increased navigation efficiency in the 2.0 versus 0.5 mA condition. Spatial memory tests also showed the development of relatively comprehensive spatial memories: bidimensional regression indicated lower distortion in sketch maps drawn following 2.0 versus 0.5 mA right temporal lobe stimulation (F=8.7, P<0.05). Data provide the first demonstration that right temporal anodal tDCS may hold potential for enhancing navigation efficiency in otherwise poor navigators. Data support neuroimaging studies showing the engagement of right temporal brain regions in developing and applying spatial memories during complex navigation tasks, and uniquely suggest that continuing research may find value in optimizing stimulation parameters (intensity, focality) as a function of individual differences.

The changing economic spatial structure of Europe

Many theoretical and practical works aim at describing the spatial structure of Europe, where spatial relations have undergone continuous change. The article gives an overview of models describing the spatial structure of Europe. The models' diversity is highlighted, without any claim to the completeness of the list of models discussed. The authors describe the economic spatial structure of Europe through bidimensional regression analysis based on a gravity model. With the help of the gravity model, they generate a spatial image of the economic spatial structure of Europe. With the images, the appropriateness of the models based on different methodological backgrounds can be justified through comparison with the authors' results. The authors aim to contribute to understanding the European economic spatial structure through a new methodological approach, rather than to create and show a new model that overwrites existing ones.

A Note on the Adaptive Estimation of a Multiplicative Separable Regression Function

We investigate the estimation of a multiplicative separable regression function from a bidimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of convergence under the MISE over Besov balls.

The Application of Gravity Model in the Investigation of Spatial Structure

In this paper the authors wish to introduce an application of the gravity model through a concrete example. In their investigation the gravity model was transformed to analyse the impact of accessibility in a way, that not only the size of gravitational forces but their direction can also be measured. Displacements were illustrated by a bi- dimensional regression. The aim of this paper to give a new perspective to the investigation of spatial structure through a Hungarian example. This makes easier the transport planning and land development modeling. In our work accessibility analysis, gravity modeling, bi-dimensional regression calculations and GIS visualization were performed.

Modelling the spatial structure of Europe

How can spatial location affect the operation of society, population or economic conditions? What is the role of neighbourhood and distance in social phenomena? In what way can a social organisation limit spatial barriers? How would spatial structures be affected by the attraction and repulsion of territorial units? Does society only use or also design regions? These questions are explored in this study. This work analyses some important issues, concepts and analysis procedures of the territorial structure of society and social processes of spatiality. It does not contain a comprehensive theory of spatiality and regional science; it is primarily a practical empirical research. Many theoretical works aim at defining the spatial structure of Europe. This article provides an overview of models describing the spatial structure of Europe. The study describes the economic spatial structure of Europe using bi-dimensional regression analysis, based on the gravity model. The spatial structure of Europe is illustrated with the help of the gravity model and spatial auto-correlation. With these patterns, it is possible to justify the appropriateness of the models based on different methodological backgrounds by comparing them with the results of this paper. The subject of field theory concepts and methods that can aid regional analyses is examined, and attempts to offer a synthesised knowledge with a wide variety of examples and methods.

The spatial structures of Europe

Our study aims at describing the spatial structure of Europe with spatial moving average, potential model and the bidimensional regression analysis based on gravity model. Many theoretical and practical works aim at describing the spatial structure of Europe. Partly zones, axes and formations, partly polycentric models appear in the literature. We illustrate their variegation by listing, without any claim to completeness (since that could be the subject of another study), a part of them. Based on our examinations, the engraving of the structures that we described can be seen. The position of the core area of EU countries clearly justifies the banana shape and in relation to it, the catching up regions take shape in several areas.

Iterative Fragmentation of Cognitive Maps in a Visual Imagery Task

It remains unclear whether spontaneous eye movements during visual imagery reflect the mental generation of a visual image (i.e. the arrangement of the component parts of a mental representation). To address this specificity, we recorded eye movements in an imagery task and in a phonological fluency (non-imagery) task, both consisting in naming French towns from long-term memory. Only in the condition of visual imagery the spontaneous eye positions reflected the geographic position of the towns evoked by the subjects. This demonstrates that eye positions closely reflect the mapping of mental images. Advanced analysis of gaze positions using the bi-dimensional regression model confirmed the spatial correlation of gaze and towns’ locations in every single individual in the visual imagery task and in none of the individuals when no imagery accompanied memory retrieval. In addition, the evolution of the bi-dimensional regression’s coefficient of determination revealed, in each individual, a process of generating several iterative series of a limited number of towns mapped with the same spatial distortion, despite different individual order of towns’ evocation and different individual mappings. Such consistency across subjects revealed by gaze (the mind’s eye) gives empirical support to theories postulating that visual imagery, like visual sampling, is an iterative fragmented processing.

BiDimRegression: Bidimensional Regression Modeling UsingR

Tobler (1965) introduced bidimensional regression to the research field of geography in 1965 to provide a method for estimating mapping relations between two planes on the basis of regression modeling. The bidimensional regression method has been widely used within geographical research. However, the applicability in assessing the degree of similarity of two-dimensional patterns has not much explored in the area of psychological research, particularly in the domains of cognitive maps, face research and comparison of 2D-data patterns. Describing Tobler's method in detail, Friedman and Kohler (2003) made an attempt to bridge the gulf between geographical methodological knowledge and psychological research practice. Still, the method has not been incorporated into psychologists' standard methodical repertoire to date. The present paper aims to make bidimensional regression applicable also for researchers and users unfamiliar with its theoretical basis. The BiDimRegression function provides a manageable computing option for bidimensional regression models with affine and Euclidean transformation, which makes it easy to assess the similarity of any planar configuration of points. Typical applications are, for instance, assessments of the similarity of facial images defined by discrete features or of (cognitive) maps characterized by landmarks. BiDimRegression can be a valuable tool since it provides estimation, statistical inference, and goodness-of-fit measures for bidimensional regression.

Comparação de configurações cartográficas através da regressão bidimensional

A COMPARASION OF CARTOGRAPHIC CONFIGURATIONS THROUGH BIDIMENSIONAL REGRESSION - Information given in ancient maps give rise to interesting problems about methodology that are not always easy to solve. Bidimensional regression, which was developed in the 1970's by W. Tobler, is a methodology that allows a comparasion to be drawn between cartographic configurations of different periods of time and permits them to be grouped or compared with current maps or even to detect any plagiarism. The exemple we present is an 18th-century nautical chart of Lisbon area compared with a current map and we examine the main methodological problems.

지도사용의 인지적 효과 측정에 관한 연구

이 연구는 공간인지 이론을 기반으로 하여 최근에 급격히 발달하고 있는 길찾기 목적의 웹지도 효과를 측정하기 위한 기본 개념과 평가틀을 설정하고 정량적 분석방법을 제안하는 것을 목적으로 한다. 이를 위해 특정 지도사용상황에서 길찾기 과제를 수행한 후 지도사용으로 얼마나 효과적으로 공간인지가 이루어졌는지를 측정하는 '인지적 지도사용효과'의 개념과 정확성, 신속성, 자신감의 분석항목을 기반으로 하는 평가틀을 제안하였다. 제안한 평가틀을 실증적으로 검증하기 위해 실험조사를 실시하고, 실험 결과물인 인지지도를 2차원 회귀분석 방법을 적용하여 실험결과를 계량화하였다. 분석결과, 공간을 정확하게 인식하거나 빠르게 회상하는 데에는 지도표현방법보다 사용자의 특성과 반복적인 지도사용 등의 요소가 영향을 미치며, 2차원 지도와 3차원 지도를 동시에 참조하는 경우 공간인지에 대한 자신감이 낮은 것으로 나타났다. 이 연구결과는 효과적일 것이라고 예상되는 새로운 지도표현방법이 실제로 그렇지 않거나, 사용자마다 효과적이라고 판단하는 지도표현방법이 다른 이유에 대한 근거를 제공해 준다. The purpose of this study was to establish an analytical framework and quantitative methodologies to analyze 'the cognitive effects of web map use' and to empirically test it. This experimental design was established based on the literature about spatial cognition. Accuracy, reaction time, and confidence within each participant were compared to measure the cognitive effects of web map use for wayfinding. Geometric accuracy of the cognitive maps was estimated and calculated based on the bidimensional regression. The experimental results showed that characteristics of map users and repetition of map use rather than types of map representation did significantly affect accuracy and reaction time of spatial cognition by using web maps. And confidence appeared to be low when the participants referred to both 2D and 3D maps for wayfinding tasks on the web maps. Understanding spatial cognition of web map users, which was suggested in the study, will help cartographers make more effectively-communicated maps.