CATMOGS (Concepts and Techniques in Modern Geography) are edited by the Quantitative Methods Study Group of the Institute of British Geographers. These guides are both for the teacher, yet cheap enough for students as the basis of classwork. Each CATMOG is written by an author currently working with the technique or concept he describes. For details of membership of the Study Group, write to the Institute of British Geographers. 1 Collins, Introduction to Markov chain analysis £5 2 Taylor, Distance decay in spatial interactions £5 3 Clark, Understanding canonical correlation analysis £5 4 Openshaw, Some theoretical and applied aspects of spatial interaction shopping models (photocopy only) £5 5 Unwin, An in geography £5 7 Goddard & Kirby, An introduction to trend surface analysis £5 6 Johnston, Classification introduction to factor analysis £5 8 Daultrey, Principal components analysis £5.50 9 Davidson, Causal inferences from dichotomous variables £5 10 Wrigley, Introduction to the use of logit models in geography £5 11 Hay, Linear programming: elementary geographical applications of the transportation problem £5 12 Thomas, An introduction to quadrat analysis (2nd edition) £5 13 Thrift, An introduction to time geography £5 14 Tinkler, An introduction to graph theoretical methods in geography £5.50 15 Ferguson, Linear regression in geography £5 16 Wrigley, Probability surface mapping. An introduction with examples and FORTRAN programs. (Fiche only) £5 17 Dixon & Leach, Sampling methods for geographical research £5 18 Dixon & Leach, Questionnaires and interviews in geographical research £5.50 19 Gardiner & Gardiner, Analysis of frequency distribution (Fiche only) £5 20 Silk, Analysis of covarience and comparison of regression lines £5 21 Todd, An introduction to the use of simultaneous-equation regression analysis in geography £5 22 Pong-wai Lai, Transfer function modelling: relationship between time series variables £5 23 Richards, Stochastic processes in one dimensional series: an introduction £5.50 24 Killen, Linear programming: the Simplex method with geographical applications £5 25 Gaile & Burt, Directional statistics £5 26 Rich, Potential models in human geography £5 27 Pringle, Causal modelling: the Simon-Blalock approach £5 28 Bennett, Statistical forecasting £5 29 Dewdney, The British census £5.50 30 Silk, The analysis of variance £5.50 31 Thomas, Information statistics in geography £5 32 Kellerman, Centrographic measures in geography £5 33 Haynes, An introduction to dimensional analysis for geographers £5 34 Beaumont & Gatrell, An introduction to Q-analysis £5.50 35 The agricultural census-United Kingdom and United States £5 36 Aplin, Order-neighbour analysis £5 …

Area cartograms: Their use and creation

We consider the problem of constructing facilities such as hospitals, airports, or malls in a country with a nonuniform population density, such that the average distance from a person's home to the nearest facility is minimized. We review some previous approximate treatments of this problem that indicate that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. We confirm this result numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density-dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.

https://arxiv.org/pdf/cond-mat/0603278.pdf

Optimal design of spatial distribution networks

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible to gain insight into patterns and trends in the world around us and have been very popular visualizations for geo-referenced data for over a century. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms. A particular focus is the study of the major cartogram dimensions: statistical accuracy, geographical accuracy, and topological accuracy. We review the history of cartograms, describe the algorithms for generating them, and consider task taxonomies. We also review quantitative and qualitative evaluations, and we use these to arrive at design guidelines and research challenges.

/pdf/the-state-of-the-art-in-cartograms-2h48oiqoup.pdf

The state of the art in cartograms

We present a new constraint-based continuous area cartogram construction method that is unique in its ability to preserve essential cues for recognition of region shapes. It automatically achieves desired region areas while maintaining correct map topology. The algorithm is compared with a number of existing methods, and results are shown to be superior in both accuracy and preservation of shape recognition cues. Through hierarchical resolution, we first perform gross adjustments upon a coarsely resampled map and later refine the map at progressively higher levels of detail.

A Constraint-Based Approach to Constructing Continuous Cartograms

The State of the Art in Cartograms

A third installment in a series of articles devoted to the compilation of transformed images focuses on computer-assisted numerical image transformations. Particular attention is devoted to algorithms developed by Tobler, Tikunov, and Pikin; Tikunov; White and Griffin; Kadmon and Shlomi; Petrov, Serbenyuk, and Tikunov; and Dougenik et al. Advantages and shortcomings of each of these methods are compared and a new algorithm is unveiled that is designed to eliminate some of the extant deficiencies in image transformation.

Numerical methods in the compilation of transformed images

A second paper from a monograph devoted to the compilation and uses of transformed cartographic images focuses on analog/manual methods of areal image transformation—of particular relevance in areas and situations in which access to large volumes of computer memory is problematic. As such, it addresses problems relating to the transformation of a second type of transformed image—in which the areas of cartographic features of interest (rather than their linear dimensions) are scaled according to a nonspatial metric.

Analog methods in the compilation of areal transformed images

This paper is devoted to the problem of compiling and using transformed images in geographic research. It discusses algorithms employed in their compilation, presents a new algorithm for this purpose, and demonstrates several applications of transformed images in geographical research (by contrasting transformed images compiled according to traditional and new methods).

The transformed image in geographical analysis

A final installment in a series of papers on transformed cartographic images in geogaphy (see Mapping Sciences and Remote Sensing, 1993, No. 4, pp. 306-319 and 1994, No. 1, pp. 33-85) focuses on their applications in more effectively depicting a variety of spatially distributed phenomena. Most applications are demonstrated using images compiled via a method developed by the authors. Specific transformed images used to illustrate the range of existing applications include those scaled according to population size, GNP, various illness rates, density of ocean vessels, oil pollution in the ocean, and fisheries and offshore oil and gas deposits.

Sabir M. Guseyn-Zade

Papers

Numerical methods in the compilation of transformed images

Analog methods in the compilation of areal transformed images

The transformed image in geographical analysis

Applications of transformed images in geographic analysis