An alternative map of the United States based on an n-dimensional model of geographic space

Geographic features have traditionally been visualized with fairly high amount of geometric detail, while relationships among these features in attribute space have been represented at a much coarser resolution. This limits our ability to understand complex high-dimensional relationships and structures existing in attribute space. In this paper, we present an alternative approach aimed at creating a high-resolution representation of geographic features with the help of a self-organizing map (SOM) consisting of a large number of neurons. In a proof-of-concept implementation, we spatialize 200,000+ U.S. Census block groups using a SOM consisting of 250,000 neurons. The geographic attributes considered in this study reflect a more holistic representation of geographic reality than in previous studies. The study includes 69 attributes regarding population statistics, land use/land cover, climate, geology, topography, and soils. This diversity of attributes is informed by our desire to build a comprehensive two-dimensional base map of n-dimensional geographic space. The paper discusses how standard GIS methods and neural network processing are combined towards the creation of an alternative map of the United States.

[1]  Jean-Claude Thill,et al.  Visual Exploration of Spatial Interaction Data with Self‐Organizing Maps , 2008 .

[2]  Stan Openshaw,et al.  Census users' handbook , 1995 .

[3]  Prostitution In Nevada,et al.  ANNALS of the Association of American Geographers , 1974 .

[4]  André Skupin.  A NOVEL MAP PROJECTION USING AN ARTIFICIAL NEURAL NETWORK , 2003 .

[5]  Michael P. Windham,et al.  Information and classification: Concepts, methods and applications , 1995 .

[6]  A. Skupin,et al.  Towards High‐Resolution Self‐Organizing Maps of Geographic Features , 2008 .

[7]  Alan M. MacEachren,et al.  Geographic visualization: designing manipulable maps for exploring temporally varying georeferenced statistics , 1998, Proceedings IEEE Symposium on Information Visualization (Cat. No.98TB100258).

[8]  Robert M. Edsall,et al.  Design and Usability of an Enhanced Geographic Information System for Exploration of Multivariate Health Statistics , 2003, The Professional Geographer.

[9]  Heidrun Schumann,et al.  Scalable Pixel-based Visual Interfaces: Challenges and Solutions , 2006, Tenth International Conference on Information Visualisation (IV'06).

[10]  Daniel A. Keim,et al.  Space‐in‐Time and Time‐in‐Space Self‐Organizing Maps for Exploring Spatiotemporal Patterns , 2010, Comput. Graph. Forum.

[11]  W. Tobler.  A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[12]  Mark Gahegan,et al.  Multivariate Analysis and Geovisualization with an Integrated Geographic Knowledge Discovery Approach , 2005, Cartography and geographic information science.

[13]  André Skupin,et al.  Visualizing Human Movement in Attribute Space , 2008 .

[14]  Mary J. McDerby,et al.  Geographic visualization : concepts, tools and applications , 2008 .

[15]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[16]  D. Dorling.  Area Cartograms: Their Use and Creation , 2011 .

[17]  Jorma Laaksonen,et al.  SOM_PAK: The Self-Organizing Map Program Package , 1996 .

[18]  Sergio J. Rey,et al.  Effects of Irregular Topology in Spherical Self-Organizing Maps , 2011 .

[19]  H. Ritter.  Self-Organizing Maps on non-euclidean Spaces , 1999 .

[20]  Masahiro Takatsuka,et al.  Spherical self-organizing map using efficient indexed geodesic data structure , 2006, Neural Networks.

[21]  W. Koppen.  Klassifikation der klimate nach temperatur, niederschlag, und jahreslauf , 1918 .

[22]  André Skupin.  Where do you want to go today [in attribute space]? , 2007 .

[23]  André Skupin,et al.  Visualizing Demographic Trajectories with Self-Organizing Maps , 2005, GeoInformatica.

[24]  Diansheng Guo,et al.  Regionalization with dynamically constrained agglomerative clustering and partitioning (REDCAP) , 2008, Int. J. Geogr. Inf. Sci..

[25]  W. Zelinsky,et al.  NORTH AMERICA'S VERNACULAR REGIONS , 1980 .

[26]  Jarkko Venna,et al.  Coloring that Reveals Cluster Structures in Multivariate Data , 2000 .

[27]  Terry G. Jordan,et al.  Perceptual Regions in Texas , 1978 .

[28]  Menno-Jan Kraak,et al.  An Integrated Exploratory Geovisualization Environment Based on Self‐Organizing Map , 2008 .

[29]  André Skupin,et al.  The world of geography: Visualizing a knowledge domain with cartographic means , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[30]  A. Skupin,et al.  Self-organising maps : applications in geographic information science , 2008 .

[31]  Masahiro Takatsuka,et al.  Geodesic self-organizing map , 2005, IS&T/SPIE Electronic Imaging.

[32]  Juan C. Duque,et al.  Supervised Regionalization Methods: A Survey , 2007 .

[33]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

[34]  C. W. Thornthwaite.  An Approach Toward a Rational Classification of Climate , 1948 .

[35]  W. Tobler.  Thirty Five Years of Computer Cartograms , 2004 .

[36]  X. Li,et al.  On the topology distortion in self-organizing feature maps , 1993, Biological Cybernetics.

[37]  Pragya Agarwal,et al.  Introduction: What is a Self‐Organizing Map? , 2008 .

[38]  M. Goodchild.  The Validity and Usefulness of Laws in Geographic Information Science and Geography , 2004 .

[39]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[40]  H. Miller.  Societies and cities in the age of instant access , 2007 .