There is a sea change in geospatial analysis, or GIScience in general, towards better understanding geographic forms and processes, or urban structure and dynamics in particular, based on geographic information. This change is mainly attributed to Web 2.0 technologies and in particular the rise of social media of various kinds (Sui and Goodchild 2011, Jiang and Miao 2014), and subsequently large amounts of social media data or volunteered geographic information (Goodchild 2007) have been collected for studying human activities in space and over time. This change has been transforming social sciences, initially developed from humanities and based on small data that are primarily estimated, sampled, and aggregated, into data-intensive computational social science (Lazer et al. 2009). For the emerging BIG data, which are accurately measured for all individual people or locations, the right-skewed or heavy-tailed distributions such as power laws, lognormal and exponential distributions are the norm (Adamic 2003, Newman 2005, Zipf 1949, Jiang 2013, Jiang and Yin 2014). The heavy-tailed distributions are also called scale free, literally meaning the lack of an average scale (or mean) for characterizing the size of things (Barabási and Réka 1999), and therefore set a clear contrast to Gauss distribution, with which the size of things can be characterized by a well-defined mean. The scale free property, also referred to as scale invariance, fractal, scaling, hierarchy, and nonlinearity, has profound implications for geospatial analysis for better understanding geographic forms and processes (Jiang 2014a, and Jiang 2014b).

This one-day tutorial aims to provide hands-on and thoughtful guidance on scaling or fractal analysis of geographic information based on maximum likelihood estimation (Clauset, Shalizi, and Newman 2009), the most robust statistical estimation on power law detection. The maximum likelihood method differs fundamentally from the conventional least squares method, which was widely used but found to be less reliable. This tutorial, mixed with lectures and hands-on exercises, attempts to address the following questions (e.g.):

What are differences between the heavy-tailed distributions?
How to detect effectively a power law from those similar?
What are differences between right-skewed and no-skewed (or Gauss-like) distributions?
How to effectively visualize data with a heavy-tailed distribution?
What are Zipf’s law, Pareto distributions, and power laws, and how are they related to each other?

Apart from these practical questions above, there are more fundamental issues to address (e.g.),

What are underlying ways of thinking for scaling analysis?
How does scaling analysis differ radically from spatial statistics?
What are implications of scaling patterns to understanding geographic forms and processes?
How is the scaling analysis related to fractal analysis?
Why is the scaling analysis essential for BIG data?
What are statistical differences between small data and BIG data?

If any of these questions is of interest or of your concern, you are very welcome to join us for the one-day event in conjunction with GIScience 2014 (Vienna - September, 23-26, 2014, http://www.giscience.org/). The tutorial is primarily for young researchers specializing in geography or GIScience in particular, but senior researchers are also welcome if seats are available. Interested participants must have an intermediate through advanced understanding of geography and cartography, and be familiar with fundamental concepts and techniques of geographic information systems. The participants must have their own laptops with basic tools such as Excel, Matlab, and ArcGIS 10.0 installed, and we will provide sample data for the hands-on exercises. To participate, you must register via this website: http://www.giscience.org/registration.html

References:
Adamic L. A. (2002), Zipf, Power-laws, and Pareto - a ranking tutorial, http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html
Barabási A.-L. and Réka A. (1999), Emergence of scaling in random networks, Science, 286(5439),509-512.
Clauset A., Shalizi C. R., and Newman M. E. J. (2009), Power-law distributions in empirical data, SIAM Review, 51(4), 661-703.
Goodchild M. F. (2007), Citizens as sensors: The world of volunteered geography, GeoJournal, 69(4), 211-221.
Jiang B. (2014a), Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity, GeoJournal, xx(x), xx-xx, Preprint: http://arxiv.org/ftp/arxiv/papers/1401/1401.5889.pdf
Jiang B. (2014b), The fractal nature of maps and mapping, International Journal of Geographical Information Science, xx(x), xx-xx, Preprint: http://arxiv.org/ftp/arxiv/papers/1406/1406.5410.pdf
Jiang B. and Miao Y. (2014), The evolution of natural cities from the perspective of location-based social media, The Professional Geographer, xx(x), xx-xx, Preprint: http://arxiv.org/ftp/arxiv/papers/1401/1401.6756.pdf
Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104(3), 530–541, DOI: 10.1080/00045608.2013.834239, Preprint: http://arxiv.org/ftp/arxiv/papers/1305/1305.0883.pdf
Jiang B. (2013), Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution, The Professional Geographer, 65 (3), 482 – 494.
Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabási, A.-L., Brewer, D., Christakis, N., Contractor, N., Fowler, J., Gutmann, M., Jebara, T., King, G., Macy, M., Roy, D., and Van Alstyne, M. (2009), Computation social science, Science, 323(5915), 721-724.
Newman M. E. J. (2005), Power laws, Pareto distributions and Zipf's law, Contemporary Physics, 46(5), 323-351.
Sui D. and Goodchild M. (2011), The convergence of GIS and social media: challenges for GIScience, International Journal of Geographical Information Science, 25(11), 1737–1748.
Zipf G. K. (1949), Human Behaviour and the Principles of Least Effort, Addison Wesley: Cambridge, MA.

Instructor:
Bin Jiang, Professor in computational geography and geoinformatics
Department of Technology and Built Environment, Division of Geomatics,
University of Gävle, SE-801 76 Gävle, Sweden
Email: bin.jiang@hig.se, Web: http://fromto.hig.se/~bjg/

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