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  • 1.
    Jiang, Bin
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Urban and regional planning/GIS-institute.
    Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution2013In: Professional Geographer, ISSN 0033-0124, E-ISSN 1467-9272, Vol. 65, no 3, p. 482-494Article in journal (Refereed)
    Abstract [en]

    This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large values in the head and a majority of small values in the tail, commonly characterized by a power law, a lognormal or an exponential function. For example, a country's population is often distributed in such a heavy-tailed manner, with a minority of people (e.g., 20 percent) in the countryside and the vast majority (e.g., 80 percent) in urban areas. This heavy-tailed distribution is also called scaling, hierarchy or scaling hierarchy. This new classification scheme partitions all of the data values around the mean into two parts and continues the process iteratively for the values (above the mean) in the head until the head part values are no longer heavy-tailed distributed. Thus, the number of classes and the class intervals are both naturally determined. We therefore claim that the new classification scheme is more natural than the natural breaks in finding the groupings or hierarchy for data with a heavy-tailed distribution. We demonstrate the advantages of the head/tail breaks method over Jenks' natural breaks in capturing the underlying hierarchy of the data. Keywords: data classification, head/tail division rule, natural breaks, scaling, and hierarchy

  • 2.
    Jiang, Bin
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Land management, GIS.
    Miao, Yufan
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management.
    The Evolution of Natural Cities from the Perspective of Location-Based Social Media2015In: Professional Geographer, ISSN 0033-0124, E-ISSN 1467-9272, Vol. 67, no 2, p. 295-306Article in journal (Refereed)
    Abstract [en]

    This article examines the former location-based social medium Brightkite, over its three-year life span, based on the concept of natural cities. The term natural cities refers to spatially clustered geographic events, such as the agglomerated patches aggregated from individual social media users' locations. We applied the head/tail division rule to derive natural cities, based on the fact that there are far more low-density areas than high-density areas on the Earth's surface. More specifically, we generated a triangulated irregular network, made up of individual unique user locations, and then categorized small triangles (smaller than an average) as natural cities for the United States (mainland) on a monthly basis. The concept of natural cities provides a powerful means to develop new insights into the evolution of real cities, because there are virtually no data available to track the history of cities across their entire life spans and at very fine spatial and temporal scales. Therefore, natural cities can act as a good proxy of real cities, in the sense of understanding underlying interactions, at a global level, rather than of predicting cities, at an individual level. Apart from the data produced and the contributed methods, we established new insights into the structure and dynamics of natural cities; for example, the idea that natural cities evolve in nonlinear manners at both spatial and temporal dimensions.

  • 3.
    Jiang, Bin
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Urban and regional planning/GIS-institute.
    Sui, Daniel
    A new kind of beauty out of the underlying scaling of geographic space2014In: Professional Geographer, ISSN 0033-0124, E-ISSN 1467-9272, Vol. 66, no 4, p. 676-686Article in journal (Refereed)
    Abstract [en]

    Geographic space demonstrates scaling or hierarchy, implying that there are far more small things than large ones. The scaling pattern of geographic space, if visualized properly (i.e., based on the head/tail breaks classification), can evoke a sense of beauty. This is our central argument. This beauty is a new type of aesthetic at a deeper structural level and differs in essence from an intuitive sense of harmony, perceived in terms of color, shape, texture, and ratio. This new kind of beauty was initially defined and discovered by Christopher Alexander, and promoted in his master work The Nature of Order. To paraphrase Mandelbrot, this is beauty for the sake of science rather than for art's sake or for the sake of commerce. Throughout the article, we attempt to argue and illustrate that the scaling of geographic space possesses this new kind of beauty, which has a positive impact on human well-being. The article further draws on the previous work of Nikos Salingaros and Richard Taylor on the beauty in architecture and arts to support our argument.

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