K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed to overcome this problem and has been shown to have better accuracy and computational efficiency than k-means. In many clustering problems though -such as when classifying georeferenced data for mapping applications-standardization of clustering methodology, specifically, the ability to arrive at the same cluster assignment for every run of the method i.e.replicability of the methodology, may be of greater significance than any perceived measure of accuracy, especially when the solution is known to be non-unique, as in the case of k-means clustering. Here we propose a simple initial seed selection algorithm for k-means clustering along one attribute that draws initial cluster boundaries along the "deepest valleys" or greatest gaps in dataset. Thus, it incorporates a measure to maximize distance between consecutive cluster centers which augments the conventional k-means optimization for minimum distance between cluster center and cluster members. Unlike existing initialization methods, no additional parameters or degrees of freedom are introduced to the clustering algorithm. This improves the replicability of cluster assignments by as much as 100% over k-means and k-means++, virtually reducing the variance over different runs to zero, without introducing any additional parameters to the clustering process. Further, the proposed method is more computationally efficient than k-means++ and in some cases, more accurate.3

Abstract:Drawing from an original dataset of urban metropolitan carbon footprints, in this paper we explore the correlations between national level climate change commitments and sub-national level inventories. We ask: Does ambitiousness in commitment have an impact on performance in footprint reduction? Does having long-term commitments affect performance in footprint reduction? Do binding national level commitments (such as those under the Kyoto Protocol) affect performance at the city level in terms of footprint reduction? To provide answers, we synthesize data from the largest repository of voluntary subnational commitments and actions towards footprint reduction and greenhouse gas inventories from around the world, the Carbonn platform. More than 500 cities report at least one action, commitment or inventory to this database. We find, using a subset of this database, perhaps counter intuitively that cities with more ambitious commitments do not necessarily have steeper reductions in emissions. Our data also suggests that having long-term self-reported goals did not make the cities perform better in terms of footprint reduction. This appeared to be true for both government and community commitments reported. Lastly, and positively, our data did reveal a statistically significant effect for cities belonging to countries that had committed to the Kyoto Protocol, suggesting the necessity of binding national (and supranational) climate targets.

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Highlights• A scaling indicator for cities is defined and calculated for 58 US cities using census data • The scaling indicator is correlated to greenhouse emissions and gasoline sales • A spatial planning tool is proposed to incorporate analysis of scaling into urban development planning 2 Abstract Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step towards quantifying the resilience borne of a complex systems' hierarchical structural composition. The scaling indicator is calculated using large census datasets and is analogous to fractal dimension in spatial analysis. Lack of numerical rigor and the resulting variation in scaling indicators -inherent in the use of box counting mechanism for fractal dimension calculation for cities-has been one of the hindrances in the adoption of fractal dimension as an urban indicator of note. The intra-urban indicator of scaling in population density distribution developed here is calculated for 58 US cities using a methodology that produces replicable results, employing large census-block wise population datasets from the 2010 US Census 2010 and the 2007 US Economic Census. We show that rising disparity -as measured by the proposed indicator of population density distribution in census blocks in metropolitan statistical areas (using US Census 2010 data) adversely affects energy consumption efficiency and carbon emissions in cities and leads to a higher urban carbon footprint. We then define a planning plane as a visual and analytic tool for incorporation of scaling indicator analysis into policy and decision-making. Keywordsurban sustainable development; complex systems; scaling indicator; fractal dimension; energy consumption; sustainable development indicator; 3