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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 15:45, 27 October 2020
, 15:45, 27 October 2020→The Elbow Method
An attempt at a paragraph justifying the 'heuristic' method:
:Our heuristic method provides an objective technique for picking a city-year layer, which identifies and maps its clusters. It uses two measures. First, we are interested in clusters rather than lines or points, so we measure the percentage of locations in clusters. Second, we want to view each city-year through the same lens. As layer indices are not comparably across city-years, we use the HCA's 'fraction complete' to measure a layer's lens.
:As an HCA progresses towards completion, it takes locations out of clusters at an increasing rate and then decreasing rate. Accordingly, a city-year plot, with the fraction complete on the x-axis and the percentage of locations in clusters on the y-axis, gives an S-curve. The inflection point of this curve marks a conceptual transition between refining clusters and dismantling them.
'''Note:''' For each layer of the HCA from i=1 to i=I, we define the HCA's fraction complete as (i-1)/(I-1). The HCA's fraction complete is then zero for the first layer when all locations are in a single hull, and one for the last layer when it has decomposed every cluster into separate locations.
