I have a series of 2D maps with values ranging 0.0 to 1.0 spread all over. The algorithm that produces them is an application of the fractional Brownian motion. Each map measures 101x101pixels or cells.
The algorithm producing these maps uses a discretized Inverse Fast Fourier Transform (FFT) in the spectral domain. The maps have a varying mean (0.0 to 1.0) but share a fixed variance which is σ2 = 1.
My question: it is said (check the attached link) that applying Moran's I to determine the clustering of a geographic dataset is sensitive to the dataset distribution, especially if the distribution is skewed. Since my algorithm produces maps which distribution is not consistent across all maps, what could be a robust algorithm for determining the clustering of my maps?
The aim is to find a method in which no influence is played by the shape of the distribution on the p-value of the clustering coefficient.
http://gis.stackexchange.com/questions/24509/robust-alternatives-to-morans-i
Since your data is skewed, I therefore suggest head/tail breaks for both clustering and visualization:
Jiang B. (2013), Head/tail breaks: A new classification scheme for data with a heavy-tailed distribution, The Professional Geographer, 65 (3), 482 – 494.
Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77.
https://www.researchgate.net/publication/270634544_Headtail_Breaks_for_Visualization_of_City_Structure_and_Dynamics?ev=prf_pub
https://www.researchgate.net/publication/230839837_HeadTail_Breaks_A_New_Classification_Scheme_for_Data_with_A_Heavy-Tailed_Distribution?ev=prf_pub
Article Head/tail Breaks for Visualization of City Structure and Dynamics
Article Head/tail Breaks: A New Classification Scheme for Data with ...
Well, I must have let you deliberately make the assumption that my distribution is skewed. My distribution is sometimes skewed, but not always. Since the algorithm generating my maps is not entirely deterministic and produces a fractal image, the shape of my distribution keeps changing.
"My distribution is sometimes skewed, but not always...."
This is a nice property, which means that ht-index can capture the change or dynamics of the distribution; see the following figure, in which the shape of the trees is changing, implying that the distribution of all their branches is changing.
https://www.researchgate.net/publication/236627484_Ht-Index_for_Quantifying_the_Fractal_or_Scaling_Structure_of_Geographic_Features?ev=prf_pub
Article Ht-Index for Quantifying the Fractal or Scaling Structure of...
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