Wasserstein metric-based Boltzmann entropy of a landscape mosaic: a clarification, correction, and evaluation of thermodynamic consistency

2021 ◽  
Author(s):  
Peichao Gao ◽  
Hong Zhang ◽  
Zhiwei Wu
Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 381 ◽  
Author(s):  
Hong Zhang ◽  
Zhiwei Wu ◽  
Tian Lan ◽  
Yanyu Chen ◽  
Peichao Gao

Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human–computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.


2000 ◽  
Vol 6 (1) ◽  
pp. 251-256 ◽  
Author(s):  
Olav Hjeljord ◽  
Per Wegge ◽  
Jørund Rolstad ◽  
Marina Ivanova ◽  
Alexander B. Beshkarev
Keyword(s):  

2013 ◽  
Vol 706-708 ◽  
pp. 613-617
Author(s):  
Fu Cheng Liu ◽  
Zhao Hui Liu ◽  
Wen Liu ◽  
Dong Sheng Liang ◽  
Kai Cui ◽  
...  

A navigation star catalog (NSC) selection algorithm via support vector machine (SVM) is proposed in this paper. The sphere spiral method is utilized to generate the sampling boresight directions by virtue of obtaining the uniform sampling data. Then the theory of regression analysis methods is adopted to extract the NSC, and an evenly distributed and small capacity NSC is obtained. Two criterions, namely a global criterion and a local criterion, are defined as the uniformity criteria to test the performance of the NSC generated. Simulations show that, compared with MFM, magnitude weighted method (MWM) and self-organizing algorithm(S-OA), the Boltzmann entropy (B.e) of SVM selection algorithm (SVM-SA) is the minimum, to 0.00207. Simultaneously, under the conditions such as the same field of view (FOV) and elimination of the hole, both the number of guide stars (NGS) and standard deviation (std) of SVM-SA is the least, respectively 7668 and 2.17. Consequently, the SVM-SA is optimal in terms of the NGS and the uniform distribution, and has also a strong adaptability.


Entropy ◽  
2017 ◽  
Vol 19 (5) ◽  
pp. 212 ◽  
Author(s):  
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Keyword(s):  

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