scholarly journals A generalization for the expected value of the earth mover’s distance

2021 ◽  
Vol 12 (2) ◽  
pp. 139-166
Author(s):  
William Q. Erickson
Keyword(s):  
Expected Value ◽  
Earth Mover’S Distance ◽  
Earth Mover's Distance ◽  
The Earth

The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions

2020 ◽  
Author(s):  
Cameron Hargreaves ◽  
Matthew Dyer ◽  
Michael Gaultois ◽  
Vitaliy Kurlin ◽  
Matthew J Rosseinsky
Keyword(s):  
Euclidean Distance ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Inorganic Crystal Structure Database ◽  
Earth Mover’S Distance ◽  
Chemical Similarity ◽  
Earth Mover's Distance ◽  
Neighbor Search ◽  
The Earth ◽  
Binary Compounds

It is a core problem in any field to reliably tell how close two objects are to being the same, and once this relation has been established we can use this information to precisely quantify potential relationships, both analytically and with machine learning (ML). For inorganic solids, the chemical composition is a fundamental descriptor, which can be represented by assigning the ratio of each element in the material to a vector. These vectors are a convenient mathematical data structure for measuring similarity, but unfortunately, the standard metric (the Euclidean distance) gives little to no variance in the resultant distances between chemically dissimilar compositions. We present the Earth Mover’s Distance (EMD) for inorganic compositions, a well-defined metric which enables the measure of chemical similarity in an explainable fashion. We compute the EMD between two compositions from the ratio of each of the elements and the absolute distance between the elements on the modified Pettifor scale. This simple metric shows clear strength at distinguishing compounds and is efficient to compute in practice. The resultant distances have greater alignment with chemical understanding than the Euclidean distance, which is demonstrated on the binary compositions of the Inorganic Crystal Structure Database (ICSD). The EMD is a reliable numeric measure of chemical similarity that can be incorporated into automated workflows for a range of ML techniques. We have found that with no supervision the use of this metric gives a distinct partitioning of binary compounds into clear trends and families of chemical property, with future applications for nearest neighbor search queries in chemical database retrieval systems and supervised ML techniques.

Comparing Fuzzy, Probabilistic, and Possibilistic Partitions Using the Earth Mover’s Distance

2013 ◽  
Vol 21 (4) ◽  
pp. 766-775 ◽  
Author(s):  
Derek T. Anderson ◽  
Alina Zare ◽  
Stanton Price
Keyword(s):  
Earth Mover’S Distance ◽  
Earth Mover's Distance ◽  
The Earth

scholarly journals Expected value of the one-dimensional earth mover’s distance

2020 ◽  
Vol 11 (1) ◽  
pp. 53-78
Author(s):  
Rebecca Bourn ◽  
Jeb F. Willenbring
Keyword(s):  
Expected Value ◽  
Earth Mover’S Distance ◽  
One Dimensional ◽  
Earth Mover's Distance ◽  
The One

scholarly journals On Markov Earth Mover's Distance

2014 ◽  
Vol 14 (04) ◽  
pp. 1450016 ◽  
Author(s):  
Jie Wei
Keyword(s):  
Goodness Of Fit ◽  
Empirical Studies ◽  
Earth Mover’S Distance ◽  
Long Distance ◽  
Chi Square ◽  
Earth Mover's Distance ◽  
The Earth ◽  
Order Of Magnitude ◽  
Kolmogorov Smirnov ◽  
System Nodes

In statistics, pattern recognition and signal processing, it is of utmost importance to have an effective and efficient distance to measure the similarity between two distributions and sequences. In statistics this is referred to as goodness-of-fit problem. Two leading goodness of fit methods are chi-square and Kolmogorov–Smirnov distances. The strictly localized nature of these two measures hinders their practical utilities in patterns and signals where the sample size is usually small. In view of this problem Rubner and colleagues developed the earth mover's distance (EMD) to allow for cross-bin moves in evaluating the distance between two patterns, which find a broad spectrum of applications. EMD-L1 was later proposed to reduce the time complexity of EMD from super-cubic by one order of magnitude by exploiting the special L1 metric. EMD-hat was developed to turn the global EMD to a localized one by discarding long-distance earth movements. In this work, we introduce a Markov EMD (MEMD) by treating the source and destination nodes absolutely symmetrically. In MEMD, like hat-EMD, the earth is only moved locally as dictated by the degree d of neighborhood system. Nodes that cannot be matched locally is handled by dummy source and destination nodes. By use of this localized network structure, a greedy algorithm that is linear to the degree d and number of nodes is then developed to evaluate the MEMD. Empirical studies on the use of MEMD on deterministic and statistical synthetic sequences and SIFT-based image retrieval suggested encouraging performances.

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