About: Earth mover's distance

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In statistics, the earth mover's distance (EMD) is a measure of the distance between two probability distributions over a region D. In mathematics, this is known as the Wasserstein metric. Informally, if the distributions are interpreted as two different ways of piling up a certain amount of earth (dirt) over the region D, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be the amount of dirt moved times the distance by which it is moved.

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  • In statistics, the earth mover's distance (EMD) is a measure of the distance between two probability distributions over a region D. In mathematics, this is known as the Wasserstein metric. Informally, if the distributions are interpreted as two different ways of piling up a certain amount of earth (dirt) over the region D, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be the amount of dirt moved times the distance by which it is moved. The above definition is valid only if the two distributions have the same integral (informally, if the two piles have the same amount of dirt), as in normalized histograms or probability density functions. In that case, the EMD is equivalent to the 1st Mallows distance or 1st Wasserstein distance between the two distributions. (en)
  • 動土者距離（earth mover's distance）或動土距離是量度兩個概率分佈之間的距離。若 （也類似），而是域的度量，則動土距離是最低的動土成本： 當中，為移動的數量，為所選擇的兩個點之間的距離。整個移動過移可以想象為將泥土移動至洞。 (zh)
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  • 動土者距離（earth mover's distance）或動土距離是量度兩個概率分佈之間的距離。若 （也類似），而是域的度量，則動土距離是最低的動土成本： 當中，為移動的數量，為所選擇的兩個點之間的距離。整個移動過移可以想象為將泥土移動至洞。 (zh)
  • In statistics, the earth mover's distance (EMD) is a measure of the distance between two probability distributions over a region D. In mathematics, this is known as the Wasserstein metric. Informally, if the distributions are interpreted as two different ways of piling up a certain amount of earth (dirt) over the region D, the EMD is the minimum cost of turning one pile into the other; where the cost is assumed to be the amount of dirt moved times the distance by which it is moved. (en)
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  • Earth mover's distance (en)
  • 動土距離 (zh)
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