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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Earth mover's distance ： ウィキペディア英語版 Earth mover's distance In computer science, 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 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 amount of dirt moved times the distance by which it is moved.〔(Formal definition )〕 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. ==Extensions== Some applications may require the comparison of distributions with different total masses. One approach is to allow for a ''partial match'', where dirt from the most massive distribution is rearranged to make the least massive, and any leftover "dirt" is discarded at no cost. Under this approach, the EMD is no longer a true distance between distributions. Another approach is to allow for mass to be created or destroyed, on a global and/or local level, as an alternative to transportation, but with a cost penalty. In that case one must specify a real parameter σ, the ratio between the cost of creating or destroying one unit of "dirt", and the cost of transporting it by a unit distance. This is equivalent to minimizing the sum of the earth moving cost plus σ times the L1 distance between the rearranged pile and the second distribution. Notationally, if $\backslash pi:P\backslash to\; Q$ is a partial function which is a bijection on subsets $P\text{'}\backslash subset\; P$ and $Q\text{'}\backslash subset\; Q$, then one is interested in the distance function :$|P-Q|\_\backslash pi\; =\; |P\backslash setminus\; P\text{'}|\; +\; |Q\backslash setminus\; Q\text{'}|$ where $P\backslash setminus\; P\text{'}$ denotes set minus. Here, $P\text{'}$ would be the portion of the earth that was moved; thus $P\backslash setminus\; P\text{'}$ would be the portion not moved, and $|P\backslash setminus\; P\text{'}|$ the size of the pile not moved. By symmetry, one contemplates $Q\text{'}\backslash subset\; Q$ as the pile at the destination that 'got there' from ''P'', as compared to the total ''Q'' that we ''want to have there''. Formally, this distance indicates how much an injective correspondence differs from an isomorphism. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Earth mover's distance」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.