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A Fast Approximation Of The Earth-moversdistance Between Multidimensional histograms

机译：多维直方图之间地球移动距离的快速逼近

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摘要

We present an efficient algorithm for computing a sub-optimal Earth Movers' Distance (EMD) between multidimensional histograms called EMD-g_f, which is not limited to any type of measurement. Some algorithms that find a cross-bin distance between histograms have been proposed in the literature. Nevertheless, most of this research has been applied on ID-histograms or on nD-histograms but with limited types of measurements. The EMD is a cross-bin distance between nD-histograms with any ground distance. Experimental validation shows that it obtains good retrieval results although the main drawback of this method is its cubic computational cost, O(z~3), z being the total number of bins. The worst-case complexity of EMD-g-f is O(z~2), although the obtained average computational cost in the experiments is near O(m~2), where m represents the number of bins per dimension, which is clearly lower than the computational cost of the EMD algorithm. Moreover, the experiments using real data show similar retrieval results.
机译：我们提出了一种有效的算法，用于计算称为EMD-g_f的多维直方图之间的次优地球移动距离（EMD），该算法不限于任何类型的测量。在文献中已经提出了一些找到直方图之间的跨仓距离的算法。但是，大多数研究已应用于ID直方图或nD直方图，但测量类型有限。 EMD是具有任意地面距离的nD直方图之间的跨仓距离。实验验证表明，尽管该方法的主要缺点是三次计算成本O（z〜3），其中z为bin的总数，但仍能获得良好的检索结果。尽管在实验中获得的平均计算成本接近O（m〜2），但EMD-gf的最坏情况下的复杂度为O（z〜2），其中m表示每个维的箱数，这显然低于EMD算法的计算成本。此外，使用实际数据进行的实验显示出相似的检索结果。

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