The Earth Mover's distance is the Mallows distance: some insights from statistics

By Elizaveta Levina, Peter J. Bickel. 2001

645 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “It is interesting that if we use other similarity measurements such as Mallows Distance (earth movers distance) (Werman et al., 1986; Levina & Bickel, 2001), other than the sine function utilized in Definition 2, more extensive metrics for two-sample test can be naturally obtained.”
Distributional Reinforcement Learning with Quantile Regression (2017, background): “The p -Wasserstein metric W p , for p ∈ [1 , ∞ ] , also known as the Mallows metric (Bickel and Freedman 1981) or the Earth Mover’s Distance (EMD) when p = 1 (Levina and Bickel 2001), is an integral probability metric between distributions.”
Sinkhorn Distances: Lightspeed Computation of Optimal Transport (2013, background): “stograms and bags-of-features in most data analysis tasks and the good performance of optimal transportation distances in practice has generated ample interest, both from a theoretical point of view (Levina and Bickel, 2001; Indyk and Thaper, 2003; Naor and Schechtman, 2007; Andoni et al., 2009) and”
On integral probability metrics, φ-divergences and binary classification (2009, background): “ce has found applications in information theory [22], mathematical statistics [23], [24], mass transportation problems [8] and is also called as the earth mover’s distance in engineering applications [25]. 3) Total variation distance and Kolmogorov distance: γF is the total variation metric when F =”
Self-Supervised Generation of Spatial Audio for 360 Video (2018, positive): “In order to measure the localization accuracy of the generated spatial audio, we propose to compute the EMD [31] between the energy maps E ( θθθ, t ) associated with φφφ ( t ) and ˆ φφφ ( t ) .”
Locally Orderless Tracking (2012, methodology): “A probabilistic analysis of EMD and its relation with the Mallows distance was proposed by [17] although that analysis differs from the proposed probabilistic framework which introduces a noise process that governs the ground distance in the EMD.”
An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison (2007, background): “Levina and Bickel [24] proved that EMD is equivalent to the Mallows distance [30] when applied to probability distributions.”
Optimal Mass Transport for Registration and Warping (2004, background): “The optimal transport problem has also been studied within the context of certain imaging applications, in particular for content-based image retrieval [30], [31], [23].”
Bayesian optimization for sensor set selection (2010, methodology): “The metric to which we appeal is the earth mover’s distance (EMD), which is well-known and widely used in image processing [13, 7].”
Supervised Word Mover's Distance (2016, background): “[19] that the WMD is a special case of the Earth Mover’s Distance (EMD) [29], also known more generally as the Wasserstein distance [20].”
Nearest-Neighbor Searching and Metric Space Dimensions (2005, background): “The above follows in part Deza and Laurent [DL97], and also Indyk and Matoušek [IM04]; the latter describe other metric constructions, including the earth-mover (or Mallows[LB01]), Fréchet, and block-edit distances.”
Submitted to Ieee Transactions on Pattern Analysis and Machine Intelligence Learning to Detect Natural Image Boundaries Using Local Brightness, Color, and Texture Cues (positive): “A second common approach avoids quantization artifacts by using the Mallows [23] or Earth Mover's distance (EMD) [24] to compare color distributions.”
Principal Differences Analysis: Interpretable Characterization of Differences between Distributions (2015, methodology): “The gradient is directly derivable from expression (3) where the nonzero Mij are determined by appropriately matching empirical quantiles (represented by sorted indices) since the univariate Wasserstein distance is simply the L2 distance between quantile functions [20].”
Unsupervised segmentation of natural images via lossy data compression (2008, background): “Levina and Bickel [14] further show that EMD is equivalent to the Mallows distance when applied to probability distributions.”
From Word Embeddings To Document Distances (2015, background): “Several publications investigate approximations of the EMD for image retrieval applications (Grauman & Darrell, 2004; Shirdhonkar & Jacobs, 2008; Levina & Bickel, 2001).”
Learned perceptual image enhancement (2017, background): “With N ordered classes of distance (cid:107) s i − s j (cid:107) l , the normalized Earth Mover’s Distance can be deﬁned as [21]: where the cumulative distribution function CDF p ( k ) = =1 p s i .”