Fast and robust Earth Mover's Distances

By Ofir Pele, Michael Werman. 2009

999 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

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Citations in the corpus

Multimodal Explanations: Justifying Decisions and Pointing to the Evidence (2018, methodology): “We use the code from [25] to compute EMD.”
Attentive Explanations: Justifying Decisions and Pointing to the Evidence (2016, methodology): “We use the code from [26] to compute EMD.”
A Fast Proximal Point Method for Computing Exact Wasserstein Distance (2018, methodology): “Same as other prime-form Wasserstein distance solvers (Pele and Werman, 2009; Cuturi, 2013), the proximal point method provide a transport plan.”
Visual saliency estimation by nonlinearly integrating features using region covariances. (2013, methodology): “The authors argued that the EMD and SIFTflow scores are the only two objective metrics that were highly consistent with human rankings.”
Unsupervised Training for 3D Morphable Model Regression (2018, methodology): “For additional validation, Table 2 shows the Earth Mover’s distance [17] between the all-pairs LFW distributions and the results of each method.”
Do News Consumers Want Explanations for Personalized News Rankings (2017, methodology): “An overview over different task recommendation approaches and evaluation methods for crowdsourcing in several areas is given by Geiger and Schader [6].”
Fast Computation of Wasserstein Barycenters (2013, background): “Wasserstein distances have many favorable properties, documented both in theory (Villani, 2009) and practice (Rubner et al., 1997; Pele and Werman, 2009).”
Evaluating Style Transfer for Text (2019, methodology): “Style Transfer Intensity Rather than count how many output texts achieve a target style, we can capture more nuanced differences between the style distributions of x and x (cid:48) , using Earth Mover’s Distance (Rubner et al., 1998; Pele and Werman, 2009).”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, methodology): “r context of machine learning, for instance, the Wasserstein distance is used for the analysis of mixture models [56,70] as well as for image processing [1,33,55,75,105], computer vision and graphics [78,79,90,102,103], data-driven bioengineering [34,57,108], clustering [49], dimensionality reductio”
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm (2018, methodology): “…e (cid:16) (cid:17) In terms of the dependence on n , this result improves on the complexity e O ( n 3 ) achieved by the network simplex method or interior point methods (Pele & Werman, 2009), applied directly to the OT optimization problem, which is a linear program (Kantorovich, 1942).”
From Word Embeddings To Document Distances (2015, methodology): “The best average time complexity of solving the WMD optimization problem scales O(p 3 log p), where p denotes the number of unique words in the documents (Pele & Werman , 2009).”
Spatio-temporal Object Detection Proposals (2014, neutral): “where dμ(n,m) = min(‖μ(n)− μ(m)‖ , 30) is the robust thresholded-distance between the color means [33], dcol(n,m) and dflow(n,m) are chi-squared distances between the color and flow histograms.”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, methodology): “In our simulations, we use the PyEMD Python library for fast computation of the earth moving distance [66]. c. Moment matching via mean squared error: where the expectation values P D and P θ are taken with respect to data and circuit distributions, respectively.”
A Fast Proximal Point Method for Computing Wasserstein Distance (2018, methodology): “Same as other prime-form Wasserstein distance solvers [20, 7], the proximal point method provide a transportation map.”