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Distance Measures for Quantifying the Differences in Microstructures
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
The Earth Mover’s Distance (EMD) is a cross bin metric for comparing histograms. It has seen significant use recently in the computer vision field for grayscale [774] and color image retrieval [868, 869]. It has been used to compare probability distributions or signatures; signatures are unnormalized distributions or histograms that can have different weights for different bins. When comparing normalized probability distributions, the EMD is equivalent to Mallow’s distance from statistics [563]. It is called the EMD because it measures the amount of work that must be done to move mass (or earth) around from the bins of one histogram to transform it to another. It is essentially a linear programming method and is based on a solution to the transportation of goods problem.
Similarity Principle—The Fundamental Principle of All Sciences
Published in Mark Chang, Artificial Intelligence for Drug Development, Precision Medicine, and Healthcare, 2020
The Earth Mover’s Distance (EMD) is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense. EMD matches perceptual similarity better than other distances used for image retrieval. The EMD is based on a solution to the transportation problems from linear optimization. It is more robust than histogram matching techniques in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms (Rubner, Tomasi, and Guibas, 1998).
DETONATE: Nonlinear Dynamic Evolution Modeling of Time-dependent 3-dimensional Point Cloud Profiles
Published in IISE Transactions, 2023
Michael Biehler, Daniel Lin, Jianjun Shi
To evaluate the performance of the proposed method, we must compare the predicted 3D shape (in the form of a 3D point cloud) against the ground-truth 3D shape, which is also represented by a point cloud. Two permutation-invariant metrics for comparing unordered point sets have been proposed in the literature (Fan et al., 2017). On the one hand, the Earth Mover’s Distance (EMD) (Rubner et al., 2000) is the solution to a transportation problem that attempts to transform one set into the other. For two equally sized subsets their EMD is defined by where is a bijection. As a loss, EMD is differentiable almost everywhere. On the other hand, the Chamfer (pseudo)-Distance (CD) measures the squared distance between each point in one set to its nearest neighbor in the other set:
SemSyn: Semantic-Syntactic Similarity Based Automatic Machine Translation Evaluation Metric
Published in IETE Journal of Research, 2023
Shweta Chauhan, Rahul Kumar, Shefali Saxena, Amandeep Kaur, Philemon Daniel
To address the above-mentioned limitations, we analyze each component of lexical-based metric and seek to address these shortcomings. In this paper, we propose an MTE score called SemSyn, which considers the semantic and syntactical properties of any language. Semantic analysis includes the term frequency-inverse document frequency (TF-IDF) and word embedding with earth mover’s distance (EMD). The syntactic analysis includes the BLEU of part of speech (POS) and dependency parsing (DP) tags to cover the syntax of sentence structure.