Journal ArticleDOI
Gromov–Wasserstein Distances and the Metric Approach to Object Matching
TLDR
This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff distance which have the goal of modeling and tackling the practical problems of object matching and comparison by proving explicit lower bounds for the proposed distance that involve many of the invariants previously reported by researchers.Abstract:
This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff distance which have the goal of modeling and tackling the practical problems of object matching and comparison. Objects are viewed as metric measure spaces, and based on ideas from mass transportation, a Gromov–Wasserstein type of distance between objects is defined. This reformulation yields a distance between objects which is more amenable to practical computations but retains all the desirable theoretical underpinnings. The theoretical properties of this new notion of distance are studied, and it is established that it provides a strict metric on the collection of isomorphism classes of metric measure spaces. Furthermore, the topology generated by this metric is studied, and sufficient conditions for the pre-compactness of families of metric measure spaces are identified. A second goal of this paper is to establish links to several other practical methods proposed in the literature for comparing/matching shapes in precise terms. This is done by proving explicit lower bounds for the proposed distance that involve many of the invariants previously reported by researchers. These lower bounds can be computed in polynomial time. The numerical implementations of the ideas are discussed and computational examples are presented.read more
Citations
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Topologically Attributed Graphs for Shape Discrimination
TL;DR: In this article , the authors introduce a family of attributed graphs for the purpose of shape discrimination, which typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data.
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Distributional Sliced Embedding Discrepancy for Incomparable Distributions.
TL;DR: The distributional sliced embedding (DSE) discrepancy as mentioned in this paper was proposed to compare two incomparable distributions, that hinges on the idea of distributional slicing, embeddings, and on computing the closed-form Wasserstein distance between the sliced distributions.
Issues in "Cross-Domain Imitation Learning via Optimal Transport" and a possible fix
TL;DR: This work is the first to use hitting-time of a Markov decision process (MDP) to solve the mathematical issues of the Gromov-Wasserstein distance and discuss the difficulty behind the algorithmic issue.
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VeML: An End-to-End Machine Learning Lifecycle for Large-scale and High-dimensional Data
TL;DR: VeML as mentioned in this paper is a version management system dedicated to end-to-end machine learning lifecycle, which addresses the high cost of building an ML lifecycle especially for large-scale and high-dimensional dataset.
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A Regularized Wasserstein Framework for Graph Kernels.
TL;DR: Wang et al. as discussed by the authors proposed a regularized Wasserstein (RW) discrepancy metric for graph kernels, which can preserve both features and structure of graphs via RW distances on features and their local variations, local barycenters and global connectivity.
References
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