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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Dissertation
Robust object pose estimation with point clouds from vision and touch
TL;DR: It is proposed that a tactile sensor can be treated as a source of dense local geometric information, and hence consider it to be a point cloud source analogous to an RGB-D camera, and incorporated into a conventional point-cloud-based articulated object tracker based on signed-distance functions.
Proceedings ArticleDOI
Gromov-Wasserstein Autoencoders
TL;DR: A novel representation learning method, Gromov-Wasserstein Autoencoders (GWAE), which directly matches the latent and data distributions and shows that GWAE models can learn representations based on meta-priors by changing the prior family without further modifying the GW objective.
Posted Content
Hawkes Processes on Graphons.
TL;DR: In this paper, the authors propose a novel framework for modeling multiple multivariate point processes with heterogeneous event types that share an underlying space and obey the same generative mechanism using graphon-based Hawkes processes.
Posted Content
Learning Graphon Autoencoders for Generative Graph Modeling.
TL;DR: The graphon autoencoder as discussed by the authors is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily, based on this model, the authors propose a novel algorithmic framework called \textit{graphon auto-encoder} to build an interpretable and scalable graph generative model.
Proceedings ArticleDOI
Cell- and Area-based ML Models: Unlocking High Precision Models for Radio Access Networks
TL;DR: In this paper , the authors discuss how cell-specific characteristics, like the radio environment, can impact area-based ML models and discuss the possibility of reusing available ML models from other cells as a way of reducing the time needed for applying ML algorithms in newly deployed cells.
References
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David G. Luenberger,Yinyu Ye +1 more
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