Matching Convolutional Neural Networks without Priors about Data

Lassance, Carlos; Vialatte, J; Gripon, Vincent

doi:10.48550/arxiv.1802.09802

Cited by 1 publication

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“…In this work, authors explored translations on grid and torus graphs, and showed that Euclidean translations of images are equivalent to neighborhood preserving properties on these graphs. It is worth noting that translations introduced in that first work were used in [13], [14] in order to propose a generalization of convolutional neural networks to irregular domains.…”

Section: Neighborhood-preserving Translationsmentioning

confidence: 99%

A neighborhood-preserving translation operator on graphs

Pasdeloup¹,

Gripon²,

Vialatte³

et al. 2017

Preprint

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In this paper, we introduce translation operators on graphs. Contrary to spectrally-defined translations in the framework of graph signal processing, our operators mimic neighborhood-preserving properties of translation operators defined in Euclidean spaces directly in the vertex domain, and therefore do not deform a signal as it is translated. We show that in the case of grid graphs built on top of a metric space, these operators exactly match underlying Euclidean translations, suggesting that they completely leverage the underlying metric. More generally, these translations are defined on any graph, and can therefore be used to process signals on those graphs. We show that identifying proposed translations is in general an NP-Complete problem. To cope with this issue, we introduce relaxed versions of these operators, and illustrate translation of signals on random graphs.

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Section: Neighborhood-preserving Translationsmentioning

confidence: 99%