1,215 research outputs found
Neighborhood Matching Network for Entity Alignment
Structural heterogeneity between knowledge graphs is an outstanding challenge
for entity alignment. This paper presents Neighborhood Matching Network (NMN),
a novel entity alignment framework for tackling the structural heterogeneity
challenge. NMN estimates the similarities between entities to capture both the
topological structure and the neighborhood difference. It provides two
innovative components for better learning representations for entity alignment.
It first uses a novel graph sampling method to distill a discriminative
neighborhood for each entity. It then adopts a cross-graph neighborhood
matching module to jointly encode the neighborhood difference for a given
entity pair. Such strategies allow NMN to effectively construct
matching-oriented entity representations while ignoring noisy neighbors that
have a negative impact on the alignment task. Extensive experiments performed
on three entity alignment datasets show that NMN can well estimate the
neighborhood similarity in more tough cases and significantly outperforms 12
previous state-of-the-art methods.Comment: 11 pages, accepted by ACL 202
Michael-Simon Sobolev inequalities in Euclidean space
Inspired by [1, 13], we prove Michael-Simon type inequalities for smooth
symmetric uniformly positive define (0, 2)-tensor fields on compact
submanifolds in Euclidean space by the Alexandrov-Bakelman-Pucci (ABP) method.Comment: 10 page
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