393,685 research outputs found
Adversarial Attack and Defense on Graph Data: A Survey
Deep neural networks (DNNs) have been widely applied to various applications
including image classification, text generation, audio recognition, and graph
data analysis. However, recent studies have shown that DNNs are vulnerable to
adversarial attacks. Though there are several works studying adversarial attack
and defense strategies on domains such as images and natural language
processing, it is still difficult to directly transfer the learned knowledge to
graph structure data due to its representation challenges. Given the importance
of graph analysis, an increasing number of works start to analyze the
robustness of machine learning models on graph data. Nevertheless, current
studies considering adversarial behaviors on graph data usually focus on
specific types of attacks with certain assumptions. In addition, each work
proposes its own mathematical formulation which makes the comparison among
different methods difficult. Therefore, in this paper, we aim to survey
existing adversarial learning strategies on graph data and first provide a
unified formulation for adversarial learning on graph data which covers most
adversarial learning studies on graph. Moreover, we also compare different
attacks and defenses on graph data and discuss their corresponding
contributions and limitations. In this work, we systemically organize the
considered works based on the features of each topic. This survey not only
serves as a reference for the research community, but also brings a clear image
researchers outside this research domain. Besides, we also create an online
resource and keep updating the relevant papers during the last two years. More
details of the comparisons of various studies based on this survey are
open-sourced at
https://github.com/YingtongDou/graph-adversarial-learning-literature.Comment: In submission to Journal. For more open-source and up-to-date
information, please check our Github repository:
https://github.com/YingtongDou/graph-adversarial-learning-literatur
Wavelets and graph -algebras
Here we give an overview on the connection between wavelet theory and
representation theory for graph -algebras, including the higher-rank
graph -algebras of A. Kumjian and D. Pask. Many authors have studied
different aspects of this connection over the last 20 years, and we begin this
paper with a survey of the known results. We then discuss several new ways to
generalize these results and obtain wavelets associated to representations of
higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets"
associated to a higher-rank graph. Here, we generalize this construction to
build wavelets of arbitrary shapes. We also present a different but related
construction of wavelets associated to a higher-rank graph, which we anticipate
will have applications to traffic analysis on networks. Finally, we generalize
the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a
third family of wavelets associated to higher-rank graphs
Closed graph theorems for bornological spaces
The aim of this paper is that of discussing Closed Graph Theorems for
bornological vector spaces in a way which is accessible to non-experts. We will
see how to easily adapt classical arguments of functional analysis over
and to deduce Closed Graph Theorems for bornological
vector spaces over any complete, non-trivially valued field, hence encompassing
the non-Archimedean case too. We will end this survey by discussing some
applications. In particular, we will prove de Wilde's Theorem for
non-Archimedean locally convex spaces and then deduce some results about the
automatic boundedness of algebra morphisms for a class of bornological algebras
of interest in analytic geometry, both Archimedean (complex analytic geometry)
and non-Archimedean
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