132 research outputs found
PageRank algorithm for Directed Hypergraph
During the last two decades, we easilly see that the World Wide Web's link
structure is modeled as the directed graph. In this paper, we will model the
World Wide Web's link structure as the directed hypergraph. Moreover, we will
develop the PageRank algorithm for this directed hypergraph. Due to the lack of
the World Wide Web directed hypergraph datasets, we will apply the PageRank
algorithm to the metabolic network which is the directed hypergraph itself. The
experiments show that our novel PageRank algorithm is successfully applied to
this metabolic network.Comment: 6 page
Directed hypergraph neural network
To deal with irregular data structure, graph convolution neural networks have
been developed by a lot of data scientists. However, data scientists just have
concentrated primarily on developing deep neural network method for un-directed
graph. In this paper, we will present the novel neural network method for
directed hypergraph. In the other words, we will develop not only the novel
directed hypergraph neural network method but also the novel directed
hypergraph based semi-supervised learning method. These methods are employed to
solve the node classification task. The two datasets that are used in the
experiments are the cora and the citeseer datasets. Among the classic directed
graph based semi-supervised learning method, the novel directed hypergraph
based semi-supervised learning method, the novel directed hypergraph neural
network method that are utilized to solve this node classification task, we
recognize that the novel directed hypergraph neural network achieves the
highest accuracies
Graph Learning and Its Applications: A Holistic Survey
Graph learning is a prevalent domain that endeavors to learn the intricate
relationships among nodes and the topological structure of graphs. These
relationships endow graphs with uniqueness compared to conventional tabular
data, as nodes rely on non-Euclidean space and encompass rich information to
exploit. Over the years, graph learning has transcended from graph theory to
graph data mining. With the advent of representation learning, it has attained
remarkable performance in diverse scenarios, including text, image, chemistry,
and biology. Owing to its extensive application prospects, graph learning
attracts copious attention from the academic community. Despite numerous works
proposed to tackle different problems in graph learning, there is a demand to
survey previous valuable works. While some researchers have perceived this
phenomenon and accomplished impressive surveys on graph learning, they failed
to connect related objectives, methods, and applications in a more coherent
way. As a result, they did not encompass current ample scenarios and
challenging problems due to the rapid expansion of graph learning. Different
from previous surveys on graph learning, we provide a holistic review that
analyzes current works from the perspective of graph structure, and discusses
the latest applications, trends, and challenges in graph learning.
Specifically, we commence by proposing a taxonomy from the perspective of the
composition of graph data and then summarize the methods employed in graph
learning. We then provide a detailed elucidation of mainstream applications.
Finally, based on the current trend of techniques, we propose future
directions.Comment: 20 pages, 7 figures, 3 table
Learning from Partially Labeled Data: Unsupervised and Semi-supervised Learning on Graphs and Learning with Distribution Shifting
This thesis focuses on two fundamental machine learning problems:unsupervised learning, where no label information is available, and semi-supervised learning, where a small amount of labels are given in
addition to unlabeled data. These problems arise in many real word applications, such as Web analysis and bioinformatics,where a large amount of data is available, but no or only a small amount of labeled data exists. Obtaining classification labels in these domains is usually quite difficult because it involves either manual labeling or physical experimentation.
This thesis approaches these problems from two perspectives:
graph based and distribution based.
First, I investigate a series of graph based learning algorithms that are able to exploit information embedded in different types of graph structures. These algorithms allow label information to be shared between nodes
in the graph---ultimately communicating information globally to yield effective unsupervised and semi-supervised learning.
In particular, I extend existing graph based learning algorithms, currently based on undirected graphs, to more general graph types, including directed graphs, hypergraphs and complex networks. These richer graph representations allow one to more naturally
capture the intrinsic data relationships that exist, for example, in Web data, relational data, bioinformatics and social networks.
For each of these generalized graph structures I show how information propagation can be characterized by distinct random walk models, and then use this characterization
to develop new unsupervised and semi-supervised learning algorithms.
Second, I investigate a more statistically oriented approach that explicitly models a learning scenario where the training and test examples come from different distributions.
This is a difficult situation for standard statistical learning approaches, since they typically incorporate an assumption that the distributions for training and test sets are similar, if not identical. To achieve good performance in this scenario, I utilize unlabeled data to correct the bias between the training and test distributions. A key idea is to produce resampling weights for bias correction by working directly in a feature space and bypassing the problem
of explicit density estimation. The technique can be easily applied to many different supervised learning algorithms, automatically adapting their behavior to cope with distribution shifting between training and test data
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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