1,392 research outputs found
Hypergraph Learning with Line Expansion
Previous hypergraph expansions are solely carried out on either vertex level
or hyperedge level, thereby missing the symmetric nature of data co-occurrence,
and resulting in information loss. To address the problem, this paper treats
vertices and hyperedges equally and proposes a new hypergraph formulation named
the \emph{line expansion (LE)} for hypergraphs learning. The new expansion
bijectively induces a homogeneous structure from the hypergraph by treating
vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple
graph, the proposed \emph{line expansion} makes existing graph learning
algorithms compatible with the higher-order structure and has been proven as a
unifying framework for various hypergraph expansions. We evaluate the proposed
line expansion on five hypergraph datasets, the results show that our method
beats SOTA baselines by a significant margin
Hypergraph Modelling for Geometric Model Fitting
In this paper, we propose a novel hypergraph based method (called HF) to fit
and segment multi-structural data. The proposed HF formulates the geometric
model fitting problem as a hypergraph partition problem based on a novel
hypergraph model. In the hypergraph model, vertices represent data points and
hyperedges denote model hypotheses. The hypergraph, with large and
"data-determined" degrees of hyperedges, can express the complex relationships
between model hypotheses and data points. In addition, we develop a robust
hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF
can effectively and efficiently estimate the number of, and the parameters of,
model instances in multi-structural data heavily corrupted with outliers
simultaneously. Experimental results show the advantages of the proposed method
over previous methods on both synthetic data and real images.Comment: Pattern Recognition, 201
Structural Deep Embedding for Hyper-Networks
Network embedding has recently attracted lots of attentions in data mining.
Existing network embedding methods mainly focus on networks with pairwise
relationships. In real world, however, the relationships among data points
could go beyond pairwise, i.e., three or more objects are involved in each
relationship represented by a hyperedge, thus forming hyper-networks. These
hyper-networks pose great challenges to existing network embedding methods when
the hyperedges are indecomposable, that is to say, any subset of nodes in a
hyperedge cannot form another hyperedge. These indecomposable hyperedges are
especially common in heterogeneous networks. In this paper, we propose a novel
Deep Hyper-Network Embedding (DHNE) model to embed hyper-networks with
indecomposable hyperedges. More specifically, we theoretically prove that any
linear similarity metric in embedding space commonly used in existing methods
cannot maintain the indecomposibility property in hyper-networks, and thus
propose a new deep model to realize a non-linear tuplewise similarity function
while preserving both local and global proximities in the formed embedding
space. We conduct extensive experiments on four different types of
hyper-networks, including a GPS network, an online social network, a drug
network and a semantic network. The empirical results demonstrate that our
method can significantly and consistently outperform the state-of-the-art
algorithms.Comment: Accepted by AAAI 1
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