While multilinear algebra appears natural for studying the multiway
interactions modeled by hypergraphs, tensor methods for general hypergraphs
have been stymied by theoretical and practical barriers. A recently proposed
adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively
costly to form and analyze in practice. We develop tensor times same vector
(TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a
low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is
the maximum hyperedge size. Our algorithms are implicit, avoiding formation of
the order $r$ adjacency tensor. We demonstrate the flexibility and utility of
our approach in practice by developing tensor-based hypergraph centrality and
clustering algorithms. We also show these tensor measures offer complementary
information to analogous graph-reduction approaches on data, and are also able
to detect higher-order structure that many existing matrix-based approaches
provably cannot.

通过开发 TTST 算法，本文提出了可以改善门坎效应的高维数据处理方法，特别针对研究高维关系模型的超图。

非均匀超图的可伸缩张量方法

Scalable tensor methods for nonuniform hypergraphs

We propose GraphNVP, the first invertible, normalizing flow-based molecular
graph generation model. We decompose the generation of a graph into two steps:
generation of (i) an adjacency tensor and (ii) node attributes. This
decomposition yields the exact likelihood maximization on graph-structured
data, combined with two novel reversible flows. We empirically demonstrate that
our model efficiently generates valid molecular graphs with almost no
duplicated molecules. In addition, we observe that the learned latent space can
be used to generate molecules with desired chemical properties.

本文提出了 GraphNVP，这是第一个可逆的基于正则化流的分子图生成模型，它将图的生成分解为两个步骤：邻接张量和节点属性的生成，通过两个新颖的可逆流，实现了图结构化数据上的精确似然最大化，我们在实证上证明了该模型能够高效生成几乎没有重复分子的有效分子图，并且发现所学习到的潜在空间可以用于生成具有期望化学性质的分子。

GraphNVP：一种用于生成分子图的可逆流模型

GraphNVP: An Invertible Flow Model for Generating Molecular Graphs

In a series of recent works, we have generalised the consistency results in
the stochastic block model literature to the case of uniform and non-uniform
hypergraphs. The present paper continues the same line of study, where we focus
on partitioning weighted uniform hypergraphs---a problem often encountered in
computer vision. This work is motivated by two issues that arise when a
hypergraph partitioning approach is used to tackle computer vision problems:
(i) The uniform hypergraphs constructed for higher-order learning contain all
edges, but most have negligible weights. Thus, the adjacency tensor is nearly
sparse, and yet, not binary. (ii) A more serious concern is that standard
partitioning algorithms need to compute all edge weights, which is
computationally expensive for hypergraphs. This is usually resolved in practice
by merging the clustering algorithm with a tensor sampling strategy---an
approach that is yet to be analysed rigorously. We build on our earlier work on
partitioning dense unweighted uniform hypergraphs (Ghoshdastidar and Dukkipati,
ICML, 2015), and address the aforementioned issues by proposing provable and
efficient partitioning algorithms. Our analysis justifies the empirical success
of practical sampling techniques. We also complement our theoretical findings
by elaborate empirical comparison of various hypergraph partitioning schemes.

本文基于之前的研究，在计算机视觉中解决超图分割的问题，并提出可以证明的高效分割算法，同时对各种超图分割方案进行了详细的实证比较。

统一超图划分：可证张量方法和采样技术

Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling  Techniques

We study both $H$ and $E/Z$-eigenvalues of the adjacency tensor of a uniform
multi-hypergraph and give conditions for which the largest positive $H$ or
$Z$-eigenvalue corresponds to a strictly positive eigenvector. We also
investigate when the $E$-spectrum of the adjacency tensor is symmetric.

研究了均匀多重超图的邻接张量的 $H$ 和 $E/Z$ 特征值，并给出了最大正 $H$ 或 $Z$ 特征值对应严格正特征向量的条件。此外，还研究了邻接张量的 $E$ 谱是否对称。