Related papers: Scalable tensor methods for nonuniform hypergraphs
We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one correspondence with the nodes of the Hierarchical Tucker…
Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…
The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…
We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the $(m+1)$-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We…
The Lagrangian of a hypergraph is a crucial tool for studying hypergraph extremal problems. Though Lagrangians of some special structure hypergraphs have closed-form solutions, it is a challenging problem to compute the Lagrangian of a…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…
By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Graph-based multi-view clustering has become an active topic due to the efficiency in characterizing both the complex structure and relationship between multimedia data. However, existing methods have the following shortcomings: (1) They…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…