Related papers: Scalable tensor methods for nonuniform hypergraphs
Information is extracted from large and sparse data sets organized as 3-mode tensors. Two methods are described, based on best rank-(2,2,2) and rank-(2,2,1) approximation of the tensor. The first method can be considered as a generalization…
Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit…
Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more…
Graph contrastive learning (GCL) has emerged as a promising approach to enhance graph neural networks' (GNNs) ability to learn rich representations from unlabeled graph-structured data. However, current GCL models face challenges with…
The t-distributed Stochastic Neighbor Embedding (tSNE) algorithm has become in recent years one of the most used and insightful techniques for the exploratory data analysis of high-dimensional data. tSNE reveals clusters of high-dimensional…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
We propose a dynamic graph representation method, showcasing its rich representational capacity and establishing some of its theoretical properties. Our representation falls under the bind-and-sum approach in hyperdimensional computing…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…