Related papers: Computing Eigenvalues of Large Scale Sparse Tensor…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
Trace formulas play a central role in the study of spectral geometry and in particular of quantum graphs. The basis of our work is the result by Kurasov which links the Euler characteristic $\chi$ of metric graphs to the spectrum of their…
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this problem; here block versions are introduced. For the computation of…
To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…
Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered…
We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…
C-eigenvalues of piezoelectric-type tensors which are real and always exist, are introduced by Chen et al. [1]. And the largest C-eigenvalue for the piezoelectric tensor determines the highest piezoelectric coupling constant. In this paper,…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Uniform hypergraphs have a natural one-to-one correspondence to tensors. In this paper, we investigate the Estrada index and subgraph centrality of an $m$-uniform hypergraph $\mathcal{H}$ via the adjacency tensor. We establish some bounds…
The hierarchical graphs and Sierpi\'nski graphs are constructed iteratively, which have the same number of vertices and edges at any iteration, but exhibit quite different structural properties: the hierarchical graphs are non-fractal and…
The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms,…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
Tensor algebra is widely used in many applications, such as scientific computing, machine learning, and data analytics. The tensors represented real-world data are usually large and sparse. There are tens of storage formats designed for…
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include…
A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating…
Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this…