相关论文: Kronecker Product of Tensors and Hypergraphs: Stru…

Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…

We propose a test for testing the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. Through defining a Kronecker product structure set, we define if a…

The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…

We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…

In this paper we present the super connectivity of Kronecker product of a general graph and a complete graph.

We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product…

For polynomial representations of $GL_n$ of a fixed degree, H. Krause defined a new internal tensor product using the language of strict polynomial functors. We show that over an arbitrary commutative base ring $k$, the Schur functor…

The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational…

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence…

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). We describe a…

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…

We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…

We propose the tensor Kronecker product singular value decomposition~(TKPSVD) that decomposes a real $k$-way tensor $\mathcal{A}$ into a linear combination of tensor Kronecker products with an arbitrary number of $d$ factors $\mathcal{A} =…

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…

Knowledge graph embedding research has mainly focused on learning continuous representations of entities and relations tailored towards the link prediction problem. Recent results indicate an ever increasing predictive ability of current…

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…