In recent years, tensor decomposition has gained increasing interest in the field of link prediction, which aims to estimate likelihood new connections forming between nodes a network. This study highlights potential Canonical Polyadic enhancing prediction complex networks. It suggests effective algorithms that not only take into account structural characteristics network but also its temporal ...

In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensorW∗ and an entrywise sparse corruption tensor V∗. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We...

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the complicated tensor networks. However, the TT decomposition highly depends on permutations of tensor dimensions, due to its strictly sequential multilinear products ...

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It has a link to an approximate joint diagonalization (AJD) of a set of matrices. In this paper, we derive (1) a new algorithm for a symmetric AJD, which is called two-sided symmetric diagonal...

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tenso...

Confronted with the high-dimensional tensor-like visual data, we derive a method for the decomposition of an observed tensor into a low-dimensional structure plus unbounded but sparse irregular patterns. The optimal rank-(R1, R2, ...Rn) tensor decomposition model that we propose in this paper, could automatically explore the low-dimensional structure of the tensor data, seeking optimal dimensio...

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought since many high-dimensional tensors have low intrinsic rank relative to the dimension of the ambient measurement space. However, the emergence of ‘big data’ poses significant computational challenges for computing this fundamental tensor decomp...

Real data tensors are typically high dimensional; however, their intrinsic information is preserved in low-dimensional space, which motivates the use of tensor decompositions such as Tucker decomposition. Frequently, real data tensors smooth in addition to being low dimensional, which implies that adjacent elements are similar or continuously changing. These elements typically appear as spatial...

We describe an approach to tensor decomposition that involves extracting a set of observable matrices from the tensor and applying an approximate joint Schur decomposition on those matrices, and we establish the corresponding firstorder perturbation bounds. We develop a novel iterative Gauss-Newton algorithm for joint matrix Schur decomposition, which minimizes a nonconvex objective over the ma...