Related papers: Tensor-Based Synchronization and the Low-Rankness …

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a…

Magnetic resonance imaging (MRI) nowadays serves as an important modality for diagnostic and therapeutic guidance in clinics. However, the {\it slow acquisition} process, the dynamic deformation of organs, as well as the need for {\it…

There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks.…

With powerful ability to exploit latent structure of self-representation information, different tensor decompositions have been employed into low rank multi-view clustering (LRMVC) models for achieving significant performance. However,…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

Spatially and temporally highly resolved depth information enables numerous applications including human-machine interaction in gaming or safety functions in the automotive industry. In this paper, we address this issue using Time-of-flight…

Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges,…

In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data…

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…