Related papers: Overview of Constrained PARAFAC Models

Factor copula models for item response data are more interpretable and fit better than (truncated) vine copula models when dependence can be explained through latent variables, but are not robust to violations of conditional independence.…

The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by…

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…

The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint…

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…

PARAFAC2 has demonstrated success in modeling irregular tensors, where the tensor dimensions vary across one of the modes. An example scenario is modeling treatments across a set of patients with the varying number of medical encounters…

In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been…

While convolutional neural networks (CNNs) have become the de facto standard for most image processing and computer vision applications, their deployment on edge devices remains challenging. Tensor decomposition methods provide a means of…

In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…

We characterise the sensitivity of several additive tensor decompositions with respect to perturbations of the original tensor. These decompositions include canonical polyadic decompositions, block term decompositions, and sums of tree…

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…

The tetrad constraint is a condition of which the satisfaction signals a rank reduction of a covariance submatrix and is used to design causal discovery algorithms that detects the existence of latent (unmeasured) variables, such as FOFC.…

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

Node embeddings have been attracting increasing attention during the past years. In this context, we propose a new ensemble node embedding approach, called TenSemble2Vec, by first generating multiple embeddings using the existing techniques…

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…

In [13], Hillar and Lim famously demonstrated that "multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard". Despite many recent advancements, the state-of-the-art methods for…