Related papers: Bayesian Sparse Tucker Models for Dimension Reduct…

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting…

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…

Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…

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…

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global…

By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model…