Related papers: Tucker Tensor Regression and Neuroimaging Analysis

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

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…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

Time-varying parameter vector autoregression provides a flexible framework to capture structural changes within time series. However, when applied to high-dimensional data, this model encounters challenges of over-parametrization and…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

We study rank selection for low-rank tensor regression under random covariates design. Under a Gaussian random-design model and some mild conditions, we derive population expressions for the expected training-testing discrepancy (optimism)…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

Noise is ubiquitous during image acquisition. Sufficient denoising is often an important first step for image processing. In recent decades, deep neural networks (DNNs) have been widely used for image denoising. Most DNN-based image…

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…

The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…

We propose a novel framework to understand the text by converting sentences or articles into video-like 3-dimensional tensors. Each frame, corresponding to a slice of the tensor, is a word image that is rendered by the word's shape. The…

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…