Related papers: JULIA: Joint Multi-linear and Nonlinear Identifica…

Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art…

Tensor completion is an important problem in modern data analysis. In this work, we investigate a specific sampling strategy, referred to as tubal sampling. We propose two novel non-convex tensor completion frameworks that are easy to…

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, (2) does not require any of the kernels to be complete a priori, and…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor…

This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

Feature and instance co-selection, which aims to reduce both feature dimensionality and sample size by identifying the most informative features and instances, has attracted considerable attention in recent years. However, when dealing with…

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…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…

Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Motivation: Estimating model parameters from experimental observations is one of the key challenges in systems biology and can be computationally very expensive. While the Julia programming language was recently developed as a high-level…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…