Related papers: Tucker-O-Minus Decomposition for Multi-view Tensor…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…
Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in…
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…
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…
Recent work has proposed the use of tensor decomposition to model repetitions and to separate tracks in loop-based electronic music. The present work investigates further on the ability of Nonnegative Tucker Decompositon (NTD) to uncover…
In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three…
An efficiency of the Tucker decomposition of amplitude tensors within the single-reference relativistic coupled cluster method with single and double excitations (RCCSD) was studied in a series of benchmark calculations for (AuCl)$_n$…
This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert…
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…
Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly…
This paper proposes low tensor-train (TT) rank and low multilinear (ML) rank approximations for de-speckling and compression of 3D optical coherence tomography (OCT) images for a given compression ratio (CR). To this end, we derive the…
The imbalanced classification problem turns out to be one of the important and challenging problems in data mining and machine learning. The performances of traditional classifiers will be severely affected by many data problems, such as…
This paper introduces mathematical frameworks that address the challenges of multi-view clustering in federated learning environments. The objective is to integrate optimization techniques based on new objective functions employing…
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…
Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…
In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…
In this thesis, we address the challenging problem of unpaired multi-view clustering (UMC), which aims to achieve effective joint clustering using unpaired samples observed across multiple views. Traditional incomplete multi-view clustering…