Related papers: Randomized Interpolative Decomposition of Separate…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
In this article we consider the iterative schemes to compute the canonical (CP) approximation of quantized data generated by a function discretized on a large uniform grid in an interval on the real line. This paper continues the research…
The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…
This paper presents a multigrid algorithm for the computation of the rank-R canonical decomposition of a tensor for low rank R. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level…
Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…
Canonical Polyadic Decomposition (CPD) represents a third-order tensor as the minimal sum of rank-1 terms. Because of its uniqueness properties the CPD has found many concrete applications in telecommunication, array processing, machine…
In recent research, Tensor Product Representation (TPR) is applied for the systematic generalization task of deep neural networks by learning the compositional structure of data. However, such prior works show limited performance in…
Multi-way data arises in many applications such as electroencephalography (EEG) classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank,…
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.…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…
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…
Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…