Related papers: Implicit Multiple Tensor Decomposition
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
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.…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
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 Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the…
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…
Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
Implicit Neural Representations (INRs) model signals as continuous, differentiable functions. However, monolithic INRs scale poorly with data dimensionality, leading to excessive training costs. We propose F-INR, a framework that addresses…
Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts…