Related papers: Tensor Topic Modeling Via HOSVD

Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

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…

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral…

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

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…

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…

This work revisits coupled tensor decomposition (CTD)-based hyperspectral super-resolution (HSR). HSR aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). The vast majority of the HSR…

This paper proposes a topic modeling method that scales linearly to billions of documents. We make three core contributions: i) we present a topic modeling method, Tensor Latent Dirichlet Allocation (TLDA), that has identifiable and…

Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study presents an innovative integration of High-Order Singular Value Decomposition (HOSVD) with Long…

The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…

Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming…

Topic modeling is traditionally applied to word counts without accounting for the context in which words appear. Recent advancements in large language models (LLMs) offer contextualized word embeddings, which capture deeper meaning and…

An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition…