Related papers: Efficient Nonparametric Tensor Decomposition for B…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Recent studies have highlighted the effectiveness of tensor decomposition methods in the Temporal Knowledge Graphs Embedding (TKGE) task. However, we found that inherent heterogeneity among factor tensors in tensor decomposition…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time. We propose a language for precisely specifying recursive, pointer-based data…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner…

Graph Neural Networks (GNNs) have demonstrated remarkable results in various real-world applications, including drug discovery, object detection, social media analysis, recommender systems, and text classification. In contrast to their vast…

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model…

Over recent years it has become well accepted that user interest is not static or immutable. There are a variety of contextual factors, such as time of day, the weather or the user's mood, that influence the current interests of the user.…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

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…

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…

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 study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…

We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…