Related papers: Graph Regularized Nonnegative Tensor Ring Decompos…

We propose a Reinforcement Learning based approach to approximately solve the Tree Decomposition (TD) problem. TD is a combinatorial problem, which is central to the analysis of graph minor structure and computational complexity, as well as…

Tensor decomposition is a fundamental technique widely applied in signal processing, machine learning, and various other fields. However, traditional tensor decomposition methods encounter limitations when jointly analyzing multi-block…

Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To…

Low-rank tensor representation (LRTR) has emerged as a powerful tool for multi-dimensional data processing. However, classical LRTR-based methods face two critical limitations: (1) they typically assume that the holistic data is low-rank,…

Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were…

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank…

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier…

Graph neural networks (GNNs) have become a powerful tool for processing graph-structured data but still face challenges in effectively aggregating and propagating information between layers, which limits their performance. We tackle this…

Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…

We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative orthant and the set of low-rank tensors, using STHOSVD and TTSVD…

Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…

In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by…

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

Hyperspectral image classification plays a pivotal role in precision agriculture, providing accurate insights into crop health monitoring, disease detection, and soil analysis. However, traditional methods struggle with high-dimensional…

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize…

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable…