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In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…

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…

Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary…

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…

Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…

Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…

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,…

Radio Frequency Neural Networks (RFNNs) have demonstrated advantages in realizing intelligent applications across various domains. However, as the model size of deep neural networks rapidly increases, implementing large-scale RFNN in…

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…

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…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

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…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…