Related papers: Generalized Canonical Polyadic Tensor Decompositio…

Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning…

Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…

Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually).…

We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale…

Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g.,…

Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by…

We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation…

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic decomposition (CPD) is unique under mild conditions, including…

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition…

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate…

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…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

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.…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…