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Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges…

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…

Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…

Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the…

The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

Advanced tensor decomposition, such as Tensor train (TT) and Tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs). However, compressing convolutional…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

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…

Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…