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Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing…

Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix…

Recently the widely used multi-view learning model, Canonical Correlation Analysis (CCA) has been generalised to the non-linear setting via deep neural networks. Existing deep CCA models typically first decorrelate the feature dimensions of…

This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor…

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 consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…

To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…

Higher-order tensor decompositions have hardly been used in muscle activity analysis despite multichannel electromyography (EMG) datasets naturally occurring as multi-way structures. Here, we seek to demonstrate and discuss the potential of…

Accurate cascaded channel state information is pivotal for extremely large-scale intelligent reflecting surfaces (XL-IRS) in next-generation wireless networks. However, the large XL-IRS aperture induces spherical wavefront propagation due…

This paper introduces DeCAL, a new method for tokenwise compression. DeCAL uses an encoder-decoder language model pretrained with denoising to learn to produce high-quality, general-purpose compressed representations from the encoder. DeCAL…

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…

Higher order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

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…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

Tensor completion aims at imputing missing entries from a partially observed tensor. Existing tensor completion methods often assume either multi-linear or nonlinear relationships between latent components. However, real-world tensors have…