Related papers: Visual Analytics Using Tensor Unified Linear Compa…

Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…

Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…

Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or…

The main idea of canonical correlation analysis (CCA) is to map different views onto a common latent space with maximum correlation. We propose a deep interpretable variational canonical correlation analysis (DICCA) for multi-view learning.…

Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…

Nowadays the deep learning technology is growing faster and shows dramatic performance in computer vision areas. However, it turns out a deep learning based model is highly vulnerable to some small perturbation called an adversarial attack.…

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…

Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

The t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l 1 norm. But…

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…

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…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a…

Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes 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…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…

Tensor computation has emerged as a powerful mathematical tool for solving high-dimensional and/or extreme-scale problems in science and engineering. The last decade has witnessed tremendous advancement of tensor computation and its…