Related papers: Tensor Neural Network Interpolation and Its Applic…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

Conventional machine learning methods are predominantly designed to predict outcomes based on a single data type. However, practical applications may encompass data of diverse types, such as text, images, and audio. We introduce…

Feature preserving image interpolation is an active area in image processing field. In this paper a new direct edge directed image super-resolution algorithm based on structure tensors is proposed. Using an isotropic Gaussian filter, the…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…

The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth…

The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to…

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…

This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Due to strong learning abilities of convolutional neural networks (CNNs), they have become mainstream methods for image super-resolution. However, there are big differences of different deep learning methods with different types. There is…

Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…

We introduce an architecture, the Tensor Product Recurrent Network (TPRN). In our application of TPRN, internal representations learned by end-to-end optimization in a deep neural network performing a textual question-answering (QA) task…

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples,…

Frame interpolation attempts to synthesise frames given one or more consecutive video frames. In recent years, deep learning approaches, and notably convolutional neural networks, have succeeded at tackling low- and high-level computer…

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…

In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…