Related papers: Multi-Branch Tensor Network Structure for Tensor-T…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

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…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…

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,…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…

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,…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…