Related papers: Quantum Higher Order Singular Value Decomposition

Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for combinatorial problems. The simulation of…

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…

We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…

Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…

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…

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…

We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converting the tensor into a tensor-train rank-1 (TTr1) series via…

We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…

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…

Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…

In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy…

A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…

Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the…

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…

Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…