Related papers: Quantum Higher Order Singular Value Decomposition
The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
In big data applications, classical ensemble learning is typically infeasible on the raw input data and dimensionality reduction techniques are necessary. To this end, novel framework that generalises classic flat-view ensemble learning to…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Quantum machine learning provides a fundamentally different approach to analyzing data. However, many interesting datasets are too complex for currently available quantum computers. Present quantum machine learning applications usually…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Advances in virtual reality have generated substantial interest in accurately reproducing and storing spatial audio in the higher order ambisonics (HOA) representation, given its rendering flexibility. Recent standardization for HOA…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
We develop an Iterative version of the Singular Value Decomposition (ISVD) that jointly analyzes a finite number of data matrices to identify signals that correlate among the rows of matrices. It will be illustrated how the supervised…
While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…
There has been a recent interest in quantum algorithms for the modelling and prediction of non-unitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known.…
The canonical polyadic decomposition (CPD) is a fundamental tensor decomposition which expresses a tensor as a sum of rank one tensors. In stark contrast to the matrix case, with light assumptions, the CPD of a low rank tensor is…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
The tensor-vector contraction (TVC) is the most memory-bound operation of its class and a core component of the higher-order power method (HOPM). This paper brings distributed-memory parallelization to a native TVC algorithm for dense…