Related papers: Randomized Algorithms for Low-Rank Matrix and Tens…
The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…
This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…
Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank…
This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor…
Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…