Related papers: Efficient algorithms for computing rank-revealing …
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully combines methods from randomized numerical linear algebra to…
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…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…
Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting a LU decomposition, it could happen that the entries of the factors L and U do not lie in R, but just in K. Having a good control on the…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…
This paper introduces the implementation of the Figaro-GPU algorithm for computing a QR and SVD decomposition over a join matrix defined by the natural join over two tables on GPUs. Figaro-GPU's main novelty is a GPU implementation of the…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
We implement exact triangle counting in graphs on the GPU using three different methodologies: subgraph matching to a triangle pattern; programmable graph analytics, with a set-intersection approach; and a matrix formulation based on sparse…
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…
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
We consider solving the low rank matrix sensing problem with Factorized Gradient Descend (FGD) method when the true rank is unknown and over-specified, which we refer to as over-parameterized matrix sensing. If the ground truth signal…
This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…
We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution of linear systems. Both techniques target the scenario…
The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm (2020) recently proposed a sparsification technique…