Related papers: A Simple Approach to Optimal CUR Decomposition
To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…
We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix $A$, such a factorization provides a low rank approximate decomposition of the form $A \approx C U R$, where $C$ and $R$…
The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of…
This work investigates the accuracy and numerical stability of CUR decompositions with oversampling. The CUR decomposition approximates a matrix using a subset of columns and rows of the matrix. When the number of columns and the rows are…
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…
Large deep learning models have achieved remarkable success but are resource-intensive, posing challenges such as memory usage. We introduce CURing, a novel model compression method based on CUR matrix decomposition, which approximates…
The Nystr\"om method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or…
In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis…
Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model,…
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…
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…
Kernel matrices (e.g. Gram or similarity matrices) are essential for many state-of-the-art approaches to classification, clustering, and dimensionality reduction. For large datasets, the cost of forming and factoring such kernel matrices…
Nystr\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a…
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…
Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…