Related papers: Low-rank approximation of parameter-dependent matr…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…
The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…
This paper presents a hierarchical low-rank decomposition algorithm assuming any matrix element can be computed in $O(1)$ time. The proposed algorithm computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross…
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…
A matrix algorithm runs at {\em sublinear cost} if it uses much fewer memory cells and arithmetic operations than the input matrix has entries. Such algorithms are indispensable for Big Data Mining and Analysis. Quite typically in that area…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Low-rank matrix approximation play a ubiquitous role in various applications such as image processing, signal processing, and data analysis. Recently, random algorithms of low-rank matrix approximation have gained widespread adoption due to…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank…
Recent advancements in large-scale pretrained models have significantly improved performance across a variety of tasks in natural language processing and computer vision. However, the extensive number of parameters in these models…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Adaptive gradient methods like Adagrad and its variants are widespread in large-scale optimization. However, their use of diagonal preconditioning matrices limits the ability to capture parameter correlations. Full-matrix adaptive methods,…
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…
In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target…
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…
By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of…