相关论文: Sparse Coresets for SVD on Infinite Streams

When rows of an $n \times d$ matrix $A$ are given in a stream, we study algorithms for approximating the top eigenvector of the matrix ${A}^TA$ (equivalently, the top right singular vector of $A$). We consider worst case inputs $A$ but…

Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…

Replay-based methods have proved their effectiveness on online continual learning by rehearsing past samples from an auxiliary memory. With many efforts made on improving training schemes based on the memory, however, the information…

Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…

Sparse matrix vector multiplication (SpMV) is central to numerous data-intensive applications, but requires streaming indirect memory accesses that severely degrade both processing and memory throughput in state-of-the-art architectures.…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…

Sparse linear algebra is crucial in many application domains, but challenging to handle efficiently in both software and hardware, with one- and two-sided operand sparsity handled with distinct approaches. In this work, we enhance an…

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…

In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of data stream, our algorithm enjoys the tightest…

Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…

Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating…

We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…

Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…