Randomized Interpolative Decomposition of Separated Representations

通过随机插值分解加速规范多adic交替最小二乘优化

Accelerating the Canonical Polyadic Alternating Least Squares Optimization via a Randomized Interpolative Decomposition

研究针对规范多adic分解的随机交替最小二乘优化，提出基于杠杆得分的采样策略，通过随机强秩揭示QR分解近似杠杆得分分布，该方法能以特定采样数实现精度，且优于先前方案，减少计算和存储开销。

随机算法用于低秩矩阵和张量分解

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

本文提出随机算法用于加速低秩矩阵和张量分解，涵盖SVD、ID、CUR等方法，并探讨其在张量分解中的应用。

Bayesian Low-Rank Interpolative Decomposition for Complex Datasets

In this paper, we introduce a probabilistic model for learning interpolative decomposition (ID), which is commonly used for feature selection, low-rank approximation, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE EC50, CCLE I…

Literature survey on low rank approximation of matrices

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 algorithms for low rank approximation. But these techniques are very expensive $(O(n^{3})$ operations are required for $n\times n$ matrices). There are several randomized algorithms available in the literature which are not so expensive as the classical techniques (but the complexity is not linear in n). So, it is very expensive to construct the low rank ap…

具备统计保证的随机降维方法

Randomized Dimension Reduction with Statistical Guarantees

本研究从计算效率出发设计基于矩阵概要的随机低秩分解降维算法，从样本效率出发研究带数据增强的学习算法并应用于医学图像分割，为高维场景下的算法提速与数据高效利用提供了有统计保证的方案。

Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to accomplish the tensor compression, provide a detailed analysis of the computational costs, provide insight into the error of the resulting approximations, and discuss the benefits of the proposed approaches. We also apply the tensor-based function approximation to develop low-rank matrix approximations to kernel matrices that describe pairwise interactions between …

$\mathcal{H}^2$ 矩阵的拟最优随机恢复

Quasi-Optimal Randomized Recovery of $\mathcal{H}^2$ Matrices

针对$\mathcal{H}^2$矩阵，提出两种基于随机草图的恢复算法，在仅需矩阵-伴随乘积下实现拟最优误差，携带恢复以更少算子应用达到与重草图相当的精度。

Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast randomized singular value decomposition algorithm in which fast block Hankel matrix-vector multiplications are implemented with minimal memory storage. This fast block Hankel matrix randomized singular value decomposition algorithm is integrated into the \texttt{Altproj} algorithm, which is a standard non-convex method for solving the robust principal component …