Probability and Computing - Randomized Algorithms and Probabilistic Analysis Michael Mitzenmacher, Eli Upfal

随机矩阵 随机矩阵理论的软件包。 希望增加足够的功能并在2021年8月发布。 例子 随机矩阵理论 随机矩阵模型 生成3 x 3随机Unit矩阵运行 RandomUnitaryMatrix(3)或等效 rand(Haar(2,3)) 生成3 x 3随机正交矩阵 RandomOrthogonalMatrix(3)或等效 rand(Haar(1,3)) 随机线性代数 如果A是一个乘m矩阵，而B是一个乘w矩阵。 运行RandomSamplingMatrix(A,B,k=2)将生成大小为m×k的随机采样矩阵S。 其中E（SS'）= I，而E（ASS'B）= AB。 对于定义，请检查代码或在2.2节末尾（在2.3节之前）查找S：= SD。

奇异值分解 (SVD) 是线性代数中非常有用的工具，具有广泛的应用。 随机奇异值分解是一种计算 SVD 的快速算法。

计算机应用和无线通信专业关于算法分析、无线网络容量计算的很好的数学基础参考书籍 B. Motwani and P. Raghavan, Randomized Algorithms . Cambridge University Press, 1995

Computational Geometry An Introduction Through Randomized Algorithms[Ketan Mulmuley] 计算几何 随机算法

Physical-layer security analysis of PSK quantum-noise randomized cipher in optically amplified links

Physical-layer security analysis of a quantum-noise randomized cipher based on the wire-tap channel model

Social networks allow rapid spread of ideas and.innovations while the negative information can also propagate.widely. When the cascades with different opinions reaching the.same user, the cascade arriving first is the most likely to be taken.by the user. Therefore, once misinformation or rumor is detected,.a natural containment method is to introduce a positive cascade.competing against the rumor. Given a budget k, the rumor.blocking problem asks for k seed users to trigger the spread of the.pos

Tianyi Zhou，Dacheng Tao等人提出的GoDec模型，适用于低秩分解。

For many computer vision problems, the most time consuming component consists of nearest neighbor matching in high-dimensional spaces. There are no known exact algorithms for solving these high-dimensional problems that are faster than linear search. Approximate algorithms are known to provide large speedups with only minor loss in accuracy, but many such algorithms have been published with only minimal guidance on selecting an algorithm and its parameters for any given problem. In this paper, we describe a system that answers the question, “What is the fastest approximate nearest-neighbor algorithm for my data? ” Our system will take any given dataset and desired degree of precision and use these to automatically determine the best algorithm and parameter values. We also describe a new algorithm that applies priority search on hierarchical k-means trees, which we have found to provide the best known performance on many datasets. After testing a range of alternatives, we have found that multiple randomized k-d trees provide the best performance for other datasets. We are releasing public domain code that implements these approaches. This library provides about one order of magnitude improvement in query time over the best previously available software and provides fully automated parameter selection.