A Blind Permutation Similarity Algorithm

Similarity of particle systems using an invariant root mean square deviation measure

Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques are needed. We present an algorithm that can test particle systems of finite size for similarity and, if they are similar, can find the optimal alignment between them. Our approach is based on an invariant version of the root mean square deviation (RMSD) measure and is capable of finding the globally optimal solution in $O(n^3)$ operations where $n$ is the num…

C-MinHash: Practically Reducing Two Permutations to Just One

Traditional minwise hashing (MinHash) requires applying $K$ independent permutations to estimate the Jaccard similarity in massive binary (0/1) data, where $K$ can be (e.g.,) 1024 or even larger, depending on applications. The recent work on C-MinHash (Li and Li, 2021) has shown, with rigorous proofs, that only two permutations are needed. An initial permutation is applied to break whatever structures which might exist in the data, and a second permutation is re-used $K$ times to produce $K$ hashes, via a circulant shifting fashion. (Li and Li, 2021) has proved that, perhaps surprisingly, even…

差分隐私单排列哈希与分箱一致加权采样

Differentially Private One Permutation Hashing and Bin-wise Consistent Weighted Sampling

本文将差分隐私与单排列哈希结合，提出含三个变体的DP-OPH框架，还扩展至分箱一致加权采样提出DP-BCWS算法，实验验证了二者在相似度搜索和分类任务上的优异效用与隐私保障。

支持特征插入与删除的最小独立排列

Minwise-Independent Permutations with Insertion and Deletion of Features

针对特征动态增删场景下重计算minHash成本高的问题，该研究首次系统性探索动态特征下的minHash适配算法，经理论分析和真实数据集实验验证，该方法在保证性能的同时大幅提升了运行速度。

Graph Similarity and Approximate Isomorphism

The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two graphs $G,H$ of the same order $n$ with adjacency matrices $A_G,A_H$, a well-studied measure of similarity is the Frobenius distance \[ \mathrm{dist}(G,H):=\min_π\|A_G^π-A_H\|_F, \] where $π$ ranges over all permutations of the vertex set of $G$, where $A_G^π$ denotes the matrix obtained from $A_G$ by permuting rows and columns according to $π$, and where $\…